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ERF. ME NT ARY treatise 


ON 


PHYSICS 





v^\ 

•\\ ^ > N 


EXPERIMENTAL AND APPLIED. 


FOR THE USE OF COLLEGES AND SCHOOLS. 


TRANSLATED AND EDITED FROM 

GANOT’S ELEMENTS DE PHYSIQUE 

ii 

(with the, Author's sanction ) 

y . by 
y 

E> ATKINSON, Ph.D., F.G.S. 

I 

PROFESSOR OF EXPERIMENTAL SCIENCE, ROYAL MILITARY COLLEGE, SANDHURST. 


(BMtioit, rtbtstfr anfr tnlnrgcb. 


ILLUSTRATED BY A COLOURED PLATE AND 668 WOODCUTS. 


NEW YORK: 

WILLIAM WOOD AND CO., PUBLISHERS, 

61 Wx\LKER STREET. 

1868. 


QC«' 


tty tnuM*, 

AUG 10 t9ft 





r 



£ 


TRANSLATOR’S PREFACE 


f 


TO 


THE FIRST EDITION. 




The Elements de Physique of Professor Ganot, of which the present 
work is a translation, has acquired a high reputation as an. Intro¬ 
duction to Physical Science. In France it has passed through Nine 
large Editions in little more than as many years, and it has been 
translated into German and Spanish. 

This reputation it doubtless owes to the clearness and conciseness 
with which the principal physical laws and phenomena are ex¬ 
plained, to its methodical arrangement, and to the excellence of its 
illustrations. In undertaking a translation, I was influenced by the 
favourable opinion which a previous use of it in teaching had 
enabled me to form. 

I found that its principal defect consisted in its too close adapta¬ 
tion to the French systems of instruction and accordingly, my chief 
labour, beyond that of mere translati’onf lias been expended in making 
such alterations and additions asjmight/fender it, more useful to the 
English student. 

I have retained throughout the use of the centigrade thermometer, 
and in some cases have expressed the smaller linear measures on the 
metrical system. These systems are now everywhere gaining ground, 
and an apology is scarcely needed for an innovation which may help 
to familiarise the English student with their use in the perusal of 
the larger and more complete works on Physical Science to which 
this work may serve as an introduction. 


Royal Military College, Sandhurst. 


E. ATKINSON. 







ADVERTISEMENT 


TO 

THE THIRD EDITION. 


The rapid sale of a large impression of the Second Edition of the 
Translation of Ganot’s Physics is mainly due to its increased adoption 
as a text-book in schools and colleges. 

The alterations in the present edition comprise 57 pages of 
additional matter, and 49 new illustrations. In making these 
alterations, while the wants of the general reader have been attended 
to, the main object of the Editor has been to render the book more 
useful as a text-book for the student of physical science. Accordingly, 
as regards new matter, the main additions have been in those 
subjects which are calculated to take a permanent place in elementary 
instruction. Some parts, too, which the experience of teachers had 
indicated as being treated with too great brevity have been expanded. 
This is more especially the case with the Book on Mechanics, for a 
complete revision of which the Editor is indebted to his colleague, 
the Rev. J. F. Twisden, of the Staff Coliege. 


Sandhurst: July 1868. 



\ 


CONTENTS. 


BOOK I. 

ON MATTER, FORCE AND MOTION. 

CHAP. PAGE 

I. Genebal Notions.1 

II. Genebal Pbopebties of Bodies.3 

III. On Fobce, Eqtjilibbium, and Motion.9 

BOOK II. 

GRAVITATION AND MOLECULAR ATTRACTION. 

I. Gbavity, Centbe of Gbayity, the Balance .... 40 

II. Laws of Falling Bodies, Intensity of Tebbestbial Gbavity, 

the Pendulum ......... 49 

III. Moleculab Fobces. .58 

BOOK III. 

ON LIQUIDS. 

I. Hydbostatics.66 

II. Capillabity, Endosmose, Effusion, Absobption, and Imbibi¬ 
tion . 95 

BOOK IV. 

ON GASES. 

I. Pbopebties of Gases. Atmosphebe. Babometebs . . .107 

II. Measubement of the Elastic Fobce of Gases . . .125 

III. Pbessube on Bodies in Aib. Balloons.133 

IV. Appabatus Founded on the Pbopebties of Aib . . .138 







X 


CONTENTS. 


BOOK Y. 

ACOUSTICS. 

CHAP. 

I. Production, Propagation, and Reflection of Sound 

II. Measurement of the Number of Vibrations . 

III. The Physical Theory of Music .... 

IV. Vibrations of Stretched Strings, and of Columns of 

V. Vibrations of Rods, Plates, and Membranes . 


BOOK YI. 

ON HEAT. 


I. 

Preliminary Ideas. Thermometers 

# * 



. 214 

II. 

Expansion of Solids 






III. 

Expansion of Liquids 





. 235 

IV. 

Expansion and Density of Cases 


• , 



. 240 

V. 

Changes of Condition. Vapours 


. , 



. 248 

VI. 

Hygrometry .... 





. 295 

VII. 

Conductivity of Solids, Liquids, 

AND 

Cases 



. 304 

VIII. 

Radiation of Heat . 


. , 



. 310 

IX. 

Calorimetry .... 


. • . 



. 348 

X. 

Steam Engines 


9 , 



. 366 

XI. 

Sources of Heat and Cold . 


, , 



. 378 

XII. 

Mechanical Equivalent of Heat 


, , 



. 390 



BOOK YII. 




ON LIGHT. 

V 



I. 

Transmission, Velocity, and Intensity of Light . 


. 395 

II. 

Reflection of Light. Mirrors .... 


. 407 

III. 

Single Refraction. Lenses. 


. 425 

IV. 

Dispersion and Achromatism. 


. 445 

V. 

Optical Instruments. 


. 462 

VI. 

The Eye Considered as an Optical Instrument . 


. 493 

VII. 

Sources of Light. Phosphorescence 


. 512 

VIII . 

Double Refraction. Interference. Polarisation 


. 516 


PAGE 
161 
175 
181 
Air . 190 

. 202 












CONTENTS. 


XI 


ft 


BOOK VIII. 

ON MAGNETISM. 


CHAP. 

I. Properties of Magnets. 

II. Terrestrial Magnetism. Compasses 

III. Laws of Magnetic Attractions and Repulsions 

IV. Processes of Magnetisation .... 


BOOK IX. 

FRICTIONAL ELECTRICITY. 

I. Fundamental Principles. 

II. Measurement of Electrical Forces. 

III. Action of Electrified Bodies on Bodies in the Natural State ; 
Induced Electricity. Electrical Machines 


BOOK X. 

DYNAMICAL ELECTRICITY. 

I. Voltaic Pile. Its Modifications ...... 

II. Detection and Measurement of Voltaic Currents 

III. Effects of the Current. 

IV. Electrodynamics. Attractions and Repulsions of Currents 

by Currents . 

V. Magnetisation by Currents. Electromagnets. Electric Tele¬ 
graphs . 

VI. Induction. 

VII. Optical Effects of Powerful Magnets. Diamagnetism 

VIII. Thermoelectric Currents. 

IX. Determination of Electrical Conductivity .... 

X. Animal Electricity. Application of Electricity to Thera¬ 

peutics . 

Elementary Outlines of Meteorology and Climatology 
Index ..... . 


PAGE 

557 

563 

574 

577 


584 

592 

600 


653 

671 

682 

704 

720 

738 

778 

782 

790 

803 

811 

844 






LIST OF TABLES 


PAGE 

Absorbing powers , . . 320 

Absorption of gases . . .105 

. — heat by gases . . .340 

-liquids . . 333, 334 

-vapours . . 335, 341 

Breaking weight of substances . 64 

Boiling point . . . 267, 268 

Combustion, heat of . . .384 

Conducting powers for heat . 306 

Conductors of electricity . . 586 

Densities of gases . . .248 

— of vapours .... 293 

Diathermanous power . .331 

Diffusion of solution . . .102 

Endosmotic equivalents . . 101 

Electrical series . . . 590 

Electromotive forces . . .657 

— force of different elements . 783 

Expansion, coefficients of solids 230,231 

-liquids . . . .238 

- gases .... 245 

Eye, dimensions of . . . 496 

— refractive indices of media of 496 

Freezing mixtures . . . 254 

Fusing points of bodies . . 249 

Glaisher’s factors . . .301 


Gravity, force of at different levels 54 


Hardness, scale of . 

PAGE 

65 

Latent heat, of evaporation 

273 

-liquefaction 

361 

Magnetic declination 

565 

— intensity .... 

573 

Radiating powers 

321 

Radiation of powders 

346 

Refraction of angle of double 

522 

Refractive indices . . 434, 

43o 

—• — of media of eye 

496 

Reflecting powers 

319 

Specific gravity of solids . 

89 

-liquids .... 

91 

— heat of solids and liquids 

355 

- gases .... 

354 

— inductive capacities 

605 

Temperatures, various remarkable 226 

— of different latitudes 

841 

— thermal springs . 

842 

Tension of aqueous vapour . 263, 

264 

— different liquids . 

264 

Undulations, length of 

517 

Velocity of sound in rocks 

168 

- gases .... 

168 

-liquids . ' . 

170 

- woods.... 

171 




ELEMENTARY TR 

ON 

PHYSICS. 



BOOK I. 

ON MATTER, FORCE, AND MOTION. 


CHAPTER I. 

GENERAL NOTIONS. 

v x 

1. Object of Physics. —The object of Physics is the study of the 
phenomena presented to us by bodies. It should, however, be added, 
that changes in the nature of the body itself, such as the decomposition 
of one body into others, are phenomena whose study forms the more 
immediate object of chemistry. 

2. Matter. —That which possesses the properties whose existence is 
revealed to us by our senses, we call matter or substance. 

All substances at present known to us may be considered as chemicai 
combinations of sixty-five elementary or simple substances. This number, 
however, may hereafter be diminished or increased by a more powerful 
chemical analysis. 

3. Atoms, Molecules. —From various properties of bodies we con¬ 
clude that the matter of which they are formed is not perfectly 
continuous, but consists of an aggregate of an immense number of 
exceedingly small portions or atoms of matter. These atoms cannot be 
divided physically, they are retained side by side, without touching each 
other, by means of certain attractions and repulsions, to which the name 
molecular forces is given. 

A group of atoms forms a molecule , so that a body may be considered 
as an aggregate of very small molecules, and these again as aggregates 
of still smaller atoms. 


£ 




2 ON MATTER, FORCE, AND MOTION. [4- 

4. iMEolecular state of bodies. —With respect to the molecules of 
bodies three different states of aggregation present themselves. 

First, the solid state, as observed in woods, stones, metals, &c., at the 
ordinary temperature. The distinctive character of this state is, that 
the relative positions of the molecules of the bodies cannot be changed 
without the expenditure of more or less force. As a consequence, solid 
bodies tend to retain whatever form may have been given to them by 
nature or by art. 

Secondly, the liquid state, as observed in water, alcohol, oil, &c. Here 
the relative position of the molecules is no longer permanent, the 
molecules glide past each other with the greatest ease, and the body 
assumes with readiness the form of any vessel in which it may be 
placed. 

Thirdly, the yaseous state, as in air. In gases the mobility of the mole¬ 
cules is still greater than in liquids; but the distinctive character of a 
gas is its incessant struggle to occupy a greater volume, or the tendency 
of its molecules to recede from each other. 

The general term jluid is applied to both liquids and gases. 

We shall see in the sequel that the state of a body depends upon the 
relations which exist between its molecular attractions and repulsions, 
and that for one and the same body these relations vary with the 
temperature. On this account most simple bodies, and many compound 
ones, may be made to pass successively through all the three states. 
Water presents the most familiar example of this. 

5. Physical phenomena, laws, and theories. —Every change 
which can happen to a body, mere alteration of its chemical constitution 
being excepted, may be regarded as a physical phenomenon. The fall of 
a stone, the vibration of a string, and the sound which accompanies it, the 
rippling of the surface of a lake, and the freezing of water, are examples 
of such phenomena. 

A. physical law is the constant relation which exists between any phe¬ 
nomenon and its cause. As an example, we have the phenomenon of 
the diminution of the volume of a gas by the application of pressure; 
the corresponding law has been determined, and is expressed by saying 
that the volume of a gas is inversely proportional to the pressure. 

The whole of the laws referring to the same class of phenomena, taken 
together, constitute a physical theory. Thus we have the theory of light, 
the theory of electricity, and, in more restricted forms, the theory of dew, 
and the theory of the mirage. 

6. Physical agents. —In our attempts to ascend from a phenomenon 
to its cause, we assume the existence of physical agents, or natural forces, 
acting upon matter; as examples of such we have gravitation, heat, light, 
magnetism, and electricity. 


GENERAL PROPERTIES OF BODIES. 


- 8 ] 


o 

O 


Since these physical agents are disclosed to us only by their effects, their 
intimate nature is completely unknown. In the present state of science, 
we cannot say whether they are properties inherent in matter, or 
whether they result from movements impressed on the mass of subtile 
and imponderable forms of matter diffused through the universe. The 
latter hypothesis is however generally admitted. This being so it may 
be further asked are there several distinct dorms of imponderable matter, 
or are they in reality but one and the same P It would seem that the latter 
opinion tends to prevail as the physical sciences extend their limits. In 
accordance with this hypothesis these subtile forms of matter are spoken 
of as imponderable fluids, since their weight is inappreciable by the aid 
of the most delicate balances. Hence arises the distinction sometimes 
made between ponderable matter , or matter properly so called, and im¬ 
ponderable matter, or physical agents. 

The term incoercible is also applied to these imponderable fluids, to 
express the impossibility of confining them in, or excluding them from, 
any closed vessel, as we do air and other gases. 



CHAPTER II. 

GENERAL PROPERTIES OF EODI^S. 


7. Different kinds of properties. —By the term properties as applied 
to bodies, we understand the different ways in which bodies present 
themselves to our senses. We distinguish general from specific properties. 
The former are shared by all bodies, and amongst them the most impor¬ 
tant are impenetrability, extension, divisibility, porosity, compressibility, 
elasticity, mobility, and inertia . 

Specific properties are such as are observed in certain bodies only, or 
in certain states of those bodies ; such are solidity , fluidity, tenacity, duc¬ 
tility, malleability, hardness, transparency, colour, &c. 

With respect to the above general properties, it may be remarked 
that impenetrability and extension might be more aptly termed essential 
attributes of matter, since they suffice to define it; and that divisibility, 
porosity, compressibility, and elasticity, do not apply to atoms, but only 
to bodies or aggregates of atoms (3). 

8. Impenetrability. — Impenetrability is the property in virtue of 
which two portions of matter cannot, at the same time, occupy the same 
portion of space. 

Strictly speaking, this property applies only to the atoms of a body. 
In many phenomena bodies appear to penetrate each other; thus, the 
volume of a compound body is always less than the sum of the volumes of 

b 2 





4 


ON MATTER. FORCE, AND MOTION. 


[a- 


its constituents ; for instance, the volume of a mixture of water and sul¬ 
phuric acid, or of water and alcohol, is less than the sum of the volumes 
before mixture. In all these cases, however, the penetration is merely 
apparent, and arises from the fact that in every body there are interstices 
or spaces unoccupied by matter. 

9. Extension.— Extension or magnitude is the property in virtue of 
which every body occupies a limited portion of space. 

Many instruments have been invented for measuring linear extension 
or lengths with great precision. Two of these, the vernier and micro¬ 
meter screw, on account of their great utility, deserve to be here 
mentioned. 

10. vernier. —The vernier forms a necessary part of all instruments 
where lengths or angles have to be estimated with precision; it derives 
its name from its inventor, a French mathematician, who died in 1637, 
and consists essentially of a short graduated scale, ab, which is made to 



slide along a fixed scale, AB, so that the graduations of both may be com¬ 
pared with each other. The fixed scale, AB, being divided into equal 
parts, the whole length of the vernier, ab , may be taken equal to nine 
of those parts, and itself divided into ten equal parts. Each of the 
parts of the vernier, ab, will then be less than a part of the scale by one 
tenth of the latter. 

This granted, in order to measure the length of any object, mn, let us 
suppose that the latter, when placed as in the figure, has a length greater 
than four but less than five parts of the fixed scale. In order to deter¬ 
mine by what fraction of a part mn exceeds four, one of the ends, a, of 
the vernier, ab, is placed in contact with one extremity of the object, mn, 
and the division on the vernier is sought which coincides with a division 
on the scale, AB. In the figure this coincidence occurs at the eighth 
division of the vernier, counting from the extremity, n, and indicates 
that the fraction to be measured is equal to T s 5 of a part of the scale, 
AB. In fact, each of the parts of the vernier being less than a part of 
the scale by ~ of the latter, it is clear that on proceeding towards 
the le±t from the point of coincidence, the divisions of the vernier are 
















GENERAL PROPERTIES OF BODIES. 


5 


- 12 ] 

respectively one, two, three, etc., tenths behind the divisions of the scale ; 
so that the extremity, n, of the object (that is to say, the eighth division 
of the vernier) is T 8 5 behind the division marked 4 on the scale ; in other 
words, the length of mn is equal to 4^ of the parts into which the scale 
AB is divided. Consequently, if the scale AB were divided into inches, 
the length of mn would be 4^=4f inches. The divisions on the scale 
remaining the same, it would be necessary to increase the length of the 
vernier in order to measure the length mn more accurately. For instance, 
if the length of the vernier were equal to nineteen of the parts on the 
scale, and this length were divided into twenty equal parts, the length 
mn could be determined to the twentieth of a part on a scale, and so 
on. In instruments, like the theodolite, intended for measuring angles, 
the scale and vernier have a circular form, and the latter usually carries 
a magnifier, in order to determine with greater precision the coincident 
divisions of vernier and scale. 

11. Micrometer screw. —Another useful little instrument for mea¬ 
suring small lengths with precision is the micrometer screw. It is used 
under various forms, but the principle is the same in all, and may be 
illustrated by a simple example. Suppose the distance between the 
threads of an accurately cut screw to be equal to — of an inch, and, the 
head of the screw to be a tolerably large circle divided into one hundred 
equal parts. If the screw is fixed in such a manner that it can only 
turn on its'axis, but neither advance nor recede, and if it work in a nut 
held between guides which prevent it from turning, then every turn of 
the screw will cause the nut to advance through the tenth part of an inch. 
If a fixed pointer be placed before the divided circle at the head of the 
screw, and the latter turned through so small an angle that only one 
division of the circle passes under the pointer, the hundredth part of a 
turn will have been given to the screw, and the nut thereby caused 
to advance or recede through the hundredth part of the distance between 
two threads—that is to say, through the part of an inch. Applica¬ 
tions of this principle to the measurement of small lengths will at once 
suggest themselves, and be readily understood when seen. 

12. Divisibility —is the property in virtue of which a body may be 
divided into distinct parts. 

Numerous examples may be cited of the extreme divisibility of matter. 
The tenth part of a grain of musk will continue for years to fill a room 
with its odoriferous particles, and at the end of that time will scarcely 
be diminished in weight. 

Blood is composed of red, flattened globules floating in a colourless 
liquid called serum. In man the diameter of one of these globules is 
less than the 3,500th part of an inch, and the drop of blood which might 
be suspended from the point of a needle would contain about a million 
of globules. 


6 ON MATTER, FORCE, AND MOTION. [l3- 

Again, the microscope has disclosed to us the existence of insects 
smaller even than these particles of blood ; the struggle for existence 
reaches even to these little creatures, for they devour still smaller ones. 
If blood runs in the veins of these devoured ones, how infinitesimal 
must be the magnitude of its component globules P 

Has then the divisibility of matter no limit P Although experiment 
fails to determine such limit, many facts in chemistry, such as the in¬ 
variability in the relative weights of the elements which combine with 
each other, would lead us to believe that a limit does exist. It is on 
this account that bodies are conceived to be composed of extremely 
minute and indivisible parts called atoms (3). 

13. Porosity. —Porosity is the quality in virtue of which interstices 
or pores exist between the molecules of a body. 

Two kinds of pores may be distin¬ 
guished : physical pores , where the 
interstices are so small that the sur¬ 
rounding molecules remain within the 
sphere of each other’s attracting or 
repelling forces; and sensible pores , or 
actual cavities across which these mo¬ 
lecular forces cannot act. The con¬ 
tractions and dilatations resulting from 
variations of temperature are due to the 
existence of physical pores, whilst in the 
organic world the sensible pores are the 
seat of the phenomena of exhalation and 
absorption. 

In wood, sponge, and a great number 
of stones, e.g. pumice stone, the sensible 
pores are apparent; physical pores never 
are. Yet, since the volume of every 
body may be diminished, we conclude 
that all possess physical pores. 

The existence of sensible pores may 
be shown by the following experi¬ 
ment :—A long glass tube, A (fig. 2), is 
provided with a copper tube, m, at the 
top, and a copper foot made to screw on 
to the plate of a machine for exhausting 
air. The bottom of the cup consists of 
Fl g- 2 - a thick piece of leather. After pouring 

mercury into the cup so as entirely to cover the leather, the air-pump is 
put in action, and a partial vacuum produced within the tube. By so 
















GENERAL PROPERTIES OF BODIES. 


7 


- 16 ] 

doing a sliower of mercury is at once produced within the tube, for the 
atmospheric pressure on the mercury forces that liquid through the pores 
of the*leather. In the same manner water or mercury may he forced 
through the pores of wood, by replacing the leather in the above ex¬ 
periment by a disc of wood cut perpendicular to the fibres. 

When a piece of chalk is thrown into water air-bubbles at once rise 
to the surface, in consequence of the air in the pores of the chalk being- 
expelled by the water. The chalk will be found to be heavier after 
immersion than it was before, and from the increase of its weight the 
volume of its pores may be easily determined. 

The porosity of gold was demonstrated by the celebrated Florentine 
experiment made in 1661. Some academicians at Florence, wishing to 
try whether water was compressible, filled a thin globe of gold with that 
liquid, and, after carefully closing the orifice hermetically, they exposed 
the globe to pressure with a view of altering its form, well knowing that 
any alteration in form must be accompanied by a diminution in volume. 
The consequence was, that the water forced its way through the pores 
of the gold, and stood on the outside of the globe like dew. This 
experiment has since been repeated with globes of other metals, and like 
results obtained. 

14. Apparent and real volumes. —In consequence of the porosity 
of bodies, it becomes necessary to distinguish between their real and 
apparent volumes. The real volume of a body is the portion of space 
actually occupied by the matter of which the body is composed; its 
apparent volume is the sum of its real volume and the total volume of 
its pores. The real volume of a body is invariable, but its apparent 
volume can be altered in various ways. 

15. Applications. —The property of porosity is utilised in filters of 
paper, felt, stone, charcoal, etc. The pores of these substances are 
sufficiently large to allow liquids to pass, but small enough to arrest the 
passage of any substances which these liquids may hold in suspension. 
Again, large blocks of stone are often detached in quarries by introducing 
wedges of dry wood into grooves cut in the rock. These wedges being 
moistened, water penetrates their pores, and causes them to swell with 
considerable force. Dry cords, when moistened, increase in diameter and 
diminish in length, a property of which advantage is sometimes taken in 
order to raise immense weights. 

16. Compressibility. —Compressibility is the property in virtue of 
which the volume of a body may be diminished by pressure. This pro¬ 
perty is at once a consequence and a proof of porosity. 

Bodies differ greatly with respect to compressibility. The most com¬ 
pressible bodies are gases: by sufficient pressure they may be made to 
occupy ten, twenty, or even a hundred times less space than they do 


8 ON MATTER, FORCE, AND MOTION. [l7- 

under ordinary circumstances. In most cases, however, there is a limit 
heyond which, when the pressure is increased, they become liquids. 

The compressibility of solids is much less than that of gases, and is 
found in all degrees. Stuffs, paper, cork, woods, are amongst the most 
compressible. Metals are so also to a great extent, as is proved by the 
process of coining, in which the metal receives the impression from the 
die. There is, in most cases, a limit beyond which, when the pressure is 
increased, bodies are fractured or reduced to powder. 

The compressibility of liquids is so small as to have remained for a 
long time undetected : it may, however, be proved by experiment, as will 
be seen in the chapter on Hydrostatics. 

17. Elasticity.— Elasticity is the property in virtue of which bodies 
resume their original form or volume, when the force which altered 
that form or volume ceases to act. Elasticity may be developed in 
bodies by pressure, traction, flexion, or torsion. In treating of the 
general properties of bodies, the elasticity developed by pressure alone 
requires consideration; the other kinds of elasticity being peculiar to 
solid bodies, will be considered amongst their specific properties (arts. 
68, 69, 70). 

Gases and liquids are perfectly elastic; in other words, they regain 
exactly the same volume when the pressure becomes the same. Solid 
bodies present different degrees of elasticity, though none present the 
property in the same perfection as liquids and gases, and in all it varies 
according to the time during which the body has been exposed to 
pressure. Caoutchouc, ivory, glass, and marble possess considerable 
elasticity; lead, clay, and fats, scarcely any. 

There is a limit to the elasticity of solids, beyond which they either 
break or are incapable of regaining their original form and volume. 
In sprains, for instance, the elasticity of the tendons has been exceeded. 
In gases and liquids, on the contrary, no such limit can be reached; they 
always regain their original volume. 

If a ball of ivory, glass, or marble, be allowed to fall upon a slab of 
polished marble, which has been previously slightly smeared with oil, 
it will rebound and rise to a height nearly equal to that from which it 
fell. On afterwards examining the ball a circular blot of oil will be 
found upon it, more or less extensive according to the height from which 
it fell. From this we conclude that at the moment of the shock the ball 
was flattened, and that its rebound was caused by its effort to regain its 
original form. 

18. mobility, motion, rest.— Mobility is the property in virtue of 
which the position of a body in space may be changed. 

Motion and rest may be either relative or absolute. By the relative 
motioti or rest of a body we mean its change or permanence of position 


GENERAL PROPERTIES OF BODIES. 


9 


- 21 ] 

with respect to surrounding bodies; by its absolute motion or rest we 
mean the change or permanence of its position with respect to ideal 
fixed points in space. 

Thus a passenger in a railway carriage may be in a state of relative 
rest with respect to the train in which he travels, but he is in a state 
of relative motion with respect to the objects (fields, houses, etc.) past 
which the train rushes. These houses again enjoy merely a state of 
relative rest, for the earth itself which bears them is in a state of 
incessant relative motion with respect to the celestial bodies of our 
solar system. In short, absolute motion and rest are unknown to 
us; in nature, relative motion and rest are alone presented to our 
observation. 

19. Inertia.— Inertia is a purely negative property of matter; it is 
the incapability of matter to change its own state of motion or rest. 

A body when Unsupported in mid-air does not fall to the earth in 
virtue of any inherent property, but because it is acted upon by the force 
of gravity. A billiard ball gently pushed does not move more and more 
slowly, and finally stop, because it has any preference for a state of rest, 
but because its motion is impeded by the friction on the cloth on which 
it rolls, and by the resistance of the air. If all impeding causes were 
withdrawn, a body once in motion would continue to move for ever. 

20. Application.— Innumerable phenomena may be explained by 
the inertia of matter. For instance, before leaping a ditch we run 
towards it, in order that the motion of our bodies at the time of leaping 
may add itself to the muscular effort then made. 

On descending carelessly from a carriage in motion, the upper part of 
the body retains its motion, whilst the feet are prevented from doing so 
by friction against the ground; the consequence is we fall towards the 
moving carriage. 

The terrible accidents on our railways are chiefly due to inertia. 
When the motion of the engine is suddenly arrested the carriages strive 
to continue the motion they had acquired, and in doing so are shattered 
against each other. 


CHAPTER III. 

ON FORCE, EQUILIBRIUM, AND MOTION. 

21. Measure of Time. —To obtain a proper measure of force it is 
necessary, as a preliminary, to define certain conceptions which are pre¬ 
supposed in that measure; and, in the first place, it is necessary to define 
the unit of time. Whenever a second is spoken of without qualification 

b 3 




10 


ON MATTER, FORCE, AND MOTION. 


[ 22 - 


it is understood to be a second of mean solar time. The exact length of 
this unit is fixed by the following consideration. The instant when the 
sun’s centre is on an observer’s meridian—in other words, the instant of 
the transit of the sun’s centre—admits of exact determination, and thus 
the interval which elapses between two successive transits also admits ot 
exact determination, and is called an apparent day. The length of this 
interval differs slightly from day to day, and therefore does not serve as 
a convenient measure of time. Its average length is free from this 
inconvenience, and therefore serves as the required measure, and is 
called a mean solar day. The short hand of a common clock would go 
exactly twice round the face in a mean solar day if it went perfectly. 
The mean solar day consists of 24 equal parts called hours, these of 60 
equal parts called minutes , and these of 60 equal parts called seconds. 
Consequently the second is the 86,400th part of a mean solar day, and is 
the generally received unit of time. 

22. Measure of Space. —Space may be either length or distance, 
which is space of one dimension; area, which is space of two dimensions; 
or volume, which is space of three dimensions. In England the standard 
of length is the British Imperial Yard, which is the distance between 
two points on a certain metal rod, kept in the Tower of London, when 
the temperature of the whole rod is 60° F.=15°-5 C. It is, however, usual 
to employ as a unit, a foot , which is the third part of a yard. In France 
the standard of length is the metre; this, too, is practically fixed by the 
distance between two marks on a certain standard rod. The relation 
between these standards is as follows ; 

1 yard = 0-914383 metre. 

1 metre = 1-093633 yards. 

The unit of length having been fixed, the units of area and volume are 
connected with it thus:—the unit of area is the area of a square, one 
side of which is the unit of length. The unit of volume is the volume 
of a cube, one edge of which is the unit of length. These units in the 
case of English measures are the square yard (or foot) and the cubic 
yard (or foot) respectively; in the case of French measures, the square 
metre and cubic metre respectively. 

23. Measure of Mass. —Two bodies are said to have equal 
masses when, if placed in a perfect balance in vacuo, they counterpoise 
each other. Suppose we take lumps of any substance, lead, butter, 
wood, stone, etc., and suppose that any one of them when placed in 
one pan of a balance will exactly counterpoise any other of them 
when placed on the opposite pan—the balance being perfect and the 
weighing performed in vacuo; this being the case, these lumps are 
said to have equal masses. That these lumps differ in many respects 


DENSITY. 


11 


- 24 ] 

from each other is plain enough; in what respects they have the 
same properties in virtue of the equality of their masses is to he ascer¬ 
tained by subsequent enquiry. 

The British unit of mass is the standard pound (avoirdupois), which 
is a certain piece of platinum kept in the Exchequer Office in London. 
This unit having been fixed, the mass of a given substance is expressed 
as a multiple or submultiple of the unit. 

It need scarcely be mentioned that many distances are ascertained and 
expressed in yards which it would be physically impossible to measure 
directly by a yard measure. In like manner the masses of bodies are 
frequently ascertained and expressed numerically which could not be 
placed in a balance and subjected to direct weighing. 

24. Density and Relative Density. —If we consider any body or 
portion of matter, and if we conceive it to be divided into any number of 
parts having equal volumes, then, if the masses of these parts are equal, 
in whatever way the division be conceived as taking place, that body is 
one of uniform density. The density of such a body is the mass of the 
unit of volume. Consequently if M denote the mass, V the volume, and 
I) the density of the body, we have 

M = YD. 

If now we have an* equal volume Y of any second substance whose 
mass is M' and density D', we shall have 

M' = YD'. 

Consequently D : D' :: M : M' j that is the densities of substances are 
in the same ratio as the masses of equal volumes of those substances. If 
now we take the density of distilled water at 4° C. to be unity, the 
relative density of any other substance is the ratio which the mass of 
any given volume of that substance at that temperature bears to the mass 
of an equal volume of water. Thus it is found that the mass of any 
volume of platinum is 22-069 times that of an equal volume of water, 
consequently the relative density of platinum is 22*069. 

The relative density of a substance is generally called its specific 
gravity. Methods of determining it are given in Book III. rt 

In French measures the cubic decimetre or litre of distilled water at 4° C. 
contains the unit of mass, the kilogramme; and therefore the mass in 
kilogrammes of Y cubic decimetres of a substance whose specific 
gravity is D, will be given by the equation 

M = VJ). 

The same equation will give the mass in grammes of the body, if V is 
given in millimetres. 

It has been ascertained that 27*7274 cubic inches of distilled water 


12 


ON MATTER, FORCE, AND MOTION. 


[ 25 - 

at the temperature 15°5 C. or 60° F. contain a pound of matter. Conse¬ 
quently, if V is the volume of a body in cubic inches, D its specific gravity , 
its mass M in lbs. avoirdupois will be given by the equation 

M _ VD 
M “27-7274 

In this equation D is, properly speaking, the relative density of the sub¬ 
stance at 60° F. when the density of water at 60° F. is taken as the unit. 

25. Velocity and its measure.— When a material point moves, it 
describes a continuous line which may be either straight or curved, and 
is called its path and sometimes its trajectory. Motion which takes 
place along a straight line is called rectilinear motion; that which takes 
place along a curved line is called curvilinear motion. The rate of the 
motion of a point is called its velocity. Velocity may he either uniform or 
variable ; it is uniform when the point describes equal spaces or portions 
of its path in all equal times; it is variable when the point describes un¬ 
equal portions of its path in any equal times. 

Uniform velocity is measured by the number of units of space described 
in a given unit of time. The units commonly employed are feet and 
seconds. If, for example, a velocity 5 is spoken of without qualification, 
this means a velocity of 5 feet per second. Consequently, if a body moves 
for t seconds with a uniform velocity v, it will describe vt feet. 

Variable velocity is measured at any instant by the number of units of 
space it would describe if it continued to move uniformlv from that 
instant for a unit of time. Thus, suppose a body to run down an inclined 
plane, it is a matter of ordinary observation that it moves more and more 
quickly during its descent; suppose that at any point it has a velocity 
15, this means that at that point it is moving at the rate of 15 ft. per 
second, or, in other words, if from that point all increase of velocity 
ceased, it would describe 15 ft. in the next second. 

26. Force.— When a material point is at rest, it has no innate power of 
changing its state of rest; when it is in motion it has no innate power 
of changing its state of uniform motion in a straight line. This property 
of matter is termed its inertia. Any cause which sets a point in motion 
or which changes the magnitude or direction of its velocity if in motion, 
is a force, (gravity , friction , elasticity of springs or gases, electrical or 
magnetic attraction or repulsion , etc. are forces. All changes observed in 
the motion of bodies can be referred to the action of one or more forces. 

27. Accelerative effect of force.— If we suppose a force to con¬ 
tinue unchanged in magnitude, and to act along the line of motion of a 
point, it will communicate in each successive second a constant increase 
of velocity. This constant increase is the accelerative effect of the force. 
Thus if at any given instant the body has a velocity 10, and if at the end 
of the first, second, third, etc., second from that instant its velocity is 


MEASURE OF FORCE. 


13 


-29] 

13, 16, 19, etc., tlie accelerative effect of the force is 3; a fact which is 
expressed by saying that the body has been acted on by an accelerating 
force 3. 

If the force vary from instant to instant, its accelerative effect will 
also vary ; when this is the case the accelerative effect at any instant is 
measured by the velocity it would communicate in a second if the force 
continued constant from that instant. 

By means of an experiment to be described below (70) it can be shown 
that at any given place the accelerative effect of gravity g is constant; 
but it is found to have different values at different places, adopting the 
units of feet and seconds it found that very approximately 

g =/(1-0 00256 Cos 2^) 

at a station whose latitude is p , where / denotes the" number 32*1724. 

28. Momentum or quantity of motion is a magnitude varying as 
the mass of a body and its velocity jointly, and therefore is expressed 
numerically by the product of the number of units of mass which it con¬ 
tains and the number of units of velocity in its motion. Thus a body 
containing 5 lbs. of matter, and moving at the rate of 12 ft. per second, 
has a momentum of 60. 

29. measure of force.— Force, when constant, is measured by the mo¬ 
mentum it communicates to a body in a unit of time. If the force varies, 
it is then measured at any instant by the momentum it would communi¬ 
cate if it continued constant for a unit of time from the instant under 
consideration. The unit of force is that force which acting on a pound 
of matter would produce in one second a velocity of one foot per second. 
Consequently if a body contains m lbs. of matter, and is acted on by a 
force whose accelerative effect is/, that force contains a number of units 
of force (F), given by the equation 

F = mf 

The weight of a body, when that term denotes a force, is the force 
exerted on it by gravity ; consequently, if m is the mass of the body, and 
g the accelerating force of gravity, the number of units of force W 
exerted on it by gravity is given by the equation 
W = mg 

or (art. 27) W = mf (1 -0*00256 Cos 2 *). 

From this it is plain that the weight of the same body will be different at 
different parts of the earth’s surface ; a fact which could be verified by 
attaching a piece of platinum (or other metal) to a delicate spring, and 
noting the variations in the length of the spring during a voyage from a 
station in the Northern Hemisphere to another in the Southern Hemi¬ 
sphere, for instance, from London to the Cape of Good Hope. 

When, therefore, a pound is used as a unit of force it must be under- 


14 


ON MATTER, FORCE, AND MOTION. 


[30- 


stood to mean the force W exerted by gravity on a pound of matter in 
London. Now, in London, the numerical value of g is 32*1912, so that 

W = 1x32*1912,* 

in other words, when a pound is taken as the unit of force it contains 
32*1912 units of force according to the measure given above. It will be 
observed that a pound of matter is a completely determinate quantity of 
matter, irrespective of locality, but gravity exerts on a pound of matter 
a pound (or 32*1912 units) of force at London and other places in about 
the same latitude as London only; this ambiguity in the term 'pound 
should be carefully noticed by the student; the context in any treatise 
will always show in which sense the term is used. 

30. Representation of forces.— Draw any straight line A B, and 
fix on any point O in it. We may suppose a force to act on the point 

0, along the line A B, either towards A or B: then 
b m o jy a 0 is called the point of application of the force, 
Fig. 3. A B its line of action ; if it acts towards A, its 

direction is 0 A, if towards B, its direction is 0 B. 
It is rarely necessary to make the distinction between the line of action 
and direction of a force ; it being very convenient to make the convention 
that the statement—a force acts on a point 0 along the line 0 A—means 
that it acts from 0 to A. Let us suppose the force which acts on 0 along 
0 A to contain P units of force j from 0 towards A measure O N con¬ 
taining P units of length, the line ON is said to represent the force. It 
will be remarked that the analogy between the line and the force is very 
complete j the line 0 N is drawn from 0 in a given direction 0 A, and 
contains a given number of units P, just as the force acts on O in the 
direction 0 A, and contains a given number of units P. It is scarcely 
necessary to add that if an equal force were to act on 0 in the opposite 
direction, it would be said to act in the direction 0 B, and would be re¬ 
presented by 0 M, equal in magnitude to 0 N. 

When we are considering several forces acting along the same line we 
may indicate their directions by the positive and negative signs. Thus 
the forces mentioned above would be denoted by the symbols +P and 
— P respectively. 

31. Forces acting; along; the same line.— If forces act on the point 
0 in the direction 0 A containing P and Q units respectively, they are 
equivalent to a single force R containing as many units as P and Q 
together, that is, 

R = P -j- Q 

If the sign + in the above equation denote algebraical addition, the equation 
will continue true whether one or both of the forces act along 0 A or O B. 
It is plain that the same rule can be extended to any number of forces,' 



PARALLELOGRAM OF FORCES. 


15 


- 33 ] 


and if several forces have the same line of action they are equivalent to 
one force containing the same number of units as their algebraical sum. 
Thus if forces of 3 and 4 units act on 0 in the direction 0 A, and a force 
of 8 in the direction 013, they are equivalent to a single force containing 
R units given by the equation 

R — 3+4- 8 = — 1; 

that is, R is a force containing one unit acting along 0 B. This force R 
is called their resultant. If the forces are in equilibrium R is equal to 
zero. In this case the forces have equal tendencies to move the point 
0 in opposite directions. 

32. Resultant and components, —In the last article we saw that a 
single force R could be found equivalent to several others: this is by 
no means peculiar to the case in which all the forces 
have the same line of action; in fact, when a ma¬ 
terial point, A (fig. 4), remains in equilibrium under 
the action of several forces, S, P, Q, it does so be¬ 
cause any one of the forces, as S, is capable of 
neutralising the combined effects of all the others. 

If the force S, therefore, had its direction reversed, 
so as to act along AR, the prolongation of AS, it 
would produce the same effect as the system of 
forces P, Q. 

Now, a force whose effect is equivalent to the 
combined effects of several other forces is called 
their resultant , and with respect to this resultant, 
the other forces are termed components. 

When the forces, P, Q, act on a point they can only have one result¬ 
ant ; but any single force can be resolved into components in an indefinite 
number of ways. 

If a point move from rest under the action of any number of forces it 
will begin to move in the direction of their resultant. 

33. Parallelogram of forces. —When two forces act on a point their 
resultant is found by the following theorem, known as the principle of 
the parallelogram of forces:— If two forces act on a point, and if lines be 
draimi from that point representing the forces in magnitude and direction, 
and on these lines as sides a parallelogram be constructed, their resultant ivill 
be represented in magnitude and direction by that diagonal which passes 
through the point. Thus, let P and Q (fig. 5), be two forces acting on the 
point A along AP and AQ respectively, and let AB and AC be taken con¬ 
taining the same number of units of length that P and Q contain units of 
force; let the parallelogram AB DC be completed, and the diagonal AD 
drawn; then the theorem states that the resultant, R, of P and Q is repre- 





16 


ON MATTER, FORCE, AND MOTION. 


[33— 


sented by AD • that is to say, P and Q together are equal to a single 
force R acting along the line AD, and containing as many units of force 
as AD contains units of length. 

Proofs of this theorem are given in treatises on Mechanics; we will 
here give an account of a direct experimental verification of its 
truth ; but before doing so we must premise an account of a very simple 
experiment. 

Let A (fig. 6), be a small pulley, and let it turn on a smooth, hard, and 
thin axle with little or no friction ; let W be a weight tied to the end of a 


Pig. 5. Fig. 6. 

fine thread which passes over the pulley: let a spring CD be attached by 
one end to the end C of the thread and by the end D to another piece of 
thread, the other end of which is fastened to a fixed point B ; a scale 
CE can be fastened by one end to the point C and pass inside the spring 
so that the elongation of the spring can be measured. Now it will be 
found on trial that with a given weight W the elongation of the spring 
will be the same whatever the angle contained between the parts of the 
string WA and BA. Also it would be found that if the whole were 
suspended from a fixed point, instead of passing over the pulley, the 
weight would in this case stretch the spring to the same extent as 
before. This experiment shows that when care is taken to diminish to 
the utmost the friction of the axle of the pulley, and the imperfect flexi¬ 
bility of the thread, the weight of W is transmitted without sensible 
diminution to B, and exerts on that point a pull or force along the line 
BA virtually equal to W. 

This being premised, the experimental proof, or illustration of the 
parallelogram of forces, is as follows :— 

Suppose H and K (fig. 7), to be two pulleys with axles made as smooth 
and fine as possible ; let P and Q be two weights suspended from fine and 
flexible threads which, after passing over 11 and K, are fastened at A to 
a third thread AL from which hangs a weight R; let the three weights 
come to rest in the positions shown in the figure. Now the point A is 
acted on by three forces in equilibrium, viz., P from A to H, Q from A 






RESULTANT OF FORCES. 


17 


- 34 ] 

to K, and R from A to L, consequently, any one of them must be equal 
and opposite to the resultant of the other two. Now if we suppose the 
apparatus to be arranged immediately in front of a. large slate, we can 
draw lines upon it coinciding with AH, AK, and AL. If now we mea¬ 
sure off along AH the part AB containing as many inches as P contains 
pounds, and along AK the part AC containing as many inches as Q con¬ 
tains pounds, and complete the parallelogram ABCD, it will be found 
that the diagonal AD is in the same line as AL, and contains as many 
inches as R weighs pounds. Consequently, the resultant of P and Q is 
represented by AD. Of course, any other units of length and force might 
have been employed.’ Now it will be found that when P, Q, and R 
are changed in any way whatever consistent with equilibrium the same 
construction can be made,—the point A will have different positions in 
the different cases; but when equilibrium is established, and the paral¬ 
lelogram ABCD is constructed, it will be found that AD is vertical, and 
contains as many units of length as R contains units of force, and conse¬ 
quently it represents a force equal and opposite to R, that is, it represents 
the resultant of P and Q. 



it 


Fig. 7. Fig. 8. 

34. Resultant of any number of forces acting on one plane on 
a point.— Let the forces, P, Q, R, S (fig. 8), act on the point A, and let 
them be represented by the lines AB, AC, AD, AE, as shown in the 
figure. First, complete the parallelogram AB FC and join AF ; this line 
represents the resultant of P and Q. Secondly, complete the parallelo¬ 
gram AFGD and join AG ; this line represents the resultant of P, Q, R. 
Thirdly, complete the parallelogram AGHE and join AH; this line re¬ 
presents the resultant of P, Q, R, S. It is manifest that the con¬ 
struction can be extended to any number of forces. A little considera¬ 
tion will show that the line AH might be determined by the following 
construction:—through B draw BF parallel to, equal to, and towards 
the same part as AC ; through F draw FG parallel, to equal to, and towards 
the same part as AD : through G draw GII parallel to, equal to, and to- 







13 


ON MATTER, FORCE, AND MOTION. 


[ 35 - 


wards the same part as AE; join AH, then AH represents the required 
resultant. 

In place of the above construction, the resultant can be determined 
by calculation in the following manner:—Through A draw any two 
rectangular axes Ax and Ay (fig. 9), and let a, 0, y be the angles 
made with the axis Ax by the lines representing the pressures, then 
P, Q, R can be resolved into P cos a, Q, cos 0 . R cos 7 , acting along 
Ax, and P sin a, Q cos/3, R cosy acting along Ay. Now the former 
set of forces can be reduced to a single force X by addition, attention 
being paid to the sign of each component; and in like manner the latter 
forces can be reduced to a single force Y, that is, 

X = P COS a + Q COS 0 -j- R cos 7 + ... 

Y = P sin a -f Q sin 0 -J- R sin 7 + ... 


Since the addition denotes the algebraical sum of the quantities on the 
right hand side of the equations, both sign and magnitude of X and Y are 
known. Suppose U to denote the required resultant, and </> the angle 
made by the line representing it with the axis Ax; 

then U cos </> == X, and U sin <p = Y 


These equations give U 2 = X 2 + Y 2 , which determines the magni¬ 
tude of the resultant, and then, since both sin </> 
and cos <p are known, <p is determined without 
ambiguity. 

Thus let P, Q, and R be forces of 100, 150, and 
120 units, respectively, and suppose xAP, xAQ,and 
xARto be angles of 45°, 120°, and 210° respectively. 
Then their components along Ax are 70*7,—75, 
—103-9, and their components along Ay are 70-7, 
129-9,—60. The sums of these two sets being re¬ 
spectively—108-2 and 140-6, we have U cos </> = 



Fig. 9. 

— 108-2 and U sin <p = 140-6. 
therefore 


U 2 = (108-2) 2 + (140-6) 2 
or U = 177-4 

therefore 177*4 cos <p = —108-2, and 177-4 sin </> = 136-7. 

If we made use of the former of these equations only, we should 
obtain </> equal to 232° 25', or 127° 35', and the result would be ambigu¬ 
ous : in like manner if we determined </> from the second equation only, 
we should have </> equal to 52° 25', or 127° 35' j but as we have both equa¬ 
tions, we know that ^ equals 127° 35', and consequently the force U is 
. completely determined as indicated by the dotted line AU. 

(jy J 35. Conditions of equilibrium of any forces acting- in one plane 
on a point. —If the resultant of the forces is zero, they^iave no joint 
tendency to move the point, and consequently are in equilibrium. This 




CONDITIONS OF EQUILIBRIUM OF FORCES. 


19 


-35] 


obvious principle enables us to deduce tbe following constructions and 
equations, which serve to ascertain whether given forces will keep a point 
at rest. 

Suppose that in the case represented in fig. 8, T is the force which 
will balance P, Q, R, S. It is plain that T must act on A along HA produced, 
and in magnitude must be proportional to HA; for then the resultant of the 
five forces will equal zero, since the broken line ABFGHA returns to the 
point A. This construction is plainly equivalent to the following : Let P, 
Q, R (fig. 10), be forces acting on the point O, as indicated, their magnitudes 
and directions being given. It is known that they are balanced by a fourth 
force, S, and it is required to determine the magnitude and direction of S. 
Take any point D, and draw any line parallel to and towards the same part 
as OP, draw AB parallel to and towards the same part as OQ, and take AB 
such that P : Q, :: DA : AB. Through B draw BC parallel to and 
towards the same part as OR, taking BC such that Q : R :: AB : BC; 
join CD ; through O draw OS parallel to and towards the same part as 
CD, then the required force S acts along OS, and is in magnitude pro¬ 
portional to CD. 




It is to be observed that this construction can be extended to any 
number of forces, and will apply to the case in which these directions 
are not in one plane, only in this case the broken line ABCD would not 
lie wholly in one plane. The above construction is frequently called the 
Polygon of Forces. 

The case of three forces acting on a point is, of course, included in the 
above ; but its importance is such that we may give a separate statement 
of it. Let P, Q, R (fig. 11), be three forces in equilibrium on the point O. 
From any point B draw BC parallel to and towards the same part OP, 
from C draw CA parallel to and towards the same part as OQ, and take CA 
such that P : Q :: BC : CA ; then, on joining AB, the third force R must 
act along OR parallel to and towards the same part as AB, and must be 
proportional in magnitude to AB. This construction is frequently called 
the Triangle of Forces. It is evident that while the sides of the triangle 




20 


ON MATTER, FORCE, AND MOTION. 


[36- 


are severally proportional to P, Q, R, the angles A, B, C are supplemen¬ 
tary to QOR, ROP, POQ respectively, consequently every trigonometri¬ 
cal relation existing between the sides and angles of ABC will equally 
exist between the forces P, Q, R, and the supplements of the angles 
between their directions. Thus in the triangle ABC it is known that the 
sides are proportional to the sines of the opposite angles ’, now since the 
sines of the angles are equal to the sines of their supplements, we at once 
conclude that when three forces are in equilibrium, each is 'proportional to 
the sine of the angle between the directions of the other two. 

We can easily obtain from the equations which determine the resultant 
of any number of forces (34), equations which express the conditions of 
equilibrium of any number of forces acting in one plane on a point: in 
fact, if U = 0 we must have X = 0 and Y = 0 ; that is to say, the 
required conditions of equilibrium are these :— 

0 = P cos o-f-Q-cos £+R cos 7+ ... 
and 0 = Psina+Q sin/8 + R sin 7+ ... 


The first of these equations shows that no part of the motion of the point 
can take place along Ax, the second that no part can take place along 
Ay. In other words, the point cannot move at all. 

36. Composition and resolution of parallel forces.— The case of 
the equilibrium of three parallel forces is merely a particular case of the 
equilibrium of three forces acting on a point. In fact let P and Q be 
two forces whose directions pass through the points A and B, and inter¬ 
sect in 0; let them be balanced by a third force R whose direction 
produced intersects the line AB in C. Now suppose 
the point 0 to move along AO, gradually receding 
from A, the magnitude and direction of R will con¬ 
tinually change, and also the point C will continually 
change its position, but will always lie between A 
and B. In the limit P and Q become parallel forces, 
acting towards the same part balanced by a parallel 
force R acting towards the contrary part through a 
point X between A and B. The question is :— First, 
on this limiting case what is the value of R ; secondly, 
what is the position of X. Now with regard to the 
first point it is plain, that if a triangle a b c were 
drawn as in art. 35, the angles a and b in the limit 
will vanish, and c will become 180°, consequently a b ultimately equals 
a c 4- c b or 

R = P + Q. 

With regard to the second point it is'plain that 

OC sin POR = OC sin AOC = AC sin CAO, 



Fig. 12. 



PARALLEL FORCES. 


21 


7 


Fig. 13. 




-36] 

and OC sin ROQ = OC sin BOC = CB sin CBO & 

therefore AC sin CAO : CB sin CBO :: sin POR : sin ROf 

:: Q : P (35) k W 

Now in the limit when OA and OB become parallel, OAB and OBA 
become supplementary, that is, their sines become equal, also AC and CB 
become respectively AX and XB; consequently 
AX : XB :: Q : P, 

a proportion which determines the position of X. This theorem at once 
leads to the rules for the composition of any two parallel forces, viz. 

I. When two parallel forces P and Q, act towards the same part, at 

rigidly connected points A and B, their a c ^ 

resultant is a parallel force acting towards 
the same part, equal to their sum, and its 
direction divides the line AB into two parts 
AC and CB inversely proportional to the 
forces P and Q. 

II. When two parallel forces P and Q 
act towards contrary parts, at rigidly con¬ 
nected points A and B of which P is the 
greater, their resultant is a parallel force 
acting towards the same part as P, equal 
to the excess of P over Q, and its direc¬ 
tion divides BA produced in a point C 
such that CA and CB are inversely pro- 
portional to P and Q. 

In each of the above cases if we were 
to apply R at the point C, in opposite 
direction to those shown in the figure, it _ 
would plainly (by the above theorem) 

balance P and Q, and therefore when it acts as shown in figs. 13 and 14 
it is the resultant of P and Q in those cases respectively. It will of 
course follow that the force R acting at C can be resolved into P and Q 
acting at A and B respectively. 

If the second of the above theorems be examined, it will be found that 
no force R exists equivalent to P and Q when those forces are equal. 
Two such forces constitute a couple, which may be defined to be two 
equal parallel forces acting towards contrary parts; they possess the 
remarkable property that they are incapable of being balanced by any 
single force whatsoever. 

In the case of more than two parallel forces the resultant of any two 
can be found, then of that and a third, and so on to any number; it 
can be shown that however great the number of forces they will either 
be in equilibrium or reduce to a single resultant or to a couple. 



Ji 




22 


ON MATTER, FORCE, AND MOTION. 


[37- 


37. Centre of parallel forces. —On referring to figs. 13 and 14, it will 
be remarked that if we conceive the points A and B to be fixed in the 
directions AP and BQ of the forces P and Q, and if we suppose those 
directions to be turned round A and B, so as to continue parallel and to 
make any given angles with their original directions, then the direction 
of their resultant will continue to pass through C j that point is therefore 
called the centre of the parallel forces P and Q. 

It appears from investigation, that whenever a system of parallel 
forces reduces to a single resultant, those forces will have a centre; that 
is to say, if we conceive each of the forces to act at a fixed point, there 
will be a point through which the direction of their resultant will pass 
when the directions of the forces are turned through any equal angles 
round their points of application in such a manner as to retain the 
parallelism of their directions. 

The most familiar example of a qentre of parallel forces is the case in 
which the forces are the weights of the parts of a body; in this case the 
forces all acting towards the same part will have a resultant, viz. their 
sum; and their centre is called the centre of gravity of the body. 

38. Moments of forces.— Let P denote any force acting from B to 
P, take A any point, let fall AN a perpendicular from A on BP. The 
product of the number of units of force in AP, and the number of units 
of length in AN is called the moment of P with respect to A. Since the 

force P can be represented by a straight line, the 
moment of P can be represented by an area. In fact 
if BC is the line representing P, the moment is 
properly represented by twice the area of the triangle 
ABC. The perpendicular AN is sometimes called 
the arm of the pressure. Now if a watch were placed 
with its face upward on the paper, the force P would 
cause the arm AN to turn round A in the contrary direc¬ 
tion to the hands of the watch. Under these circumstances, it is usual 
to consider the moment of P with respect to the point A to be positive. If 
P acted from C toB, it would turn NA in the same direction as the hands 
of the watch, and now its moment is reckoned negative. 

The following remarkable relation exists between any forces actino- 
in one plane on a body and their resultant. Take the moments of the 
forces and of their resultant with respect to any one point in the 
plane. Then the moment of the resultant equals the sum of the moments 
of the several forces, regard being had to the signs of the moments. 

If the point about which the moments are measured be taken in the 
direction of the resultant, its moment with respect to that point will be 
zero; and consequently the sum of the moments with respect to such 
point will be zero. 



35 NT CP 
Pig. 15. 




LEVERS. 


23 


- 40 ] 


39. Equality of Action and Reaction. —We will proceed toexemplify 
some of the principles now laid down by investigating the conditions of 
equilibrium of bodies in a few simple cases; but before doing so we must 
notice a law which holds good whenever a mutual action is called into 
play between two bodies. Reaction is always equal and contrary to 
action; that is to say, the mutual actions of two bodies on each other are 
alxvays forces equal in amount and opposite in direction. This law is per¬ 
fectly general, and is equally true when the bodies are in motion as well 
as when they are at rest. A very instructive example of this law has 
already been given (33), in which the action on the spring CD (fig. 6) 
is the weight W transmitted by the string to C, and balanced by the 
reaction of the ground transmitted from B to D. Under these circum¬ 
stances, the spring is said to be stretched by a force W. If the spring 
were removed, and the thread were continuous from A to B, it is clear that 
any part of it is stretched by two equal forces, viz. an action and'reaction, 
each equal to W, and the thread is said to sustain a tension W. When a 
body is urged against a smooth surface, the mutual action can only 
take place along the common perpendicular at the point of contact. If, 
however, the bodies are rough, this restriction is partially removed, and 
now the mutual action can take place in any direction not making an 
angle greater than some determinate angle with the common perpen¬ 
dicular. This determinate angle has different values for different sub¬ 
stances, and is sometimes called the limiting angle of resistance, sometimes 
the angle of repose. 

40. The Lever is a name given to any bar straight or curved, AB, rest¬ 
ing on a fixed point or edge c called the 

fulcrum. The forces acting on the lever 
are the iveight or resistance Q, the power 
P, and the reaction of the fulcrum. 

Since these are in equilibrium, the re¬ 
sultant of P and Q must act through C, 
for otherwise they could not be balanced 
by the reaction. Draw cb at right angles 
to QB and ca to PA produced ; then ob- [ 
serving that P X ca, andQ X cb are the mo¬ 
ments of P and Q with respect to c, and 
that they have contrary signs, we have 
by art. 38, 

P x ca = Q X cb; 

an equation commonly expressed by the 
rule, that in the lever the power is to the 



Fig. 16. 


weight in the inverse ratio of their arms. 

Levers are divided into three kinds, according to the position of the 
fulcrum with respect to the points of application of the power and the 












24 


ON MATTER, FORCE, AND MOTION. 


[ 41 - 


weight. In a lever of the first kind the fulcrum is between the power 
and resistance, as in fig. 16. In a level * of the second kind the resistance is 
between the power and the fulcrum, as in a wheelbarrow or a pair of 
nutcrackers ; in a lever of the third kind the power is between the fulcrum 
and the resistance, as in a pair of tongs or the treadle of a lathe. 

41. The Sing le Pulley. —In the case of the single fixed pulley, shown 
in fig. 17, it follows at once from (33) that when the forces P and Q are 
in equilibrium they will be equal, the axle of the pulley 
being supposed perfectly smooth and the thread perfectly 
flexible. The same conclusion follows directly from the 
principle of moments; for the resultant of P and Q 
must pass through C, or otherwise they would cause the 
pulley to turn ; now their moments are respectively P X 
CM and Q x CN, and since these have opposite signs we have (38) 

< • P x CM = Q x CN. 



Pig 17. 



But CM and CN being equal, this equation shows that P and Q are 
equal. In the case of the single moveable pulley, shown in fig. 18, we 
have one end of the rope fastened to a point A in a beam. 
The pulley is consequently supported by two forces, viz. P 
and the reaction of the fixed point which is equal to P; 
these two forces support Q and the weight of the pulley 
w. In the case represented in the figure^ the parts of the 
rope are parallel, consequently (36) 

2P = Q-f w. 

When several pulleys are united into one machine, they 
J Q constitute a system of pulleys ; such are—the Block and 
Pig. 18. Tackle, the Barton, White’s Pulley, &c. 

42. The inclined plane. —A very instructive and useful application of 
the resolution of forces is to be found in the case of a body supported on 
an inclined plane. Let AB (fig. 19), be the plane, AC its base, and BC its 
height; let a body M considered as a point, 
whose mass is M and weight Mg or Q, be suj 
ported on it by a force P acting along MB. 
The plane is supposed smooth, and therefore 
reacts on M with a force R at right angles to 
- AB. Draw CD at right angles to AB, then 
the point M is held at rest by forces P, Q, R, 
whose directions are severally parallel to the sides of the triangle DBC 
which is similar to CBA. Hence 



Fig. 19. 


P : R : Q::BD : DC : CB::BC : CA : AB 
BC = AB sin A and CA = AB cos A 
P = Q sin A and R = Q cos A. 


or since 
we have 










WEDGES AND SCREWS. 


25 


- 44 ] 

Or the same fact may he stated in this form, when a mass M is placed on 
an inclined plane, its pressure on. the plane is Mg cos A and its force 
down the plane is sin A. In the above case these forces are balanced 
by P and R respectively. 

Thus suppose BC and CA to be 9 ft. and 12 ft., respectively, then 
AC will equal 15 ft. Consequently, if the weight of Q is 360 lbs. it 
produces on the plane a perpendicular pressure of 288 lbs., and requires 
for its support a force of 216 lbs. acting up the plane. 

43. The wedge.— This instrument is nothing but a moveable inclined 
plane. It is used in several forms, of which the annexed is, perhaps, the 
best for showing the action of the forces called into play. AB is a fixed 
table. ACDE is a piece whose lateral motion is prevented by a fixed 
guide F. ABC is a wedge whose angle is such that one of its faces is in 
contact with a face of ACDE as shown in the figure. ABC being forced 
forward by P, overcomes the resistance Q acting on ACDE. The various 
forces called into play are represented in the 
diagram, namely, P, Q, the reaction of the 
table S, the mutual action between the pieces 
R, Rj and the reaction T of the guide F. We 
will suppose the angles B, D, E, and EAB to 
be right angles, and that P and Q act at right 
angles to DE and BC respectively. Moreover, 
since the surfaces in contact are smooth, S acts 
in a direction at right angles to AB, R and 
Rj to AC, and T to AE. Through C draw CG at right angles to AC ; 
then the body ABC being kept in equilibrium by three forces, P, R, S, 
whose directions are respectively parallel to the sides of the triangle 
DGC, we have 

P : R :: DG : GC 

The body ACDE being kept in equilibrium by three forces, T, R 1? Q, 
whose directions are respectively parallel to the side of the triangle 
DGC, we have 

R, : Q :: GC : CD 

Now R and R x are equal, being the mutual actions of the two bodies 
ABC, ACDE ; therefore, compounding the ratios, we have 

P : Q :: DG : DC 

or, by similar triangles, 

P : Q :: CB : BA 

a proportion equivalent to the equation 

P = Q tan A 

44. The screw. —It will be remarked that when the wedge is used 



c 







26 


ON MATTER, FORCE, AND MOTION. 


[ 44 - 


as in the last article, Q cannot be many times greater than P, and also 
that the space through which P can lift Q is limited. The screw is 
merely a modification of the wedge by which the limits of its application 
in both these respects are extended. To explain this it may he observed 
that if the thread of a screw were reduced to a line, it would become a 
curve called the helix , running in whorls round the cylinder ; the distance 
between any two consecutive turns measured parallel to the axis of the 
cylinder being constant, and called the pitch of the screw. Now if ABC 
(fig. 20) were wrapped round a cylinder, whose dimensions were such 
that the base AB coincided with the circumference of the base of the 
cylinder, and the height BC with the pitch, the hypothenuse CA could 
be brought into coincidence with one whorl of the helix. Under these 
circumstances, the angle BAC (A) is called the inclination of the thread, 
and if r denote the radius of the base of the cylinder, h the pitch of the 
screw, we shall have, since ABtanA equals BC (fig. 20), 

2irr tan A == h 

Moreover, if ACPE were wrapped round the inside of a hollow cylinder 

or nut (fig. 21) of equal radius it would 
take the form of a helix, or companion 
screw cut on the inside of the nut; and 
if the screw were placed within the 
nut the two helices would be in exact 
contact. If now we suppose the 
power to act "at the end of an arm, we 
shall have transformed the wedge of 
fig. 20 into a screw, one end of which 
works on a fixed table with a move- 
able nut. The annexed figure shows 
the arrangement, half the nut being 
removed in order to show how the 
thread of the screw works within the 
groove of the companion. When the 
arm is turned in the direction indicated 
by P the point B will pass to B', but, 
as the nut is kept by the guides G, H 
from turning with the screw, it must 
now occupy the point C of the com¬ 
panion, and consequently the nut must 
be lifted so that C comes to B'. If the 
nut were fixed the screw would be 
depressed by the same amount, when P acts as indicated. 

If the screw were turned by a force P' acting tangentially to the base 



























FRICTION. 


27 


- 45 ] 

of the cylinder, it is plain that when all frictions are neglected the rela¬ 
tion between P' and Q must be the same as that between P and Q in the 
last article, that is, 

P' = Q tan A 

or 2 tit P' = 

but P acting perpendicularly at the end of an arm a will have (by equality 
of moments) the same tendency as P' to turn the screw, provided 

P V = Pa 

and therefore the relation between P and Q is given by the equation 

2na P = Q h 

or the power has to the resistance the same ratio which the pitch of the 
screw has to the circumference of the circle described by the end of the 
arm; for example, if h equal 1 inch, a equal 2ft., a power of 100 lbs. 
would overcome a resistance not exceeding 15,000 lbs. 

45. Friction. —To investigate the effect of the friction of the parts of 
machines on the relation connecting the power and resistance would take 
us far beyond our present limits, but the following points may be men¬ 
tioned. If there were no friction there would generally be one ratio 
existing between the power and the resistance, that equilibrium may be 
possible ; thus in the single fixed pulley the ratio is one of equality, so 
that if is not equal to Q (fig. 17) motion will ensue. If, however, the 
axle of the pulley is rough so as to turn with friction on its bearing, 
there will be two limiting ratios, such that if the ratio of P : Q have 
any intermediate value the machine will be at rest. Thus, suppose Q, 
to be 20 lbs., the friction on the axle may be such that if P exceed 
21 lbs. it will lift Q, and will allow Q to drop if it be less than 19 lbs. 
If P have any value intermediate to 19 and 21 it will balance Q. In the 
same manner on an inclined plane if the plane be smooth and if P act as 
supposed in (42) unless P were exactly equal to Q sin A, the body 
would move either up or down the plane. But if the plane be rough 
this is no longer true ; there will in this case be two forces, namely, P' 
greater and P" less than QsinA, such that the former will just not 
draw the body up the plane, and the latter will just not allow the body 
to slide down the plane, and then any force P intermediate to P' and P" 
will support Q. Moreover, if the body be left without support on the 
plane it will slide down however small the inclination, if the plane be 
smooth, but if the plane be rough it will not slide down, though unsup¬ 
ported/unless the inclination exceed a certain angle, whose magnitude, 
though different for different substances, is virtually the same for the 
same substances, and is in fact the angle of repose mentioned in (39). 
This fact is of the utmost importance in the practical application of the 

c 2 


28 


ON MATTER, FORCE, AND MOTION. 


[ 46 - 


wedge (54). For if tlie angle of inclination A of the wedge (fig. 20) be 
less than the angle of repose, Q will not force the wedge out, even when P 
ceases to act. Now in practice the wedge is commonly driven forward 
by a blow ; but, as we shall see in sequel, a blow is a large force exerted 
for a short time, consequently a blow will cause a resistance Q, even 
when very great, to yield through a small space, thus each blow struck 
on the back of BC (fig. 20) will cause the wedge to advance a little, 
and, as Q cannot force it back, it will stay in the position to which it has 
been advanced, and consequently by a succession of such blows it can be 
caused to advance through any requisite space. 

46. Uniformly accelerated rectilinear motion.— Let us suppose a 
body containing m units of mass to move from rest under the action of a 
force containing F units, the body will move in the line of action of the 
force, and will acquire in each second an additional velocity f given by 
the equation 

F = mf 

consequently, if v is its velocity at the end of t seconds, we have 

® - ft a) 


To determine the space it will describe in t seconds, we mav reason as 
follows. The velocity at the time t being ft that at a time t + r 
will be/(* + t). If the body moved uniformly during the time r with 
the former velocity it would describe a space s equal to ftr, if with 
the latter velocity a space s t equal to f(t -f- t)t. Consequently, 


therefore, when t is indefinitely small, the limiting values of .s and s are 
equal. Now since the body’s velocity is continually increasing during 

the time r, the space actually described is 
greater than s and less than s t But since 
the limiting values of s and s, are equal, 
the limiting value of the space described is 
the same as that of s or <q. In other words, 
if we suppose the whole time of the body’s 
motion to be divided into any number of 
equal parts, if we, determine the velocity of 
the body at the beginning of each of these 




T 



s 


h. 

R 


£ 


ZL 

f 



e 





E V OH 


Fig. 22. 


parts, and if we ascertain the spaces de¬ 
scribed on the supposition that the body moves uniformly during each por¬ 
tion of time, the limiting value of the sum of these spaces will be the space 
actually described by the body. Draw a line AC and at A construct an angle 
CAB, whose tangent equals./, divide AC into any number of equal parts 
in D, E, F, ... and draw PD, QE, BF, ... BC at right angles to AC, then 












-46] UNIFORMLY ACCELERATED MOTION. 29 

since PD = AD x /, QE = AE x /, RF = AFx /, BC = AC x /. 
etc., PD will represent the velocity of the body at the end of the time 
represented by AD, and similarly QE, RE, ... BC, will represent the 
velocity at the end of the times AE, AF, ... AC. Complete the rect¬ 
angles Be, E f, F <7 ... These rectangles represent the space described by 
the body during the second, third, fourth, ... portions of the time on the 
above supposition. Consequently the space actually described during 
the time AC is the limit of the sum of the rectangles • the limit being 
continually approached as the number of parts into which AC is divided is 
continually increased. But this limit is the area of the triangle ABC that 
is ^AC X CB or ^AC X AC x f. Therefore, if AC represents the time 
t during which the body describes a space, s, we have 

« = kF ( 2 ) 

Since this equation can be written 

2 fs =f 2 t 2 

we find, on comparing this with equation (1), that 

v 2 = 2 fs (3) 

To illustrate these equations let us suppose the accelerative effect of the 
force to be 6, that is to say, that in virtue of the action of the force, the 
body acquires in each successive second an additional velocity of 6 ft. per 
second, and let it be asked what, on the supposition of the body moving 
from rest, will be the velocity acquired and the space described at the 
end of 12 seconds ; equations (1) and (2) enable us to answer that at that 
instant it will be moving at the rate of 72 ft. per second and will have 
described 432 ft. 

The following important result follows from equation (2). At the end 
of the first, second, third, fourth, etc. second of the motion the body will 
have described £/, X 4, x 9, \f x 1G, etc. ft., and consequently 
during the first, second, third, fourth, etc. second of the motion will have 
described \f, \f X 3, \f X 6, £/ X 7, etc. ft., namely, spaces in arith¬ 
metical progression. 

The results of the above article can be stated in the form of laws 
which apply to the state of a body moving from a state of rest:— 

I. The velocities are proportional to the times during which the motion 
has lasted. 

II. The spaces described are proportional to the squares of the times 
employed in their description. 

III. The spaces described are proportional to the squares of the velocities 
acquired during their description. 

IV. The spaces described in equal successive periods of time increase by a 
constant quantity. 


30 


ON MATTER, FORCE, AND MOTION. 


[ 47 - 


Instead of supposing the body to begin to move from a state of rest we 
may suppose it to have an initial velocity V, in the direction of the force. 
In this case equations (1) (2) and (3) can be easily shown to take the 
following forms respectively: 

v = V + ft 
s = Yt + if P 
v* = V 2 + 2/s 

If the body move in a direction opposite to that of the force, f must be 
reckoned negative. 

47. Motion on an inclined plane. —Referring to (42), suppose the 
force P not to act; then the mass M is acted on by an unbalanced 
force M g sin A, in the direction MA, consequently the accelerating force 
down the plane is #sin A, and the motion becomes a particular case of 
that discussed in the last article. If it begin to move from rest, it 
will at the end of t seconds acquire a velocity v given bv the equation 

v = gt sin A 

and will describe a length s (ft.) of the plane given by the equation 

s — igt 2 sin A 

Also, if v is the velocity acquired while describing s feet of the plane 

v 2 = 2 gs sin A 

Hence (fig. 19) if a body slides down the plane from B to A the velocity 
which it acquires at A equals V'2g .AB sin A or \/2g.BC. that is to say, 
the velocity which the body has at A does, not depend on the angle A, 
but only on the perpendicular height BC. The same would be true if 
for BA we substituted any smooth curve, and hence we may state 
generally, that when a body moves along any smooth line under the 
action of gravity, the change of velocity it experiences in moving from 
one point to another is that due to the veHical height of the former point 
above the latter. 

48. Composition of velocities. —The rule for the composition of 
velocities is the same as that for the composition of forces ; this follows 
evidently from the fact that forces are measured by the momentum they 
communicate, and are therefore to one another in the same ratio as the 
velocities they communicate to the same body. Thus (fig. 5. art. 33) if 
the point has at any instant a velocity AB, in the direction AP, and 
there is communicated to it a velocity AC in the direction AQ it will 
move in the direction AR with a velocity represented by AB. And 
conversely the velocity of a body represented by AD can be resolved into 
two component velocities AB and AC. This suggests ‘the method of 
determining the motion of a body when acted on by a force in a direction 
transverse to the direction of its velocity, namely, suppose the time to be 
divided into a great number of intervals, and suppose the velocity actually 



MOTION IN A CIRCLE. 


31 


-49] 

communicated by the force to be communicated at once, then by the com¬ 
position of velocities we can determine the motion during each interval, 
and therefore during the whole time j the actual motion is the limit to 
which the motion, thus determined, approaches when the number of 
intervals is increased. 

49. iviotion in a circle. —Let ABCD ... be a regular polygon inscribed 
in a circle whose centre is O. Draw the diameter BOM. Produce AB 
to H, making BH equal to AB, join CH, this line is parallel to BO. 
Draw CK parallel to BH and CL at right angles to BO. Join CM. 
Suppose a body whose mass is M to describe AB with a velocity V in a 
time t , suppose that at B there is suddenly communicated to it in the 
direction BO, a velocity ft which is the 
same velocity as a force M f would com¬ 
municate gradually in the same time t, it 
will move during the next short time t, 
with the velocity compounded of V and ft, 
now since BH equals Yt, if f is such that 
BK equals ft X t the body will describe 
BC, in the second interval. It will be ob¬ 
served that as BC and AB are equal and 
are described in equal times t the velocity 
along BC is the same as along AB, that is, 
the effect of the composition is to change 
the direction, not the amount of the velocity. 

When the body is at the point C we 
may suppose a velocity ft to be communicated in the direction CO, and 
then at the end of the third interval the body will be at D. On this 
supposition therefore the body will describe the polygon ABCD... with 
a uniform velocity V. Now from similar triangles MCB, BCL we have 
MB : BC :: BC : BL 

or 2r : Yt :: Yt : %(ft) x t 

where r denotes the radius of the circle; 
therefore fr — V 2 

This is true for all values of t, and therefore also when t is indefinitely 
small. Now by diminishing t we merely increase the number of sides of 
the polygon, therefore when t is indefinitely small, the motion takes place 
in the circle, and the force M/acts continuously towards the centre. 

This is a most important mechanical truth, it may therefore be well to 
illustrate as well as prove it. Suppose a mass containing 6 lbs. of 
matter to describe a circle whose radius is 5 ft. with an uniform velocity 
of 20 ft. per second. The force acting on it tending to the centre will 
contain 6 X 20 2 ■+■ 5 or 480 units of force. In virtue of its inertia the 


ii 



Fig. 23. 






32 


ON MATTER, FORCE, AND MOTION. 


[ 50 - 


body tends at each point to move along the tangent at that point, conse¬ 
quently a force must continually act on it towards the centre to deflect 
it from the tangent, and keep it moving in the circle; in the above case 
the force contains 480 units, which is nearly 15 lbs. of force. 

50. Motion in a vertical circle. —Let ACDB be a circle whose plane 
is vertical and radius denoted by r. Suppose a 
point placed at A, and allowed to slide down 
the curve, what velocity will it have acquired on 
reaching any given point P ? Draw the vertical 
diameter CD, join CA, CP, and draw the hori¬ 
zontal lines AMB and PNP'. Now assuming the 
curve to be smooth the velocity acquired in 
falling from A to P is that due to MN the vertical 
height of A above P (47), if, therefore, v denote 
the velocity of the point at P we shall have 
v 2 = 2 g. MN 
Now by similar triangles DCP, PCN we have 
DC : CP :: CP : CN 


D 



consequently, if we denote by s the chord CP, 

2r . NC = s 2 

in like manner if a denote the chord CA, 


therefore 


2 r . MC = a 2 
2 r . MN = a 2 —s 2 


and — 9- ( a 2 _ s 2 ) 

It will be remarked that v will have equal values when s has the same value 
whether positive or negative, and for any one value of s there are two 
equal values of v, one positive and one negative. That is to say, since 
CP' is equal to CP, the body will have the same velocity at P' that it 
has at P, and at any point the body will have the same velocity whe¬ 
ther it is going up the curve or down the curve. Of course it is in¬ 
cluded in this statement that if the body begins to move from A it will 
just ascend to a point B on the other side of C, such that A and B are in 
the same horizontal line. It will also be remarked that at C the value 
of s is zero, consequently, if V is the velocity acquired by the body in 
falling from A to C we have 

v = 

and, on the other hand, if the body begins to move from C with a velo¬ 
city V it will reach a point A such that the chord AC or a is given by 





MOTION OF A SIMPLE PENDULUM. 


33 


- 51 ] 

the same equation. In other words, the velocity at the lowest point is 
proportional to the chord of the arc described. 

51. Motion of a simple pendulum.— By a simple pendulum is 
meant a heavy particle suspended by a fine thread from a fixed point, 
about which it oscillates without friction. So 
far as its changes of velocity are concerned 
they will be the same as those of the point 
in the previous article, for the tension of the 
thread acting at each position in a direction 
at right angles to that of the motion of the 
point will no more affect its motion than the 
reaction of the smooth curve affects that of 
the point in the last article. The time of 
an oscillation, that is the time in which the 
point moves from A to B, can be easily as¬ 
certained when the arc of vibration is small, that is, when the chord and 
the arc do not sensibly differ. 

Thus, let AB (fig. 25) equal the arc or chord ACB (fig. 24) with cen¬ 
tre C and radius AC or a describe a circle, and suppose a point to de¬ 
scribe the circumference of that circle with a uniform velocity V or 

ci^J . At any instant let the point be at Q, join CQ, draw the tangent 

QT, also draw QP at right angles and QN parallel to AB, then the angles 
NQT and CQP are equal. Now the velocity of Q resolved parallel to 

AB is V cos TNQ ora y? cos CQP, that is, if CP equals s the velocity 

of Q parallel to AB is] 

/?. PQ or A («*_„») 

^ r ^ r 

But if we suppose a point to move along AB in such a manner that its 
velocity in each position is the same as that of the oscillating body, its 

velocity at P would also equal(« 2 - s 2 ) and, therefore, this point 

would describe AB in the same time that Q describes the semi-circum¬ 
ference ACB. If then t be the required time of an oscillation we have 

t z=z 7 tCI -5- (l 'L 7 r 

r 

This result is independent of the length of the arc of vibration, provided 
its amplitude , that is AB, be small. It is evident from the formula that the 
time of a vibration is directly proportional to the square root of its 
length, and inversely proportional to the square root of the accelerating 
force of gravitv. 

c 3 








34 ON MATTER, FORCE, AND MOTION. [ 52 - 

As an example of the use of the formula we may take the following : 
—It has been found by careful experiment that 39T3983 inches is the 
length of a simple pendulum, whose time of oscillation at Greenwich is 
one second, the formula at once leads to an accurate determination of the 
accelerating force of gravity ; for using feet and seconds as our units we 
have t — 1, r = 3-26165, and -n- stands for the known number 3-14159, 
therefore the formula gives us 

g = (3-14159) 3 x 3-26165 = 32-1912 
This is the value employed in (29). 

52. Graphic representation of the changes of velocity of an 
oscillating body.— The changes, which the velocity of a vibrating body 
undergoes may be graphically represented as follows :—Draw a line of 
indefinite length and mark off AH to represent the time of one vibration, 



Fig. 26. 


HH' to represent the time of the second vibration, and so on. During 
the first vibration the velocity increases from zero to a maximum at the 
half vibration, and then decreases during the second half vibration from 
the maximum to zero. Consequently, if a curved line or arc AQH is 
drawn, the ordinate QM at any point Q will represent the velocity of the 
body at the time represented by AM. If a similar curved line or arc 
HPH' be drawn, the ordinate PN of any point P will represent the velo¬ 
city at a time denoted by AN. But since the direction of the velocity in 
the second oscillation is contrary to that of the velocity in the first oscil¬ 
lation, the ordinate NP must be drawn in the contrary direction to that 
of MQ. If, then, the curve be continued by a succession of equal arcs 
alternately on opposite sides of AD, the variations of the velocity of the 
vibrating body will be completely represented by the 
varying magnitudes of the ordinates of successive 
points of the curve. 

53. Conical pendulum.— When a point P is 
suspended from a point A as a simple pendulum it caiNw 
be caused to describe a horizontal circle with a uni¬ 
form velocity V. A point moving in such a manner 
constitutes what is called a conical pendulum, and 
admits of many useful and interesting applications. 
We will, in this place, ascertain the relation which 
exists between the length r of the thread, AP, the angle of the cone 
PAN' or 9, and the velocity V. Since the point P moves in a circle, whose 








IMPULSIVE FORCES. 


- 54 ] 


do 


radius is PN with a velocity V, a force R must act on it in the direc¬ 
tion PN given by the equation (49) 


R = M . 


v*_ 

PN 


Now the only forces acting are the tension of the thread T along PA, 
and the weight of the body vertically, consequently their resultant 
must be a force R acting along PN. And therefore these forces will be 
parallel to the sides of the triangle ANP. So that (35) 


therefore 


or 


Now 






V 2 =g 


fN 2 

* AN 



• A 

> IcUA 


PN = r sin 0 and AN = PN . tan G 

therefore 

Y 2 = gr sin 0 tan 0 

One conclusion from this may be noticed. With centre A and radius 
AP, describe the arc PC. Now when the angle PAC is small, the 
sine, PN, does not sensibly differ from the chord, nor the cosine, AN, 
from the radius, therefore in this case we have 

V2 = ^ (ch ar^ OTV = ( chd - PM V^ 

On comparing this result with (50) we see that when the angle PAM 
is small the velocity of P moving in a conical pendulum is the same as P 
would have at the lowest point C if it oscillated as a simple pendulum; 
consequently, if we conceive the point P to be making small oscilla¬ 
tions about the point A, and denote the velocity at the lowest point by 
V, and if when at the extreme point of the arc of vibration, there is com¬ 
municated to it a velocity V in a direction at right angles to the plane of 
vibration, its motion will be changed into that of a conical pendulum. 

54. Impulsive forces. —When a force acts on a body for an inappreci¬ 
ably short time, and yet sensibly changes its velocity, it is termed an instan¬ 
taneous or impulsive force. Such a force is called into play when one 
body strikes against another. A force of this character is nothing but a 
finite though verv large force, acting for a time so short that its duration 
is nearly, or quite, insensible. In fact, if M is the mass of the body, and 
the force contains M/ units, it will, in a time t, communicate a velocity 
ft ; now, however small t may be, M/ and therefore/ may be so large 



ON MATTER. FORCE, AND MOTION. 



[ 54 - 


that/£ may be of sensible or even considerable magnitude. Thus if M 
contain a pound of matter, and if the force contain ten thousand units, 
though t were so short as to be only the y3oo^ °f a second, the velocity 
communicated by the force would be one of 10 ft. per second. It is also 
to be remarked that the body will not sensibly move while this velocity 
is being communicated; thus, in the case supposed, the body would only 
move through jft 2 or the ^th °f a foot while the force acts upon it. 

When one body impinges on another it follows from the law of the 
equality of action and reaction (39) that whatever force the first body 
exerts upon the second, the second will exert an equal force upon the first 
in the opposite direction; now forces are proportional to the momenta gener¬ 
ated in the same time; consequently these forces generate during the whole, 
or any part of the time of impact in the bodies respectively equal momenta 
with contrary signs: and consequently the sum of the momenta of the 
two bodies will remain constant during and at the end of the impact. It is 
of course understood that if the two bodies move in contrary directions 
their momenta have opposite signs and the sum is an algebraical sum. In 
order to test the physical validity of this conclusion, Newton made a 
series of experiments which may be briefly described thus:—two balls A 
and B are hung from points 0, D, in the same horizontal line by threads 
Eg CD e h i n suc h a manner that their centres A 

and B are in the same horizontal line. 
With centre C and radius CA describe 
a semicircle EAF, and with centre D 
and radius DB describe a semicircle 
GBH on the wall in front of which the 
balls hang. Let A be moved back to 
B, and be allowed to descend to A ; it 
there impinges on B, both A and B 
will now move along the arcs AF and BH respectively, let A and B 
come to their highest points at r and k respectively. Now if V denote 
the velocity with which A reaches the lowest point, v and u the velocities 
with which A and B leave the lowest points after impact, and r the 
radius AC, it appears from ^50) that 



V = chd . AR 


• V = chd. A r ^/d, and u — chd . B k ^ 1 


therefore if A and B are the masses of the two balls, the momentum at 
the instant before impact was A x chd . AR and the momentum after 
impact was A x chd . Ar + B x chd . B k. Now when the positions of 
the points R, r, and k had been properly corrected for the resistance of 
the air, it was found that these two expressions were equal to within 
quantities so small that they could be properly referred to errors of 





COLLISION OF TWO BODIES. 


37 


- 56 ] 

observation. The experiment succeeded equally under every variation, 
whether A impinged on B at rest or in motion, and whatever the 
materials of A and B might be. 

55. Direct collision of two bodies. —Let A and B be two bodies 
moving with velocities Y and U respectively, along the same line, and let 
their mutual action take place in that line; if the one overtake the other 
what will be their respective velocities at the instant after impact? We 
will answer this question in two extreme cases. 

i. Let us suppose the bodies to be quite inelastic. In this case, when 
A touches B, it will continue to press against B until their velocities are 
equalised, when the mutual action ceases. For whatever deformation the 
bodies may have undergone, they have no tendency to recover their 
shapes. If, therefore, x is their common velocity after impact, we shall 
have Ax + B# their joint momentum at the end of impact, but their 
momentum before impact was AV + BU. Whence 

(A + B) x = AY + BU 
an equation which determines x. 

ii. Let us suppose the bodies perfectly elastic. In this case they 
recover their shapes, with a force exactly equal to that with which they 
were compressed. Consequently, the whole momentum lost by the one, 
and gained by the other, must be exactly double of that lost while com¬ 
pression took place, that is up to the instant at which their velocities were 
equalised. But these are respectively AY - Ax and B.r — BU therefore 
if v and u are the required final velocities 

Ay = AV — 2(AV — Ax) or v = — V + 2x 
B u = BU + 2(Bx - BU) or u = 2x -U 

therefore 

(A +B)v= 2BU + (A - B)V 

and 

(A + B )u= 2AV - (A - B)U . 

The following conclusion from these equations may be noticed : suppose a 
ball A moving with a velocity V, to strike directly an equal ball B at 
rest. In this case A = B, and U = 0, consequently v = 0 and u = V, 
that is the former ball A is brought to rest, and the latter B moves on 
with a velocity V. If now B strike od a third equal ball C at rest, B 
will in turn be brought to rest, and C will acquire the velocity V. And the 
same is true if there is a fourth, or fifth, or indeed any number of balls. 
This result may be shown with ivory balls, and if carefully performed 
is a very remarkable experiment. 

56. Work and energy. —If the point of application of a force moves 
in a straight line, and if the part of the force resolved along this line acts in 


38 ON MATTER, FORCE, AND MOTION. [ 56_ 

the direction of the motion, the product of that component and the length 
of the line is the work done by the force. If the component acts in the 
opposite direction to the motion, the component may be considered as a 
resistance and the product is work done against the resistance. Thus, in 
(42) if we suppose M to move up the plane from A to B, the work done 
by P is P x AB ; the work done against the resistance Q is Q sin A x AB. 
It will be observed that if the forces are in equilibrium during the motion, 
so that the velocity of M is uniform, P equals Q sin A, and consequently 
the work done by the power equals that done against the resistance. 
Also since AB sin A equals BC the work done against the resistance 
equals Q x BC. In other words, to raise Q from A to B requires the 
same amount of work as to raise it from C to B. 

For strictly scientific purposes a unit of work is taken to be the work 
done by a unit of force when its point of application moves through one 
foot in the direction of its action. If, as is frequently done, a unit of 
work is defined to be a force of one pound exerted through one foot, 
attention must be paid to the remark in (29) regarding the meaning of the 
term 'pound when considered as a unit of force. This unit may be con¬ 
veniently distinguished as a ‘ foot-pound.’ To raise a pound of matter 
through one foot requires more or less than a ‘ foot-pound ’ of work, 
according as the force of gravity on that pound of matter exceeds or falls 
short of32T912 units. 

By the term energy or vis viva is meant a quantity proportional to the 
product of the mass of a body m and the square of its velocity v, it is 
most conveniently measured by £ma 2 . If a force containing P units 
acts on a body whose mass is m causing to move from rest over A feet, the 
force will do PA units of work, or if P equals mf it will do mfh units of 
work. "Now if v is the velocity of the body at the end of the A feet, w r e 
know that v 2 equals 2/A (46). Therefore 

PA or mfh = ^mv* 

That is to say, the work done by the force equals the energy of the body. 
In the same manner, if the body have an initial velocity V, so that, 
when the force begins to act, it have already an energy £mV 2 , the work 
done by the force will equal the change in the energy of the body or 
%m (y 1 — V 2 ). 

It deserves particular notice that if the point of application of the force 
moves in a direction at right angles to that of the force, the force, does no 
work, and therefore will not communicate energy to the body, nor cause 
its velocity to undergo change. A conspicuous example of this fact is 
furnished by the case of circular motion discussed in (49). Here the 
only force is MV 2 -s-r which acts on the body along the radius, and, there¬ 
fore, at right angles to the direction of the motion at each instant, in 
consequence it does no work, and the velocity of the body is uniform. 


CONSERVATION OF ENERGY. 


39 


-57] 

57. The conservation* of energy.— If we conceive a machine to 
move uniformly without friction it may be proved that the work done bv 
the power exactly equals that done against the resistance. We have 
seen in (56) that this is the case with one simple machine—the inclined 
plane. It is obviously so too in the case of the screw ; for, on examin¬ 
ing (44) it is plain that if the arm makes one complete turn the resistance 
is raised through a height equal to the pitch of the screw. Now as P 
acts tangentially to the circle described by the end of the arm it does 
2ira P units of work, and the work done against Q equals Q h, and these 
have been shown to be equal in the article (44) referred to. It can also 
be shown to be true in all other cases. This is the principle which is 
frequently stated thus :—that what is gained in power is lost in velocity. 
In fact, the whole efficacy and value of machines consist in this that, by 
diminishing the velocity of the point of application of the resistance, we 
may overcome the resistance, however large, by a given force. 

If we suppose the machine to move subject to friction and with a 
variable velocity, the above principle undergoes the following extension. 
If the work done against the resistance, that done against the frictions of 
the parts of the machine, that which exists in the changed energy of the 
parts of the machine be added together, their sum will equal the work 
done by the power. If we understand the term machine to mean any 
system of bodies moving, under the action of given forces, this principle 
is what has been generally called the conservation of vis viva. 

This principle has of late undergone a remarkable extension, which 
maybe explained as follows. Referring to (56) we have seen that to 
raise M from A to B requires My x BC units of work. Now if it fell 
from B to G it would acquire My x BC units of energy, consequently M 
placed at B may be held to contain My x BC units of potential energy 
more than when it is placed at C or any other point in the horizontal line 
AC. Again, it has been ascertained that for every unit of work done 
against friction there is an exact equivalent of heat, and that amount of 
heat can be made to yield the same number of units of work. In like 
manner, when the form of a body is changed by the action of forces 
either the work done against the internal forces will remain stored up as 
potential energy as in a compressed spring, or will have been replaced by 
the development of an equivalent of heat. Now this being premised we 
see that the energy communicated to any body of system of bodies, is 
withdrawn from some fund of energy previously existing; thus, the 
energy communicated to the piston of a steam engine is withdrawn from 
the heat of the steam: we also see that of the energy thus communicated 
none is destroyed, but is merely distributed, and exists either as potential 
energy, or as motion of the bodies acted on, or has been replaced by an equi¬ 
valent of heat. This fact is called the conservation of force, or more properly 
the conservation of energy. 


40 


GRAVITATION AND MOLECULAR ATTRACTION. 


[ 58 - 




BOOK II. 

GRAVITATION AND MOLECULAR ATTRACTION. 


CHAPTER I. 

GRAVITY, CENTRE OF GRAVITY, THE BALANCE. 

58. Universal attraction, its laws. — Universal attraction is a force 
in virtue of which the material particles of all bodies tend incessantly to 
approach each other; it is a mutual action, however, which all bodies, at 
rest or in motion, exert upon one another, no matter how great or how 
small the space between them may be, or whether this space be occupied 
or unoccupied by other matter. 

A vague hypothesis of the tendency of the matter of the earth and 
stars to a common centre was adopted even by Democritus and Epicurus. 
Kepler assumed the existence of a mutual attraction between the sun, 
the earth, and the other planets. Bacon, Galileo, and Hooke, also recog¬ 
nised the existence of universal attraction. But Newton was the first 
who established the law and the universality of gravitation. 

Since Newton’s time the attraction of matter by matter was experi¬ 
mentally established by Cavendish. This eminent English physicist 
succeeded by means of a delicate torsion balance (80) in rendering visible 
the attraction between a large leaden and a small copper ball. 

The attraction between any two bodies is the resultant of the attrac¬ 
tions of each molecule of the one upon every molecule of the other 
according to the law of Newton, which may be thus expressed: the at¬ 
traction between two material particles is directly proportional to the product 
of their masses, and inversely proportional to the square of their distances 
asunder. To illustrate this, we may take the case of two spheres which, 
owing to their symmetry, attract each other just as if their masses were 
concentrated in their centres. If without other alteration the mass of one 
sphere were doubled, trebled, etc., the attraction between them would 
be doubled, trebled, etc. If, however, the mass of one sphere being 
doubled, that of the other were increased three times, the distance 
between their centres remaining the same, the attraction would be in¬ 
creased six times. Lastly, if, without altering their masses, the distance 
between their centres were increased from 1 to 2, 3, 4, ... . units, the 




GRAVITY, CENTRE OF GRAVITY, THE BALANCE. 1 


41 


- 59 ] 


attraction would be diminished to the 4tli, 8 th, 16th, .... part of its 
former intensity. In short, if we define the unit of attraction as that 
which would exist between two units of mass whose distance asunder 
was the unit of length, the attraction of two molecules, having the masses 

w and in', at the distance r,/would be expressed by m /* n . 

59. Terrestrial gravitation. —The tendency of any body to fall 
towards the earth is due to the mutual attraction of that body and the 
earth; or, to terrestrial gravitation, and is, in fact, merely a particular 
case of universal gravitation. 

At any point Of the earth’s surface, the direction of gravity, that is the 
line which a falling body describes, is called the vertical line. The ver¬ 
tical lines drawn at different points of the earth’s surface converge very 
nearly to the earth’s centre. For points situated on the same meridian 
the angle contained between the vertical lines equals the difference 
between the latitudes of those points. 

The directions of the earth’s attraction upon neighbouring bodies, or 
upon different molecules of one and the same body, must, therefore, be 
considered as parallel, for the two vertical lines form the sides of a tri¬ 
angle whose vertex is near the earth’s centre, about 4,000 miles distant, 
and whose base is the small distance between the molecules under con¬ 
sideration. 

A plane or line is said to be horizontal when it is perpendicular to the 
vertical line. 

The vertical line at any point of the globe is generally determined 
by the plumb-line (fig. 29), which consists of a weight 
attached to the end of a string. It is evident that 
the weight cannot be in equilibrium unless the direction 
of the earth’s attraction upon it passes through the 
point of support, and therefore coincides with that of 
the string. 

The horizontal plane is also determined with great 
ease, since it coincides, as will be afterwards shown, 
with the level surface of every liquid when in a state of 
equilibrium. 

When the mean figure of the earth has been approxi¬ 
mately determined, it becomes possible to compare the ^ 
direction oF the plumb line at any place with that of the jp } g 29 
normal to the mean figure at that place. When any 
difference in these directions can be detected, it constitutes a deviation of 
the plumb-line, and is due to the attraction of some great mass of matter 
in the neighbourhood, such as a mountain. Thus in the case of the 
mountain of Schehallien, in Perthshire, it was found by Dr. Maskelyne 





42 GRAVITATION AND MOLECULAR ATTRACTION. [ 60 - 

that the angle between the directions of two plumb-lines, one at a 
station to the north, and the other to the south of the mountain, was 
greater by 11" 6 than the angle between the normals of the mean surface 
of the earth at. those points; in other words, each plumb-line was 
deflected by about 6" towards the mountain. By calculating the volume 
and mass of the mountain, it was inferred from this observation, that the 
mean density of the mountain was to that of the earth in the ratio of 
5 : 9, and that the mean density of the earth is about five times that of 
water,—a result agreeing pretty closely with that deduced from Caven¬ 
dish’s experiments referred to in the last article. 

60. Centre of gravity, its experimental determination.— Into 
whatever position a body may be turned with respect to the earth, there 
is a certain point, invariably situated with respect to the body, through 
which the resultant of the attracting forces between the earth and it's 




several molecules always passes. This point is called the centre of gravity ; 
it may be within or without the body, according to the form of the latter; 
its existence, however, is easily established by the following considera¬ 
tions : Let in, m', m", in'". . . (fig. 30) be molecules of anybody. The 
earth’s attraction upon these molecules will constitute a system of parallel 
forces, having a common vertical direction, whose resultant, according to 
(36), will be found by seeking first the resultant of the forces which 
act on any two molecules, m, and m', then that of this resultant, and a 
third force acting on m", and so on until we arrive at the final resultant 
W, representing the weight of the body, and applied at a certain point 
G. If the body be now turned into the position shown in fig. 31, the 
molecules m, m', m". . . will continue to be acted on by the same forces- 
as before, the resultant of the forces on m and in' will still pass through 
the same point o in the line mm% the following resultant will again pass 
through the same point o' in om", and so on up to the final resultant P, 
which will still pass through the same point G, which is the centre of 
gravity. 

To find the centre of gravity of a body is a purely geometrical 













- 61 ] GRAVITY, CENTRE OF GRAVITY, THE BALANCE. ' 43 

problem; in many cases, however, it can be determined immediately. 
For instance, the centre of gravity of a right line of uniform density is 
the point which bisects its length; in the circle and sphere it coincides 
with the geometrical centre ; in cylindrical bars it is the middle point 
of the axis. The centre of gravity of a plane triangle is in the line 
which joins any vertex with the middle of the opposite side, and at a 
distance from the vertex equal to two-thirds of this line ; in a cone or 
pyramid it is in the line which joins the vertex with the centre of 
gravity of the base, and at a distance from the vertex equal to three- 
fourths of this line. These rules, it must be remembered, presuppose that 
the several bodies are of uniform density. 




In order to determine experimentally the centre of gravity of a body, 
it is suspended by a string in two different positions as shown in figs. 32 
and 33 ; the point where the directions AB and CD of the string in the 
two experiments intersect each other is the centre of gravity required. 
For the resultant of the earth’s attraction being a vertical force applied 
at the centre of gravity, the body can only be in equilibrium when this 
point lies vertically under the point of suspension, that is in the prolongation 
of the suspended string. But the centre of gravity being in AB as well 
as in CD must coincide with the point of intersection of these two lines. 

61. Equilibrium of heavy bodies. —Since the action of gravity 
upon a body reduces itself to a single vertical force applied at the centre 
of gravity and directed towards the earth’s centre, equilibrium will be 
established only when this resultant is balanced by the resultant of other 
forces and resistances acting on the body at the fixed point through 
which it passes. 

When only one point of the body is fixed, it will be in equilibrium it 
the vertical line through its centre of gravity passes through the fixed 
point. If more than one point is supported, the body will be in equili- 









44 GRAVITATION AND MOLECULAR ATTRACTION. [ 62 - 

brium if a vertical line through the centre of gravity passes through a 
, point within the polygon formed by joining the points of support. 

The leaning tower of Pisa continues to stand because the vertical line 
drawn through its centre of gravity passes within its base. 

It is easier to stand on our feet than on stilts, because in the latter 
case the smallest motion is sufficient to cause the vertical line through 
the centre of gravity of our bodies to pass outside the supporting base, 
which is here reduced to a mere line joining the feet of the stilts. Again, 
it is impossible to stand on one leg if we keep one side of the foot and 
head close to a vertical wall, because the latter prevents us from throwing 
the body’s centre of gravity vertically above the supporting base. 

62. Different states of equilibrium.— Although a body supported 
by a fixed point is in equilibrium whenever its centre of gravity is in the 
vertical line through that point, the fact that the centre of gravity tends 
incessantly to occupy the lowest possible position leads us to distinguish 
between three states of equilibrium— stable, unstable, neutral. 

A body is said to be in stable equilibrium if it tends to return to its first 
position after the equilibrium has been slightly disturbed. Every body 
is in this state when its position is such that the slightest alteration of 
the same elevates its centre of gravity; for the centre of gravity will 
descend again when permitted, and after a few oscillations the body will 
return to its original position. 

The pendulum of a clock continually oscillates about its position of 
stable equilibrium, and an egg on a level table is 
in this state when its long axis is horizontal. 
We have another illustration in the toy repre¬ 
sented in the adjoining fig. 34. A small figure 
cut in ivory is made to stand on one foot at the 
top of a pedestal by being loaded with two leaden 
balls, a, b, placed sufficiently low to throw the 
centre of gravity, g, of the whole compound body 
below the foot of the figure. After being dis¬ 
turbed the little figure oscillates like a pendulum, 
having its point of suspension at the toe, and its 
centre of gravity at a lower point, g. 

A body is said to be in unstable equilibrium , 
when after the slightest disturbance it tends to 
depart still more from its original position. A 
body is in this state when its centre of gravity is 
Fig. 34. vertically above the point of support, or higher 

than it would be in any adjacent position of the 
body. An egg standing on its end or a stick balanced upright on the 
finger is in this state. 




45 


- 63 ] gravity, centre of gravity, the balance. 

Lastly, if in any adjacent position a body still remains in equilibrium, 
its state of equilibrium is said to be neutral. In this case an alteration 



JD. P. 


Fig. 35. 

in the position of the body neither raises nor lowers its centre of gravity. 
A perfect sphere resting on a horizontal plane is in this state. 

Fig. 35 represents three cones A, B, C, placed respectively in stable, 



Fig. 36. 


unstable, and neutral equilibrium upon a horizontal plane. The letter </ 
in each shows the position of the centre of gravity. 

63. The balance. —The balance is an instrument for determining the 
relative weights or masses of bodies. There are many varieties. 

The ordinary balance (fig. 36) consists of a lever of the first kind, called 
















46 GRAVITATION AND MOLECULAR ATTRACTION/ [ 64 - 

the beam , with its fulcrum in the middle; at the extremities of the beam 
are suspended two scale pans; one intended to receive the object to be 
weighed, and the other the counterpoise. The fulcrum consists of a steel 
prism, a , commonly called a knife edge , which passes through the beam, 
and rests with its sharp edge, or axis of suspension, upon two supports; 
these are formed of agate, or polished steel, in order to diminish the 
friction. A needle or pointer is fixed to the beam, and oscillates with it 
in front of a graduated arc, n ; when the beam is perfectly horizontal the 
needle points to the zero of the graduated arc. 

Since by (40) two equal forces in a lever of the first kind cannot be in 
equilibrium unless their leverages are equal, the length of the arms aA 
and «B ought to remain equal during the process of weighing. To secure 
this the scales are suspended from hooks, whose curved parts have sharp 
edges, and rest on similar edges at the ends of the beam. In this manner 
the scales are supported on mere points, which remain unmoved during 
the oscillations of the beam. This mode of suspension is represented in 
the above figure. 

64. Conditions to be satisfied by a balance. —A good balance 
ought to satisfy the following conditions: 

i. The two arms of the beam ought to be precisely equal, otherwise 
according to the principle of the lever, unequal weights will be required 
to produce equilibrium. To test whether the arms of the beam are 
equal, weights are placed in the two scales until the beam becomes hori¬ 
zontal ; the contents of the scales being then interchanged, the beam will 
remain horizontal if its arms are equal, but if not, it will descend on the 
side of the longer arm. 

ii. The balance ought to be in equilibrium when the scales are empty, 
for otherwise unequal weights must be placed in the scales in order to 
produce equilibrium. It must be borne in mind, however, that the arms 
are not necessarily equal, even if the beam remains horizontal when the 
scales are empty; for this result might also be produced by giving to the 
longer arm the lighter scale. 

iii. The beam being horizontal, its centre of gravity ought to be in the 
same vertical line with the edge of the fulcrum, and a little below the latter , 
for otherwise the beam would not be in stable equilibrium (62). 

The effect of changing the position of the centre of gravity may be 
shown by means of a beam (fig. 37) whose fulcrum, being the nut of a 
screw, a can bo raised or lowered by turning the screw-head, b. 

When the fulcrum is at the top of the groove c, in which it slides, the 
centre of gravity of the beam is below its edge, and the latter oscillates 
freely about a position of stable equilibrium. By gradually lowering 
the fulcrum its edge may be made to pass through the centre of gravity 
of the beam when the latter is in neutral equilibrium ; that is to say, it 


GRAVITY, CENTRE OF GRAVITY, THE BALANCE. 


47 


-65] 


no longer oscillates, but remains in equilibrium in all positions. When 
the fulcrum is lowered still more, the centre of gravity passes above its 



Fig. 37. 

edge, the beam is in a state of unstable equilibrium, and is overturned by 
the least displacement. 

65. Sensitiveness of the balance.— A balance is said to be sensitive 
when a very small difference between the weights in the scales causes a 
perceptible deflection of the pointer. 

Let A and B (figs. 38 and 39) be the points from which the scale pans 
are suspended, and C the axis of suspension of the beam. A, B, and C 


Fig. 38. 


Fig. 39. 




are supposed to be in the same straight line, according to the usual ar¬ 
rangement. Suppose weights P and Q to be in the pans suspended from 
A and B respectively, and let G be the centre of gravity of the beam, 
then the beam will come to rest in the position shown in the figure 
where the line DON is vertical, and ECG is the direction of the pointer. 
According to the above statement the greater the angle ECD for a given 
difference between P and Q the greater is the sensitiveness of the balance. 
Draw GN at right angles to CG. 

Let W be the weight of the beam, then from the properties of the 
lever it follows that measuring moments with respect to C, the moment 
of P equals the sum of the moments of Q and W, a condition which at 
once leads to the relation 

(P-Q) . AC=W. GN 

























48 


GRAVITATION AND MOLECULAR ATTRACTION. 


[ 66 - 

Now it is plain that for a given value of CG the angle GCN (that is 
ECD, which measures the sensibility) is greater as GN is greater: and from 
the formula it is plain that for a given value of P—Q we shall have GN 
greater as AC is greater, and as W is less. Again, for a given value of GN 
the angle GCN is greater as CG is less. Hence the means of rendering 
a balance sensitive are:—(i.) To make the arms of the balance long, 
(ii.) To make the weight of the beam as small as is consistent with its 
rigidity, (iii.) To bring the centre of gravity of the beam a very little 
below the point of support. Moreover, since friction will always oppose 
the action of the force that tends to preponderate, the balance will be 



Fig. 40. 


rendered more sensitive by diminishing friction; to secure this advan¬ 
tage the edges from which the beam and scales are suspended are made 
as sharp as possible, and the supports on which they rest are very hard. 
And further, the pointer is made long since its elongation renders a given 
deflection more perceptible by increasing the arc which its extremity 
describes. 

66. Physical and chemical balances.— Fig. 40 represents one of 
the accurate balances constructed by Deleuil of Paris, and used for 
chemical analysis. Its sensitiveness is such that when charged, with 
a kilogramme (1,000 grms.) in each scale, an excess of a milligramme 













































LAWS OF FALLING BODIES. 


49 


- 68 ] 

(Woo °f a grm.) in either scale produces a very perceptible deflection of 
the index. 

In order to protect the balance from air-currents, dust, and moisture, 
it is always, even when weighing, surrounded by a glass case, whose front 
slides up and down, to enable the operator to introduce the objects to be 
weighed. 

In order to preserve the edge of the fulcrum as much as possible, the 
whole beam, BB, with its fulcrum K, can be raised from the support on 
which the latter rests by simply turning the button O outside the 
case. 

The horizontality of the beam is determined by means of along index, 
which points downwards to a graduated arc near the foot of the support¬ 
ing pillar. 

Lastly, the button C serves to alter the sensitiveness of the balance; 
by turning it, the centre of gravity of the beam can be made to approach 
or recede from the fulcrum (64). 

67. Method of double weighing.— Notwithstanding the inaccuracy 
of a balance, the true weight of a body may always be determined by it. 
To do so, the body to be weighed is placed in one scale, and shot or sand 
poured into the other until equilibrium is produced; the body is then 
replaced by known weights until equilibrium is re-established. The 
sum of these weights will necessarily be equal to the weight of the body, 
for, acting under precisely the same circumstances, both have produced 
precisely the same effect. 


CHAPTER II. 

LAWS OF FALLING BODIES. INTENSITY OF TERRESTRIAL GRAVITY. THE 

PENDULUM. 

68. Laws of falling bodies. —Since a body falls to the ground in 
consequence of the earth’s attraction on each ol its molecules, it follows 
that, everything else being the same, all bodies, great and small, light and 
heavy, ought to fall with equal rapidity, and a lump of sand without 
cohesion should, during its fall, retain its original form as perfectly as if 
it were compact stone. The fact that a stone falls more rapidly than a 
feather is due solely to the unequal resistances opposed by the air to the 
descent of these bodies; in a vacuum all bodies fall with equal rapidity. 
To demonstrate this by experiment a glass tube about two yards long 
(tier. 41) may be taken, having one of its extremities completely closed, 

D 




50 


GRAVITATION AND MOLECULAR ATTRACTION. 


[ 69 - 



and a brass cock fixed to the other. After having introduced bodies of 
different weights and densities (pieces of lead, paper, feather, etc.) into 
the tube, the air is withdrawn from it by an 
air pump, and the cock closed. If the tube be 
now suddenly reversed, all the bodies will fall 
equally quickly. On introducing a little air 
and again inverting the tube, the lighter bodies 
become slightly retarded, and this retardation 
increases with the quantity of air introduced. 

The resistance opposed by the air to falling 
bodies is especially remarkable in the case of 
liquids. The Staubbach in Switzerland is a 
good illustration; an immense mass of water 
is seen falling over a high precipice, but before 
reaching the bottom it is shattered by the air 
into the finest mist. In a vacuum, however, 
liquids fall like solids without separation of 
their molecules. The water hammer illustrates 
this; the instrument consists of a thick glass 
tube about a foot long, half filled with water, 
the air having been expelled by ebullition 
previous to closing one extremity with the 
blow-pipe. When such a tube is suddenly 
inverted the water falls in one undivided mass 
against the other extremity of the tube, and 
produces a sharp dry sound, resembling that 
which accompanies the shock of two soWd 
bodies. 

From Newton’s law (58) it follows, that 
when a body falls to the earth, the force of 
attraction which causes- it to do so increases 
as the body approaches the earth. Unless the 
height from which the body falls, however, 
be very great, this increase will be altogether 
inappreciable, and the force in question may 
be considered as constant ^and continuous. If 
the resistance of the air were removed, there- 
Fig. 41 . fore, the motion of all bodies falling to the 

earth would be uniformly accelerated, and would obey the laws already 
explained (40). 

69. Attwood’s machine. —Several instruments have been invented 
for illustrating and experimentally verifying the laws of falling bodies. 
Galileo, who discovered these laws in the early part of the seventeenth 





















LAWS OF FALLING BODIES. 


51 


-69] 


century, illustrated them by means of_ bodies falling 
planes. The great object of 
all such instruments is to di¬ 
minish the rapidity of the fall 
of bodies without altering the 
character of their motion, for 
by this means their motion 
may not only be better ob¬ 
served, but it will be less 
modified by the resistance of 
the air. 

The most convenient in¬ 
strument of this kind is that 
invented by Attwood at the 
end of the last century, and 
represented in fig. 42. It 
consists of a stout pillar of 
wood about 2^ yards high, at 
the top of which is a brass 
pulley whose axle rests and 
turns upon four other wheels, 
called friction wheels, inas¬ 
much as they serve to dimi¬ 
nish friction. Two equal 
weights, M and M 7 , are at¬ 
tached to the extremities of a 
fine silk thread which passes 
round the pulley; a time¬ 
piece, H, fixed to the pillar, 
is regulated by a seconds 
pendulum, P, in the usual 
way—that is to say, the oscil¬ 
lations of the pendulum are 
communicated to a ratchet, 
whose two teeth, as seen in 
the figure, fit into those of 
the ratchet wheel. The axle 
of this wheel gives motion to 
the seconds hand of the dial, 
and also to an excentric be¬ 
hind the dial, as shown at E 
by a separate figure. This 
excentric plays against the Pig- 42. 

d 2 


down inclined 
































































GRAVITATION AND MOLECULAR ATTRACTION. 


52 


[ 69 - 


extremity of a lever, D, which it pushes until the latter no longer 
supports the small plate, i, and thus the weight M, which at first rested 
on this plate, is suddenly exposed to the free action of gravity. The 
excentric is so constructed that the little plate i falls precisely when 
the hand of the dial points to zero. 

The weights M and M' being equal hold each other in equilibrium ; 
the weight M, however, is made to descend slowly by putting a small 
bar or overweight m upon it; and to measure the spaces which it 
describes, the rod or scale, Q, is divided into feet and inches, com¬ 
mencing from the plate i. To complete the instrument there are a 
number of plates, A, A', C, O', and a number of rings, B, B', which 
may be fixed by screws at any part of the scale. The plates arrest 
the descending weight M, the rings only arrest the bar or overweight 
m, which was the cause of motion, so that after passing through them 
the weight M, in consequence of its inertia, will move on uniformly 
with the velocity it had acquired on reaching the ring. The several 
parts of the apparatus being described, a few words will suffice to ex¬ 
plain the method of experimenting. 

Let the hand of the dial be placed behind the zero point, the lever 
D adjusted to support the plate t, on which the weight M with its 
overweight m rests, and the pendulum put in motion. As soon as the 
hand of the dial points to zero the plate i will fall, the weights M and 
m will descend, and by a little attention and a few trials it will be 
easy to place a plate A so that M may reach it exactly as the dial 
indicates the expiration of one second. To make a second experiment 
let the weights M and m, the plate i, and the lever D, be placed as at 
first; remove the plate A, and in its place put a ring, B, so as to arrest 
the overweight m just when the weight M would have reached A; on 
putting the pendulum in motion again it will be easy, after a few 
trials, to put a plate, C, so that the weight M may fall upon it 
precisely when the hand of the dial points to two seconds. Since 
the overweight m in this experiment was arrested by the ring B at the 
expiration of one second, the space BC was described by M in one 
second purely in virtue of its own inertia, and consequently, by (32) 
BO will indicate the velocity of the falling mass at the expiration of 
one second. 

Proceeding in the same manner as before, let a third experiment be 
made in order to ascertain the point B' at wffiicli the weight M and m 
arrive after the lapse of two seconds, and, putting a ring at B', ascertain 
by a fourth experiment the point O' at which M arrives alone three 
seconds after the descent commenced; BC' will then express the 
velocity acquired after a descent of two seconds. In a similar manner 
by a fifth and sixth experiment, we may determine the space OB" 


LENGTH OF COMPOUND PENDULUM. 


-70] 


described in three seconds, and the velocity B"C" acquired during those 
three seconds, and so on; we shall find that B'C' is twice, and B"C" 
three times as great as BC—in other words, that the velocities BC, 
B'C', B"C", increase in the same proportion as the times 2, 3, . . . 
seconds) employed in their acquirement. By the definition (46), there¬ 
fore, the motion is uniformly accelerated. The same experiments will 
also serve to verify and illustrate the four laws of uniformly accelerated 
motion as enunciated in (46). For example, the spaces OB, OB', OB", 

.described from a state of rest in 1, 2, 3, ... . seconds, will be 

found to be proportional to the numbers 1, 4, 9, . . . that is to 
say, to the squares of those numbers of seconds, as stated in the 
third law. 

Lastly, if the overweight m be changed, the acceleration or velocity 
BC acquired per second will also be changed, and we may easily verify 
the assertion in (29), that force is proportional to the product of the mass 
moved into the acceleration produced in a given time. For instance, 
assuming the pulley to be so light that its inertia can be neglected, if m 
weighed half an ounce, and M and M' each 15| ounces, the acceleration 
BC would be found to be six inches ; whilst if m weighed 1 ounce, and 
M and M' each 63£ ounces, the acceleration BC would be found to be 
three inches. 

Now in these cases the forces producing motion, that is the overweights, 
are in the ratio of 1:2; while the products of the masses and the acce¬ 
lerations are in the ratio of (^+15f4-15J) x6 to (l-f-63^-f 63£) x3, 
that is, they are also in the ratio of 1:2. Now the same result is ob¬ 
tained in whatever way the magnitudes of m, M, and M' are varied, and 
consequently in all cases the ratio of the forces producing motion equals 
the ratio of the momenta generated. 

70. Zieng’th of the compound pendulum.— The formula for the 
time of vibration of a simple pendulum, and the conclusions deduced 
from it (51) are also applicable to the compound pendulum, though in 
this case it will be necessary to define accurately what is meant by the 
length of such a pendulum. A compound pendulum being formed of a 
heavy rod terminated by a greater or less mass, it follows that the several 
material points of the whole system will strive to perform their oscil¬ 
lations in different times, their distances from the axis of suspension being 
different, and the more distant points requiring a longer time to complete 
an oscillation. From this, and from the fact that being points of the 
same body they must oscillate together, it follows that the motion of the 
points near the axis of suspension will be retarded, whilst that of the 
more distant points will be accelerated, and between the two extremities 
there will necessarily be a series of points whose motion will be neither 
accelerated nor retarded, but which will oscillate precisely as if they 
were perfectly free and unconnected with the other points of the system. 



54 GRAVITATION AND MOLECULAR ATTRACTION. [ 71 - 

These points, being- equidistant from the axis of suspension, constitute a 
parallel axis known as the axis of oscillation ; and it is to the distance be¬ 
tween these two axes that the term length of the compound pendulum is 
applied; we may say, therefore, that the length of a compound pendulum is 
that of the simple pendulum which would describe its oscillations in the same 
time. 

Huyghens, the celebrated Dutch physicist, discovered that the axes of 
suspension and oscillation are mutually convertible—that is to say, the 
time of oscillation will remain unaltered when the pendulum is sus¬ 
pended from its axis of oscillation. This remarkable fact enables us to 
determine experimentally the length of a compound pendulum. To do 
so the pendulum is inverted and suspended from a second and moveable v 
axis, which, after some trials, is placed so that the inversion does not 
affect the number of oscillations made in a given time; the length re¬ 
quired is then the distance between the two axes, and on giving to l the 
value thus determined, the formula of (51) for the simple pendulum 
becomes applicable to the compound pendulum, whose oscillations, in 
vacuo , obey the same laws. 

The length of the seconds pendulum—that is to say, of the pendulum 
which makes one oscillation per second—varies, of course, with the in¬ 
tensity of gravity; at the level of the sea it is, according to Sabine, 

39-02074 inches at the Equator (St. Thomas), 

39-13983 „ at London, and 
39-21469 „ at Spitzbergen. 

According to the formula of (51), therefore, the accelerative effect of 
gravity at the above places is obtained by simply multiplying the above 
numbers reduced to feet by the square of 3-14159. Consequently bg or 
the space described in the first second of its motion by a body falling in 
vacuo from a state of rest (46) is 

16-0467 feet at the Equator, 

16-0956 „ at London, and 
16-1264 „ at Spitzbergen. 

From observations of this kind, after applying the necessary corrections, 
and taking into account the effect of rotation (73), the form of the earth 
can be deduced. 

71. Verification of the laws of the pendulum.— In order to verify 
the laws of the simple pendulum (51) we are compelled to employ a com¬ 
pound one, whose construction differs as little as possible from that of 
the former. For this purpose a small sphere of a very dense substance, 
such as lead or platinum, is suspended from a fixed point by means of 
a very fine thread. A pendulum thus formed oscillates almost like a 
simple pendulum, whose length is equal to the distance of the centre of 
the sphere from the point of suspension. 


PENDULUM 


- 71 ] 


OD 


In order to verify the isochronism of small oscillations, it is merely 
necessary to count the number of oscil¬ 
lations made in equal times, as the 
amplitudes of these oscillations diminish 
from 3 degrees to a fraction of a degree j 
this number is found to be constant. 

That the time of vibration is propor¬ 
tional to the square root of the length 
is verified by causing pendulums, whose 
lengths are as the numbers 1, 4, 9, ... . 
to oscillate simultaneously. The corre¬ 
sponding numbers of oscillations in a 
given time are then found to be propor¬ 
tional to the fractions 1, etc. . . . , 
which shows that the times of oscilla¬ 
tion increase as the numbers 1, 2, 3, 

.... etc. 

By taking several pendulums of ex¬ 
actly equal length B, C, D, (fig. 43) but 
with spheres of different substances, lead, 
copper, ivory, it is found that, neglecting 
the resistance of the air, these pendu¬ 
lums oscillate in equal times, thereby 
showing that the accelerative effect of 
gravity on all bodies is the same at the Fig 43 

same place. 

Bv means of an arrangement resembling the above, Newton verified 
the fact that the masses of bodies are determined by the balance; which, 
it will be remarked, lies at the foundation of the measure of force (29 ). 
For it will be seen on comparing (50) and (51) with (47) that the law 
of the time of a small oscillation is obtained on the supposition that the 
force of gravity on all bodies is represented by M g, in which M is deter¬ 
mined by the balance. In order to verify this, he had made two round 
equal wooden boxes; he filled one with wood, and as nearly as possible in 
the centre of oscillation of the other he placed an equal weight of gold. 
He then suspended the boxes by threads eleven feet long, so that they 
formed pendulums exactly equal so far as weight, figure, and resistance 
of the air -were concerned. Their oscillations were performed in exactly 
the same time. The same results w,ere obtained when other substances 
were used, such as silver, lead, glass, sand, salt, wood, water, corn. Now 
all these bodies had equal weights, and if the inference that therefore 
they had equal masses had been erroneous by so much as the one 
thousandth part of the whole, the experiment would have detected it. 










56 


GRAVITATION AND MOLECULAR ATTRACTION. 


[72- 



72. Application of the pendulum to clocks. —The regulation of the 
motion of clocks is effected by means of pendulums, that of watches by 

balance-springs. Pendulums were first applied 
to this purpose by Huyghens in 1658, and in the 
same year Hooke applied a spiral spring to the 
balance of a watch. The manner of employing 
the pendulum is shown in fig. 44. The pen¬ 
dulum rod passing between the prongs of a fork 
a communicates its motion to a rod b, -which 
oscillates on a horizontal axis o. To this axis is 
fixed a piece mn called an escapement or cratch, 
terminated by two projections or pallets, which 
work alternately with the teeth of the escapement 
wheel R. This wheel being acted on by the 
weight tends to move continuously, let us say, 
in the direction indicated by the arrow-head. 
Now if the pendulum is at rest, the wheel is 
held at rest by the pallet m, and with it the 
whole of the clockwork and the weight. If, 
however, the pendulum moves and takes the 
position shown by the dotted line, m is raised, 
the wheel escapes from the confinement in which 
it was held by the pallet, the weight descends, 
and causes the wheel to turn until its motion is arrested by the other pallet 
n) which in consequence of the motion of the pendulum will be brought 
into contact with another tooth of the escapement wheel. In this man¬ 
ner the descent of the weight is alternately permitted and arrested—or, 
in a word, regulated—by the pendulum. By means of a proper train 
jf wheel work the motion of the escapement is communicated. to the 
hands of the clock ; and consequently their motion, too, is regulated by 
the pendulum. 

73. Causes wliioh modify the intensity of terrestrial gravi¬ 
tation. —The intensity of the force of gravity at the earth’s surface is 
modified by two causes; viz. by the form, and by the rotation of the 
earth. 

i. If the earth were a sphere of uniform density the resultant of 
the attractions which its parts exert on an external point would be 
the same as if the whole of its mass were collected at its centre, and 
therefore the attraction at all points of its surface would be the same. 
In consequence of the flattening of the earth at its poles, this is no longer 
exactly, but only very nearly true; and the att "action on an external 
point is only nearly inversely as the square of its distance from the earth’s 
centre. As a further consequence of the flattening at the poles, the 


Fig. 44. 






PENDULUM. 


57 


- 73 ] 

distance from the centre of a point on the surface decreases as we proceed 
from the equator to either pole; hut as the distance decreases the attrac¬ 
tion will increase, and consequently the force of gravity increases as the 
latitude increases, being least at the equator, and greatest at the poles. 
This is what would be true if, other things remaining the same, the 
earth were at rest. 

ii. In consequence of the earth’s rotation, the force of gravity under¬ 
goes a further modification. If we imagine a body relatively at rest 
on the equator, it really shares the earth’s rotation, and describes, in 
the course of one day, a circle whose centre and radius are the centre 
and radius of the earth. Now since a body in motion tends by reason 
of its inertia to move in a straight line, it follows that to make it move 
in a circle, a force must be employed at each instant to deflect it from 
the tangent (49). Consequently a certain portion of the earth’s attrac¬ 
tion must be employed in keeping the above body on the surface of the 
earth, and only the remainder is sensible as weight or accelerating force. 
It appears from calculation that on the equator the ^th part of the 
earth’s attraction on any body is thus employed, so that the magnitude 
of g at the equator is less by the —th part of what it would be were 
the earth at rest. If the body, instead of being on the equator, is in 
any given latitude, it will describe in one day a circle coinciding with 
the parallel of latitude on which it is situated. Now when bodies 
describe in the same time circles of different radii, it can be deduced 
from (49) that the forces required to keep them in those circles are 
proportional to their radii. ‘Hence the force required in the case of a body 
in any given latitude is less than that required if the body were on the 
equator, and less as the latitude is greater, consequently were gravity 
diminished by the whole amount of this force the diminution would be 
less the nearer the body is to either pole. But since the force is ’pro¬ 
duced only by an indirect action of gravity, it appears that the diminu¬ 
tion is thereby rendered still less as the latitude is greater. On the 
whole, therefore, the force of gravity increases as we pass from the 
equator to either pole, in consequence of the rotation of the earth. 

It will be remarked that both causes, viz. the flattening of the earth 
at the poles, and its rotation, concur in producing an increase in the 
sensible force of gravity as the observer leaves the equator and approaches 
either pole. 




58 


GRAVITATION AND MOLECULAR ATTRACTION. 


|74 


CHAPTER III. 

MOLECULAR FORCES. 

74. Nature of molecular forces. —The various phenomena which 
bodies present show that their molecules are under the influence of two 
contrary forces, one of which tends to bring them together, and the other 
to separate them from each other. The first force, which is called 
molecular attraction, varies in one and the same body with the distance 
only. The second force, which is due to the action of heat, varies with 
the intensity of this agent, and with the distance. It is the mutual 
relation between these forces, the preponderance of the one or the other, 
which determines the molecular state of a body (4),—whether it be solid, 
liquid, or gaseous. 

Molecular attraction is only exerted at infinitely small distances. Its 
effect is inappreciable when the distance between the molecules is appre¬ 
ciable. The laws which regulate this force are not known. 

According to the manner in which it is regarded, molecular attraction 
is designated by the terms cohesion, affinity, or adhesion. 

75. Cohesion.— Cohesion is the force which unites two molecules of 
the same nature ; for example, two molecules of water, or two molecules 
of iron. Cohesion is strongly exerted in solids, less strongly in liquids, 
and scarcely at all in gases. Its intensity decreases as the temperature 
increases, because then the repulsive force due to heat increases. Hence 
it is that when solid bodies are heated they first liquefy, and are 
ultimately converted into the “gaseous state, provided that heat produces 
in them no chemical change. 

Cohesion varies not only with the nature of bodies, but also with the 
arrangement of their molecules; for example, the difference between 
tempered and untempered steel is due to a difference in the molecular 
arrangement produced by tempering. It is to the modifications which 
this force undergoes that many of the properties of bodies are due, such 
as tenacity, hardness, and ductility. 

In large masses of liquids, the force of gravity overcomes that of 
cohesion. Hence liquids acted upon by the former force have no 
special shape ; they take that of the vessel in which they are contained. 
But in smaller masses cohesion gets the upper hand, and liquids present 
then the spheroidal form. This is seen in the drops of dew on the 
leaves of plants ; it is also seen when a liquid is placed on a solid which 
it does not moisten j as, for example, mercury upon wood. The ex¬ 
periment may also be made with water, by sprinkling upon the surface of 


MOLECULAR EORCES. 


59 


- 77 ] 

the wood some light powder, such as lycopodium or lampblack, and 
then dropping some water on it. The following pretty experiment is 
an illustration of the force of cohesion causing a liquid to assume 
the spheroidal form. A saturated solution of sulphate .of zinc is 
placed in a narrow-necked bottle, and a few drops of bisulphide of 
carbon, coloured with iodine, made to float on the surface. If pure 
water be now carefully added, so as to rest on the surface of the sulphate 
of zinc solution, the bisulphide collects in the form of a flattened spheroid, 
which presents the appearance of blown coloured glass, and is larger than 
the neck of the bottle, provided a sufficient quantity has been taken. 

76. Affinity.— Chemical affinity is the force which is exerted between 
molecules not of the same kind. Thus, in water, which is composed of 
oxygen and hydrogen, it is affinity which unites these elements, but it is 
cohesion which binds together two molecules of water. In compound 
bodies cohesion and affinity operate simultaneously, while in simple 
bodies cohesion has alone to be considered. 

To affinity are due all the phenomena of combustion, and of chemical 
combination and decomposition. 

The causes which tend to weaken cohesion are most favourable to 
affinity; for instance, the action of affinity between substances is facili¬ 
tated by their division, and still more by reducing them to a liquid or 
gaseous state. It is most powerfully exerted by a body in its nascent 
state, that is, the state in which the body exists at the moment it is 
disengaged from a compound ; the body is then free, and ready to obey 
the feeblest affinity. An increase of temperature modifies affinity differ¬ 
ently under different circumstances. In some cases, by diminishing 
cohesion, and increasing the distance between the molecules, heat 
promotes combination. Sulphur and oxygen, which at the ordinary 
temperature are without action on each other, combine to form sulphur¬ 
ous acid when the temperature is raised : in other cases heat tends to 
decompose compounds by imparting to their elements an unequal 
expansibility. It is for this reason that many metallic oxides, as for 
example those of silver and mercury, are decomposed, by the action of 
heat, into gas and metal. 

77. Adhesion. —The molecular attraction exerted between bodies in 
contact is called adhesion. 

i. Adhesion takes place between solids. If two leaden bullets are cut 
with a penknife so as to form two equal and brightly polished surfaces, 
and the two faces are pressed and turned against each other until they 
are in the closest contact, they adhere so strongly as to require a force 
of more than 100 grammes to separate them. The same experiment 
may be made with two equal pieces of glass, which are polished and 
made perfectly plane. When they are pressed one against the other, the 


GO GRAVITATION AND MOLECULAR ATTRACTION. [ 78 - 

adhesion is so powerful that they cannot be separated without break¬ 
ing. As the experiment succeeds in vacuo, it cannot be due to atmo¬ 
spheric pressure, but must be attributed to a reciprocal action between 
the two surfaces. The attraction also increases as the contact is pro¬ 
longed, and is greater in proportion as the contact is closer. 

ii. Adhesion also takes place between solids and liquids. If we dip 
a glass rod into water, on withdrawing it a drop will be found to collect 
at its lower extremity, and remain suspended there. As the weight of 
the drop tends to detach it, there must necessarily be some force superior 
to this weight which maintains it there : this force is the force of 
adhesion. 

iii. The force of adhesion operates, lastly, between solids and gases. If 
a glass or metal plate be immersed in water, bubbles will be found to 
appear on the surface. As air cannot penetrate into the pores of the 
plate, the bubbles could not arise from the air which had been expelled. 
It is solely due to the layer of air which covered the plate, and moistened 
it like a liquid. In many cases when gases are separated in the nascent 
state on the surface of metals—as in electrolysis—the layer of gas which 
covers the plate has such a density that it is susceptible of very ener¬ 
getic chemical actions. 

Under the heads capillarity, endosmose effusion, absorption , and imbibition, 
we shall presently study a series of phenomena which are due to mole¬ 
cular attraction. 


CHAPTER IV. 

PROPERTIES PECULIAR TO SOLIDS. 

78. Various special properties. —After having described the 
principal properties common to solids, liquids, and gases, we shall 
discuss the properties peculiar to solids. They are, elasticity of traction, 
elasticity of torsion, elasticity of flexure, tenacity, ductility, and hardness. 

•79. Elasticity of traction.— Elasticity, as a general property of 
matter, has been already mentioned (17), but simply in reference to 
the elasticity developed by pressure. In solids it may also be called 
into play by traction, by torsion, and by flexure. 

In order to study the laws of the elasticity of traction, Savart used 
the apparatus represented in fig. 45. It consists of a wooden support 
from which are suspended the rods or wires taken for experiment. At 
the lower extremity there is a scale pan, and on the wire two points, A 
and B, are marked, the distance between which is measured bv means 
of the cathetometer, before the weights are added. 





PROPERTIES PECULIAR TO SOLIDS. 


01 


- 79 ] 

The cathetometer consists of a strong- brass support, K, divided into 
millimeters, and which can be adjusted in a vertical position by means of 
levelling screws and the plumb line. A small telescope, exactly at right 
angles to the scale, moves up 
and down, and is provided 
with a vernier which measures 
fiftieths of a millimeter. By 
fixing the telescope succes¬ 
sively on the two points A and 
B, as represented in the figure, 
the distance between these 
points is obtained on the gra¬ 
duated scale. Placing then 
weights in the pan, and measur¬ 
ing again the distance A and 
B, the elongation is obtained. 

When the limit of elasticity 
has not been exceeded, the trac¬ 
tion of rods and wires is sub¬ 
ject to the following laws :•— 

I. Hods and wires possess 
perfect elasticity: that is, they 
assume their original length as 
soon as the traction ceases. 

II. For the same substance 

and the same diameter, the elon¬ 
gation is proportional to the 
force of traction and to the 
length. Fi «' «• 

III. For rods or wires of the same length and substance, but of diffei'ent 
magnitude, the elongation is in inverse ratio of the squares of the diameters. 

These laws can be expressed by the formula 



where e denotes the elongation, l the length, and A the area of the 
section of the rod, F the force tending to produce elongation, and F 
a constant depending on the material of the rod called the modulus of 
elasticity. 

Both calculation and experiment show that when bodies are lengthened 
by traction their volume increases. 

From numerous experiments on the elasticity of metals made by M. 
Wertheim it results that the modulus of elasticity changes as the tem¬ 
perature varies. Between 15° and 200° he found the change to be 















GRAVITATION AND MOLECULAR ATTRACTION. 


[ 80 - 


generally one of decrease. Iron and some specimens of steel, however, 
presented a conspicuous exception. 

80. Elasticity of torsion. —The laws of the torsion of wires were 


determined by Coulomb, by means of an ap- 
paratus^called the torsion balance (fig. 46). 
It consists of a metallic wire, clasped at its 
upper extremity in a support, A, and holding 
at the other extremity a metallic sphere, B, 
to which is affixed an index, C. Immediately 
below this there is a graduated circle, CD. 
If the needle is turned from its position of 
equilibrium through a certain angle which is 
the angle of torsion, the force necessary to 
produce this effect is called the force of torsion. 
When after this deflection, the sphere is left 
to itself, the reaction of torsion produces its 
effect, the wire untwists itself, and the sphere 
rotates round its vertical axis with increasing 
rapidity until it reaches its position of equili¬ 
brium. It does not, however, rest there; in 




^ virtue of its inertia it passes this position, and 
the wire undergoes a torsion in the opposite 
direction. The equilibrium being again de- 


c 


Fig. 46. 


stroyed the wire again tends to untwist itself, the same alterations are 
again produced, and the needle does not rest at zero of the scale until after 
a certain number of oscillations about this point have been completed. 

By means of this apparatus Coulomb found that when the amplitude 
of the oscillations is within certain limits, the oscillations are subject to 
the following laws :' 

I. The oscillations are very nearly isochronous. 

II. For the same wire, the angle of torsion is 'proportional to the moment 
of the force of torsion. 

III. With the same for.ce of torsion, and with wires of the same diameter , 
the angles of torsion are proportional to the lengths of the wires. 

IV. The same force of torsion being applied to wires of the same length, 
the angles of torsion are inversely proportional to the fourth powers of the 
diameters. 

Wertheim has examined the elasticity of torsion in the case of stout 
rods by means of a different apparatus, and finds that it is also subject 
to these laws. He has further found that, all dimensions being the 
same, different substances undergo different degrees of torsion, and 






- 82 ] 


PROPERTIES PECULIAR TO SOLIDS. 


63 


The laws of torsion may he enunciated in the formula w-ri —^ in 

jl r 4 

which w is the angle of torsion, F the moment of the force of torsion, l 
the length of the wire, r its diameter, and A the specific torsion-coeffi¬ 
cient. 

81. Elasticity of flexure. —A solid, when cut into a thin plate, and 
fixed at one of its extremities, after haying been more or less.bent, strives 
to return to its original position when left to itself. This property is very 
distinct in steel, caoutchouc, wood, and paper. 

The elasticity of flexure is applied in a vast variety of instances, for 
example in bows, watch springs, carriage springs; in spring balances it is 
used to determine weights, in dynamometers to determine the force of 
agents on prime movers ; and, as existing in wool, hair, and feathers, it 
is applied to domestic uses in cushions and mattresses. 

Whatever be the kind of elasticity, there is, as has been already said, 
a limit to it—that is, there is a molecular displacement, beyond which 
bodies are broken, or at any rate do nof regain their primitive form. This 
limit is affected by various causes. The elasticity of many metals is in¬ 
creased by hardening , whether by cold, by means of the draw-plate, by 
rolling, or by hammering. Some substances, such as steel, cast iron, and 
glass, become both harder and more elastic by tempering (85). 

Elasticity, on the other hand, is diminished by annealing , which con¬ 
sists in raising the body to a temperature lower than that necessary for 
tempering, and allowing it to cool slowly. It is by this means that the 
elasticity of springs may be regulated at pleasure. Glass when it is 
heated, undergoes a true tempering on being rapidly cooled, and hence, in 
order to prevent too great a fragility of glass objects, they are reheated 
in a furnace, and are carefully allowed to cool slowly, so that the particles 
have time to assume their most stable position. 

82. Tenacity. — Tenacity is the resistance which bodies oppose to 
traction. It is determined in different bodies by forming them into 
cylindrical or prismatic wires, and ascertaining the weight necessary to 
break them. 

Tenacity is directly proportional to the breaking weight , and inversely 
proportional to the area of a transverse section of the wire. 

Tenacity diminishes with the duration df the traction. A small force 
continuously applied for a long time will often break a wire, which 
would not at once be broken by a larger weight. 

Not only does tenacity vary with different substances, but it also varies 
with the form of the body. Thus, with the same sectional area, a 
cylinder has greater tenacity than a prism. The quantity of matter being 
the same, a hollow cylinder has greater tenacity than a solid one; and 


GRAVITATION AND MOLECULAR ATTRACTION. 


G4 


[ 83 - 


the tenacity of this hollow cylinder is greatest when the external radius 
is to the internal one in the ratio of 11 to 5. 

The shape has also the same influence on the resistance to crushing, as 
it has on the resistance to traction. A hollow cylinder with the same 
mass, and the same weight, offers a greater resistance than a solid cylin¬ 
der. It is for this reason that the bones of animals, the feathers of birds, 
the stems of corn and other plants, offer greater resistance than if they 
were solid, the mass remaining the same. 

Tenacity, like elasticity, is different in different directions in bodies. In 
wood, for example, both the tenacity and the elasticity are greater in the 
direction of the fibres than in a transverse direction. And this difference 
obtains in general in all bodies, the texture of which is not the same in 
all directions. 


The following table gives the breaking weight in pounds for wires 
having a sectional area of a square millimeter: 


Antimony, cast . 

. 1-47 

Copper, annealed 

69'52 

Bismuth, „ . 

. 2-13 

„ drawn . 

. 90-20 

Lead, „ . 

. 4-86 

Iron, annealed . 

. 110-55 

„ drawn 

. 5-19 

„ drawn 

. 140-71 

Tin, „ . , 

. 6-60 

Cast steel, drawn 

. 184-36 

„ cast 

. 9T5 



Zinc, annealed . 

. 31-68 

Wood in the direction of the fibres. 

„ drawn 

. 34-58 



Gold, annealed . 

. 24-20 

Mahogany . 

. 11-0 

„ drawn 

. 61-60 

Oak . 

. 15-4 

Silver, annealed 

. 36-08 

Beech . 

. 17-6 

„ drawn 

. 63-80 

Fir . . 

. 19-8 

Platinum, annealed . 

. 58-85 

Ash 

. 26-4 

„ drawn 

. 77-00 

Box 

. 30-8 


In this table the bodies are supposed to be at the ordinary tempe¬ 
rature. At a higher temperature the tenacity rapidly decreases. M. 
Seguin, sen., who has recently made some experiments on this point with 
iron and copper, has obtained the following values for the tenacity, in 
pounds, of millimeter wire at different temperatures: 

Iron . , at 10°, 132-0 ; at 370°, 118-8 j at 500°, 77*0; 

Copper . „ 46-2; „ 16-9; „ 0. 

83. Ductility. —Ductility is the property in virtue of which a great 
number of bodies change their forms by the action of traction or 
pressure. 

With certain bodies, such as clay, wax, etc., the application of a very 
little force is sufficient to produce a change \ with others, such as the 
resins and glass, the aid of heat is needed, while with the metals, more 









PROPERTIES PECULIAR TO SOLIDS. 


-85] 


65 


powerful agents must be used, such as percussion, the draw-plate, or the 
rolling-mill. 

Malleability is that modification of ductility which is exhibited by 
hammering. The most malleable metal is gold, which has been beaten 
into leaves about the 300000 an thick. 

The most ductile metal is platinum. Wollaston obtained a wire of it 
000003 of an inch in diameter. This he effected by covering with silver 
a platinum wire OOl of an inch in diameter, so as to obtain a cylinder 
02 inch in diameter only, the axis of which was of platinum. This was 
then drawn out in the form of wire as fine as possible ; the two metals 
wore equally extended. When this wire was afterwards treated with 
dilute nitric acid the silver was dissolved, and the platinum wire left intact. 
The wire was so fine that 1,060 yards only weighed 075 of a grain. 

84. Hardness. —Hardness is the resistance which bodies offer to being 
scratched or worn by others. It is only a relative property, for a body 
which is hard in reference to one body maybe soft in reference to others. 
The relative hardness of two bodies is ascertained by trying which of 
them will scratch the other. Diamond is the hardest of all bodies, for it 
scratches all, and is not scratched by any. The hardness of a body is 
expressed by referring it to a scale of hardness : that usually adopted is— 

1. Talc 4. Fluorspar 8. Topaz 

2. Rock salt 5. Apatite 9. Corundum 

3. Calcspar 6. Felspar 10. Diamond 

7. Quartz 

Thus the hardness of a body which would scratch felspar, but would be 
scratched by quartz, would be expressed by the number 6-5. 

The pure metals are softer than their alloys. Hence it is that for 
jewellery and coinage gold and silver are alloyed with copper to increase 
their hardness. 

The hardness of a body has no relation to its resistance to compression. 
Glass and diamond are much harder than wood, but the latter offers far- 
greater resistance to the blow of a hammer. Hard bodies are often used 
for polishing powders; for example, emery, pumice, and tripoli. Diamond, 
being the hardest of all bodies, can only be ground by means of its own 
powder. 

85. Temper. —By sudden cooling after they have been raised to a high 
temperature, many bodies acquire great hardness. This operation is 
called tempering. All cutting instruments are made of tempered steel. 
There are, however, some few bodies upon which tempering produces 
quite a contrary effect. An alloy of one part of tin and four parts of 
copper, called tamtam metal , is ductile and malleable when rapidly cooled, 
but hard and brittle as glass when cooled slowly. 



66 


ON LIQUIDS 


[ 86 - 


BOOK III. 

ON LIQUIDS. 


CHAPTER I. 

HYDROSTATICS. 

86. Object of Hydrostatics. —The science of hydrostatics treats of the 
conditions of the equilibrium of liquids, and of the pressures they exert, 
whether within their own mass or on the sides of the vessels in which 
they are contained. 

The science which treats of the motion of liquids is hydrodynamics , 
and the application of the principles of this science to conducting and 
raising water in pipes is known by the name of hydraidics. 

87. General characters of liquids.— It has been already seen (4) 
that liquids are bodies whose molecules are displaced by the slightest 
force. Their fluidity, however, is not perfect, there is always a sufficient 
adherence between their molecules to produce a greater or less viscosity. 

Gases also possess fluidity, but in a higher degree than liquids. The 
distinction between the two forms of matter is that liquids are almost 
incompressible and are comparatively inexpansible, while gases are 
eminently compressible, and expand spontaneously. 

The fluidity of liquids is seen in the readiness with which they take 
all sorts of shapes. Their compressibility is established by the following 
experiment. 

88. Compressibility of liquids.— From the experiment of the Flo¬ 
rentine Academicians (13), liquids were for a long time regarded as being 
completely incompressible. Since then, researches have been made on 
this subject by various physicists, which have shown that liquids are 
really compressible. 

The apparatus used for measuring the compressibility of liquids has 
been named the piezometer (irtefa, I compress, /xerpoi/, measure). That 
shown in fig. 47 is the form invented by Oersted as improved 



HYDROSTATICS. 


G7 


- 88 ] 



by MM. Pespretz and Saigey; it consists of a strong glass cylinder 
with very thick sides and an internal dia¬ 
meter of about 3^ inches. The base of the 
cylinder is firmly cemented into a wooden 
foot, and on its upper part is fitted a me¬ 
tallic cylinder closed by a cap which can 
be unscrewed. In this cap there is a fun¬ 
nel, R, for introducing water into the cy¬ 
linder, and a small barrel hermetically 
closed by a piston, which is moved by a 
screw, P. 

In the inside of the apparatus there is a 
glass vessel, A, containing the liquid to be 
compressed. The upper part of this vessel 
terminates in a capillary tube, which dips 
under mercury, 0. This tube has been 
previously divided into parts of equal capa¬ 
city, and it has been determined how many 
of these parts the vessel A contains. The 
latter is ascertained by finding the weight, 

P, of the mercury which the reservoir, A, 
contains, and the weight, p, of the mercur)' - 
contained in a certain number of divisions, 
n , of the capillary tube. If N be the num¬ 
ber of divisions of the small tube con¬ 
tained in the whole reservoir, we have Fig. 47. 


N P 

— =—, from which the value of N is obtained. There is further a ma¬ 
nometer. This is a glass tube, B, containing air, closed at one end, and 
the lower extremity of which dips under mercury. When there is no 
pressure on the water in the cylinder, the tube B is completely full of 
air ; but when the water within the cylinder is compressed hy means of 
the screw P, the pressure is transmitted to the mercury, which rises in 
the tube, compressing the air which it contains. A graduated scale fixed 
on the^side of the tube shows the reduction of volume, and this reduction 
of volume indicates the pressure exerted on the liquid in the cylinder, as 
will be seen in speaking of the manometer (164). 

In making the experiment, the vessel A is filled with the liquid to be 
compressed, and the end dipped under the mercury. By means of the 
funnel R the cylinder is entirely filled with water. The screw P being 
then turned the piston moves downwards, and the pressure exerted upon 
the water is transmitted to the mercury and the air; in consequence of 
which the mercury rises in the tube, B, and also in the capillary tube. 











68 


ON LIQUIDS. 


[ 89 - 


Tbe ascent of mercury in the capillary tube shows that the liquid in the 
vessel A has diminished in volume, and gives the amount of its com¬ 
pression, for the capacity of the whole vessel A in terms of the graduated 
divisions on the capillary tube has been previously determined. 

In his first experiments, Oersted assumed that the capacity of the 
vessel A remained the same, its sides being compressed both internally 
and externally by the liquid. But mathematical analysis proves that 
this capacity diminishes in consequence of the external and internal 
pressures. Colladon and Sturm have made some experiments allowing 
for this change of capacity, and have found that for a pressure equal to 
that of the atmosphere, mercury experiences a compression of 0-000005 
parts of its original volume ; water a compression of 0-00005, and ether 
a compression of 0*000133 parts of its original bulk. 

For water and mercury it was also found that within certain limits the 
decrease of volume is proportional to the pressure. 

Whatever be the pressure to which a liquid has been subjected, 
experiment shows that as soon as the pressure is removed the liquid 
regains its original volume, from which it is concluded that liquids are 
perfectly elastic. 

89. Equality of pressures, Pascal’s law. —By considering liquids 
as perfectly fluid, and assuming them to be uninfluenced by the action 
of gravity, the following law has been established. It is often called 
Pascal’s law, for it was first enunciated by that distinguished geome¬ 
trician. 

Pressure exerted anywhere upon a mass of liquid is transmitted undimi¬ 
nished in all directions, and acts ivith the same force on all equal surfaces, 
and in a direction at right angles to those surfaces. 

To get a clearer idea of the truth of this principle, let us conceive a 
vessel of any given form in the sides of which are placed various cylin¬ 
drical apertures, all of the same size, and 
closed by moveable pistons. Let us, further, 
imagine this vessel to be filled with liquid and 
withdrawn front the action of gravity; the 
pistons will, obviously, have no tendency to 
move. If now upon the piston A (fig. 48), 
which has a surface a, a weight of P pounds 
be placed, it will be pressed inwards, and the- 
pressure will be transmitted to the internal 
faces of each of the pistons, B, C, D, and E, 
which will each be forced outwards by a 
pressure P, their surfaces being equal to that 
of the first piston. Since each of the pistons undergoes a pressure P, 
equal to that on A, let us suppose two of the pistons united so as to 














COMPRESSIBILITY OF LIQUIDS. 


- 90 ] 


69 


constitute a surface 2a, it will have to support a pressure 2P. Similarly, 
if the piston were equal to 3 a, it would experience a pressure of 3P; 
and if its area were 100 or 1000 times that of a, it would sustain a 
pressure of 100 or 1000 times P. In other words, the pressure on any 
part of the internal walls of the vessel would be proportional to the 
surface. 

The principle of the equality of pressure is assumed as a consequence 
of the constitution of fluids. By the following experiment it can be 
shown that pressure is transmitted in all directions, although it cannot 
be shown that it is equally transmitted. A cylinder provided with a 



piston is fitted into a hollow sphere (fig. 49), in which small cylindrical 
jets are placed perpendicular to the sides. The sphere and the cylinder 
being both filled with water, when the piston is moved the liquid spouts 
forth from all the orifices, and not merely from that which is opposite to 
the piston. 

The reason why a satisfactory quantitative experimental demonstration 
of the principle of the equality of pressure cannot be given is, that the 
influence of the weight of the liquid and of the friction of the pistons 
cannot be eliminated. 

PRESSURE PRODUCED IN LIQUIDS BY GRAVITY. 

90. Vertical downward pressure, its laws. —Any given liquid 
being in a state of rest in a vessel, if we suppose it to be divided into 
horizontal layers of the same density, it is evident that each layer 
supports the weight of those above it. Gravity, therefore, produces 
internal pressures in the mass of a liquid which vary at different points. 
These pressures are submitted to the following general laws 

I. The pressure in each layer is proportional to the depth. 

II. With different liquids and the same depth, the pressure is proportional 
to the density of the liquid. 

III. The pressure is the same at all points of the same horizontal layer. 







70 ON LIQUIDS. [ 91 - 

The two first laws are self-evident; tlie third necessarily follows from 
the first and from Pascal’s principle. 

91. Vertical upward pressure. —The pressure which the upper 
layers of a liquid exert on the lower layers causes them to exert an equal 
reaction in an upward direction, a necessary consequence of the principle 
of transmission of pressure in all directions. This upward pressure is 
termed the buoyancy of liquids ; it is very sensible when the hand is 
plunged into a liquid, more especially one of great density, like mercury. 

The following experiment (fig. 50) serves to exhibit the upward 
pressure of liquids. A large open glass tube 
A, one end of which is ground, is fitted with 
a ground glass disc, 0, or still better with a 
thin card or piece of mica, the weight of which 
may be neglected. To the disc is fitted a 
string, C, by which it can be held against the 
bottom of the tube. The whole is then im¬ 
mersed in water, and now the disc does not 
fall, although no longer held by the string ; it 
is consequently kept in its position by the 
upward pressure of the water. If water be 
now slowly poured into the tube, the disc will 
only sink -when the height of the w r ater inside 
the tube is equal to the height outside. It 
follows thence that the upward pressure on 
the disc is equal to the pressure of a column of water, the base of which 
is the internal section of the tube A, and the height the distance from 
the disc to the outer surface of the liquid. Hence the upward pressure 
of liquids at any point is governed by the same laivs as the downward 
pressure. 

92. Pressure is independent of the form of the vessel.— The 

pressure exerted by a .liquid, in virtue of its weight, on any portion of 
the liquid, or on the sides of the vessel in which it is contained, depends 
on the depth and density of the liquid, but is independent of the form of 
vessel and of the quantity of the liquid. 

This principle, which follows from the law of the equality of pressure, 
may be experimentally demonstrated by many forms of apparatus. The 
following is the one most frequently used, and is due to Haldat. It 
consists of a bent tube, ABC (fig. 51), at one end of which, A, is fitted 
a stop-cock, in which can be screwed two vessels, M and P, of the same 
height, but different in shape and capacity, the first being conical, and 
the other nearly cylindrical. Mercury is poured into the tube, ABC, 
until its level nearly reaches A. The vessel M is then screwed on and 
filled with water. The pressure of the water acting on the mercury 











-92] PRESSURE PRODUCED ON LIQUIDS BY GRAVITY. 71 

causes it to rise in tlie tube C, and its height may be marked by means 
of a little collar,«, which slides up and down the tube. The level of 
the water in M is also marked by means of the moveable rod o. When 
this is done M is then emptied by means of the stop-cock, unscrewed 
and replaced by P. When water is now poured in this, the mercury, 
which had resumed its original level in the tube ABC, again rises in C 
and when the water in P has the same height as it had in M, which is 
indicated by the rod o, the mercury will have risen to the height it had 
before, which is marked by the collar a. Hence the pressure on the 
mercury in both cases is the same. This pressure is therefore independent 



Fig. 51. 


of the shape of the vessels, and, consequently, also of the quantity of 
liquid. The base of the vessel is obviously the same in both cases; it is 
the surface of the mercury in the interior of the tube A. 

From a consideration of these principles it will be readily seen that 
a very small quantity of water can produce considerable pressures. 
Let us imagine any vessel, a cask, for example, filled with water and 
with a long narrow tube tightly fitted into the side. If water is poured 
into the tube, there will be a pressure on the bottom of the cask equal 
to the weight of a column of water whose base is the bottom itself, 
and whose height is equal to that of the water in the tube. The pres¬ 
sure may be made as great as we please; by means of a narrow thread 
of water forty feet long, Pascal succeeded in bursting a very solidly 
constructed cask. 

















72 


ON LIQUID?. 


[ 93 - 


The toy known as the hydrostatic belloics depends on the same prin¬ 
ciple, and we shall presently see a most important application of it in 
the hydraulic press. 

From the principle just laid down, the pressures produced at the 
bottom of the sea may be calculated. It will be presently demonstrated 
that the pressure of the atmosphere is equal to that of a column of 
seawater about thirty-three feet high. At sea the lead has frequently 
descended to a depth of thirteen thousand feet; at the bottom of some 
seas, therefore, there must be a pressure of four hundred atmospheres. 

93. Pressure on the sides of vessels.— Since the pressure caused 
by gravity in the mass of a liquid is transmitted in every direction, 
according to the general law of the transmission of fluid pressure, it 
follows that at every point of the side of any vessel a pressure is ex¬ 
erted, at right angles to the side, which we will suppose to be plane. 
The resultant of all these pressures is the total pressure on the sides. 
But since these pressures increase in proportion to the depth, and also 
in proportion to the horizontal extent of the side, their resultant can 
only be obtained bv calculation, which shows that the total pressure on 
any given portion of the side is equal to the weight of a column of liquid, 
which has this portion of the side for its base , and ivhose height is the 
vertical distance from the centre of gravity of the portion to the surface of 
the liquid. If the side of a vessel is a curved surface the same rule gives 
the pressure on the surface, but the total pressure is no longer the re - 
sultant of the fluid pressures. 

The point in the side supposed plane at which the resultant of all the 
pressure is applied is called the centre of pressure, and is always below 
the centre of gravity of the side. For if the pressures exerted at different 
parts of the plane side were equal, the point of application of their re¬ 
sultant, the centre of pressure, would obviously coincide with the centre 
of gravity of the side. But since the pressures increase with the depth, 
the centre of pressure is necessarily below the centre of gravity. This 
point is determined by calculation, which leads to the following results : 
—i. With a rectangular side whose upper edge is level with the water, 
the centre of pressure is at two-thirds of the line which joins the middle 
of the horizontal sides measured from the top. ii. With a triangular 
side whose base is horizontal, and coincident with the level of the water, 
the centre of pressure is at the middle of the line which joins the vertex 
of the triangle with the middle of the base. iii. With a triangular side 
whose vertex is level with the water, the centre of pressure is in the line 
joining the vertex and the middle of the base, and at three-fourths of 
the distance of the latter from the vertex. 

94. Hydrostatic paradox.— W r e have already seen that the pressure 
on the bottom of a vessel depends neither on the form of the vessel 


73 


- 95 ] CONDITIONS OF THE EQUILIBRIUM OF LIQUIDS. 

nor on the quantity of the liquid, but simply on the height of the 
liquid above Jhe bottom. But the pressure thus exerted must not he 
confounded with the pressure which the vessel itself exerts on the body 
which supports it. The latter is always equal to the combined weight 
of the liquid and the vessel in which it is contained, while the former 
may be either smaller or greater than this weight, according to the form 
of the vessel. This fact is usually termed the hydrostatic paradox , because 
at first sight it appears paradoxical. 

CD (fig. 52) is a vessel composed of two cylindrical parts of unequal 
diameters, and filled with water to a. From 
what has been said before, the bottom of the 
vessel CD supports the same pressure as if 
its diameter were everywhere the same as that 
of its lower part; and it would at first sight 
seem that the scale MN of the balance, in 
which the vessel CD is placed, ought to show 
the same weight as if there had been placed 
in it a cylindrical vessel having the same height 
of water, and having the diameter of the part 
D. But the pressure exerted on the bottom of 
the vessel is not all transmitted to the scale MN ; 
for the upward pressure upon the surface no of 
the vessel is precisely equal to the weight of 
the extra quantity of water which a cylindrical vessel would contain, and 
balances an equal portion of the downward pressure on m. Consequently, 
the pressure on the plate MN is simply equal to the weight of the 
vessel CD and of the water which it contains. 

CONDITIONS OF THE EQUILIBRIUM OF LIQUIDS. 

95. Equilibrium of a liquid in a single vessel. —In order that 
a liquid may remain at rest in a vessel of any given form, it must satisfy 
the two following conditions:— 

I. Its surface must be, everywhere, perpendicular to the resultant of the 
forces which act on the molecules of the liquid. 

II. Every molecule of the mass, of the liquid must be subject in every 
direction to equal and contrary pressures. 

The second condition is self-evident; for if, in two opposite directions, 
the pressures exerted on any given molecule were not equal and contrary, 
the molecule would be moved in the direction of the greater pressure, 
and there would be no equilibrium. Thus the second condition follows 
from the principle of the equality of pressures, and from the reaction 
which all pressure causes on the mass of liquids. 

E 







74 


ON LIQUIDS- 


[ 96 - 


To prove the first condition, let us suppose that mp is the resultant of 
all the forces acting upon any molecule m on the surface (fig. 53), and 
that this surface is inclined in reference to the force mp. The latter 

can consequently he decomposed into two 
forces, mq and mf\ the one perpendicular to 
the surface of the liquid and the other to the 
direction mp. Now the first force, mq, would 
be destroyed by the resistance of the liquid, 
while the second would move the molecule 
pig, 53 , in the direction mf, which shows that equi¬ 

librium is impossible. 

If gravity be the force acting on the liquid, the direction mp is vertical; 
hence, if the liquid is contained in a basin or vessel of small extent, the 
surface ought to be plane and horizontal (59), because then the direction 
of gravity is the same in every point. But the case is different with 
liquid surfaces of greater extent, like the ocean. The surface will be 
perpendicular to the direction of gravity; but as this changes from one 
point to another, and always tends towards a point near the centre of the 
earth, it follows that the direction of the surface of the ocean will change 
also, and assume a nearly spherical form. 

96. Equilibrium of the same liquid in several communicating 
vessels.— When several vessels of any given form communicate with 
each other, there will be equilibrium when the liquid in each vessel 

satisfies the two preceding con¬ 
ditions (95), and further, when 
the surfaces of the liquids in all 
the vessels are in the same hori¬ 
zontal plane. 

In the vessels ABCD (fig. 54), 
which communicate with each 
other, let us consider any trans¬ 
verse section of the tube mn\ the 
liquid can only remain in equi¬ 
librium as long as the pressures 
which this section supports from 
m in the direction of n, and from 
n in the direction of m, are equal 
and opposite. Now it has been 
already proved that these pres¬ 
sures are respectively equal to the weight of a column of water, whose 
base is the supposed section, and whose height is the distance from the 
centre of gravity of this section to the surface of the liquid. If we con¬ 
ceive then, a horizontal plane, mn, drawn through the centre of gravity 



Fig. 54. 

















CONDITIONS OF THE EQUILIBRIUM OF LIQUIDS. 


75 


- 98 ] 


of this section, it will be seen that there will only be equilibrium as long 
as the height of the liquid above this plane is the same in each vessel, 
which demonstrates the principle enunciated. 

97. Equilibrium of superposed liquids.— In order that there should 
be equilibrium when several heterogeneous liquids are superposed in the 
same vessel, each of them must satisfy the conditions necessary for a 
single liquid (95) ; and further, there will be stable equilibrium only when 
the liquids are arranged in the order of their decreasing densities from the 
bottom upwards. 

The last condition is experimentally demonstrated by means of the 
phial of four elements. It consists of a long narrow bottle containing 
mercury, water saturated with carbonate of potass, alcohol coloured red, 
and naphtha. When the phial is shaken the liquids mix, but when it is 
allowed to rest they separate: the mercury sinks to the bottom, then 
comes the water, then the alcohol, and then the naphtha. This is the 
order of the decreasing densities of the bodies. The water is saturated 
with carbonate of potass to prevent its mixing with the alcohol. 

This separation of the liquids is due to the same cause as that which 
enables solid bodies to float on the surface of a liquid of greater density 
than their own. It is also from this principle that fresh water, at the 
mouths of rivers, floats for a long time on the denser salt water of the 
sea; and it is for the same reason that cream, which is lighter than milk, 
rises to the surface. 

98. Equilibrium of two different liquids in communicating 
vessels. —When two liquids of different 
densities, which do not mix, are con¬ 
tained in two communicating vessels, 
they will be in equilibrium when, in 
addition to the preceding principles, 
they are subject to the following: that 
the heights above the horizontal surface of 
contact of two columns of liquid in equi¬ 
librium are in the inverse ratio of their 
densities . 

To show this experimentally, mercury 
is poured into a bent glass tube, mn, 
fixed against an upright wooden support 
(fig. 55), and then water is poured into 
one of the legs, AB. The column of 
water, AB, pressing on the mercury at 
B, lowers its level in the leg AB, and Fig. 55. 

raises it in the other by a quantity, GD; 

so that if, when equilibrium is established we imagine a horizontal 






























76 


ON LIQUIDS. 


[ 99 - 


plane, BC, to pass through B, the column of water in AB will balance 
the column of mercury CI). If the heights of these two columns are 
then measured, by means of the scales, it will be found that the height 
of the column of water is about 13^ times that of the height of the 
column of mercury. We shall presently see that the density of mercury 
is about 13£ times that of water, from which it follows that the heights 
are inversely as the densities. 

It may be added that the equilibrium cannot exist unless there is a 
sufficient quantity of the heavier liquid for part of it to remain in both legs 
of the tube. 

The preceding principle may be deduced by a very simple calculation. 
Let d and d' be the densities of water and mercury, and h and h' their 
respective heights, and let g be the force of gravity. The pressure on B 
will be proportional to the density of the liquid, to its height, and to the 
force of gravity; on the whole, therefore, to the product dhy. • Similarly 
the pressure at C will be proportional to d'h'y. But in order to produce 
equilibrium, dhy must be equal to d'h'y, or dh—d'h'. This is nothing- 
more than an algebraical expression of the above principle; for since the 
two products must always be equal, d' must be as many times greater 
than d, as h' is less than h. 

In this manner the density of a liquid may be calculated. Suppose 
one of the branches contained water and the other oil, and their heights 
were respectively 15 inches for the oil, and 14 inches for the water. The 
density of water being taken as unity, and that of oil being called x, we 
shall have 

15 x .i- = 14 x 1; whence x = ^ = 0-933. 

15 


APPLICATIONS OF THE PRECEDING HYDROSTATIC PRINCIPLES. 

99. Hydraulic press. —The law of the equality of pressure has 
received a most important application in the hydraidic press, a machine 
by which enormous pressures may be produced. Its principle is due to 
Pascal, but it was first constructed by Bramah in 1796. 

It consists of a cylinder, B, with very strong thick sides (fig. 56), in 
which there is a cast iron ram, P, working water tight in the collar of the 
cylinder. On the ram P there is a cast iron plate on which the substance 
to be pressed is placed. Four strong columns serve to support and fix a 
second plate Q. 

By means of a leaden pipe, K, the cylinder B, which is filled with 
water, communicates with a small force pump, A, which works by means 
of a lever, M. When the piston of this pump p ascends, a vacuum is 
produced and the water rises in the tube a, at the end of which there is 



- 99 ] APPLICATIONS OF HYDROSTATIC PRINCIPLES. 77 

a rose, to prevent the entrance of foreign matters. When the piston p 
descends, it drives the water into the cylinder by the tube K. 


Fig. 50. 


Fig. csf>7 represents a section, on a larger scale, of the system of valves 
necessary in working the apparatus. The valve o, below the piston p, 


Fig. 57. 

opens when the piston rises, and closes when it descends. The valve o, 
























































78 


ON LIQUIDS. 


[ 100 - 

during this descent, is opened by the pressure of the water, which 
passes by the pipe K. The valve i is a safety valve, held by a weight 
which acts on it by means of a lever. By weighting the latter to a 
greater or less extent the pressure can be regulated, for as soon as there 
is an upward pressure greater than that of the weight upon it, it opens 
and water escapes. A screw r serves to relieve the pressure, for when 
it is opened it affords a passage for the efflux of the water in the cy¬ 
linder B. 

A most important part is the leather collar n, the invention of which 
by Bramah removed the difficulties which had been experienced in 
making the large ram work water-tight when submitted to great pres¬ 
sures. It consists of a circular piece of stout leather, saturated with 
oil so as to be impervious to water, in the centre of which a circular 
hole is cut. This piece is bent, so that a section of it represents a 
reversed U, and is fitted into a groove n made in the neck of the cy¬ 
linder. This collar being concave downwards, in proportion as the pres¬ 
sure increases it fits the more tightly against the ram P on one side and 
the neck of the cylinder on the other, and quite prevents any escape of 
water. 

The pressure which can be obtained by this press depends on the 
relation of the piston P to that of the piston p. If the former has a 
transverse section fifty or a hundred times as large as the latter, the 
upward pressure on the large piston will be fifty or a hundred times 
that exerted upon the small one. By means of the lever M an additional 
advantage is obtained. If the distance from the fulcrum to the point 
where the power is applied is five times the distance from the fulcrum to 
the piston p, the pressure on p will be five times the power. Thus, if 
a man acts on M with a force of sixty pounds, the force transmitted 
by the piston p will be 300 pounds, and the force which tends to raise 
the piston P will be 30,000 pounds, supposing the section of P is a 
hundred times that of p. 

The hydraulic press is used in all cases in which great pressures are 
required. It is used in pressing cloth, in extracting the juice of beet 
root, and in expressing oil from seeds; it also serves to test the strength 
of cannon, of steam boilers, and of chain cables. The parts composing 
the tubular bridge which spans the Menar Straits were raised by means 
of an hydraulic press. The cylinder of this machine, the largest which 
has ever been constructed, was nine feet long and twenty-two inches in 
internal diameter ; it was capable of raising a weight of two thousand 
tons. 

100. Water level.— The water level is an application of the conditions 
of equilibrium in communicating vessels. It consists of a metal tube 
bent at both ends, in which are fitted glass tubes D and E (fig. 58). It 


- 101 ] APPLICATIONS OF HYDROSTATIC PRINCIPLES. 79 

is placed on a tripod, and water poured in until it rises in both legs. 
When the liquid is at rest, the level of the water in both tubes is the. 
same—that is, they are both in the same horizontal plane. 

This instrument is used in levelling, or ascertaining how much one 
point is higher than another. If, for example, it is desired to find the 



Fig. 58. 


difference between the heights of B and A, a levelling-staff is fixed on 
the latter place. This staff consists of a rule formed of two sliding 
pieces of wood, and supporting a piece of tin plate M, in the centre of 
which there is a mark. This staff being held vertically at A, an observer 
looks at it through the level along the surfaces D and E, and directs the 
holder to raise or lower the slide until the mark is in the prolongation 

Fig. 59. 




Fig. 60. 


of the line DE. The height AM is then measured, and, subtracting it 
from the height of the level, the height of the point A above B is 
obtained. 

101. Spirit level.— The spirit level is both more delicate and more 
accurate than the water level. It consists of a glass tube, AB (fig. 59), 
very slightly curved, that is, the lube, instead of being a true cylinder as it 

















80 


ON LIQUIDS. 


[ 102 - 


seeras to be, is in fact slightly curved in such a manner that its axis is an 
arc of a circle of very large radius; it is filled with spirit with the exception 
of a bubble of air, which tends to occupy the highest part. The tube is placed 
in a brass case, CD (fig. 60), which is so arranged that when it is in a 
perfectly horizontal position the bubble of air is exactly between the two 
points marked in the case. 

To take levels with this apparatus, it is fixed on a telescope, which 
can consequently be placed in a horizontal position. 

102. Artesian wells.— All natural collections of water exemplify the 
tendency of water to find its level. Thus, a group of lakes, such as the 
great lakes of North America, may be regarded as a number of vessels in 
communication, and consequently the waters tend to maintain the same 
level in all. This, too, is the case with the source of a river and the sea, 
and as the latter is on the lower level the river continually flows down 
to the sea along its bed , which is, in fact, the means of communication 
between the two. 



Perhaps the most striking instance of this class of natural phenomena 
is that of artesian wells. These wells derive their name from the pro¬ 
vince of Artois, where it has long been customary to dig them, and from 
whence their use in other parts of France and Europe was derived. It 
seems, however, that at a very remote period wells of the same kind 
were dug in China and Egypt. 

To understand the theory of these wells, it must be premised that the 
strata composing the earth’s crust are of two kinds : the one permeable 
to water, such as sand, gravel, etc.; the others impermeable, such as 
clay. Let us suppose, then, a geographical basin of greater or less extent, 
in which the two impermeable layers AA, BB (fig. 61), enclose between 
them a permeable layer MM. The rain-water falling on the part of this 
layer which comes to the surface, which is called the outcrop , will filter 



BODIES IMMERSED IN LIQUIDS. 


81 


- 103 ] 


through it, and following the natural fall of the ground will collect in 
the hollow of the basin, whence it cannot escape owing to the imperme¬ 
able strata above and below 7- it. If now a vertical hole be sunk down to 
the water-bearing stratum, the water striving to regain its level will 
spout out to a height which depends on the difference between the levels 
of the outcrop and of the point at which the perforation is made. 

The waters which feed Artesian wells often come from a distance of 
sixty or seventy miles. The depth varies in different places. The well 
at Grenelle is 1800 feet deep; it gives 656 gallons of water in a minute, 
and is one of the deepest and most abundant which has been made. The 
temperature of the water is 27° C. It follows from the law of the in¬ 
crease of temperature with the increasing depth below the surface of the 
ground, that, if this well were 210 feet deeper, the water would have all 
the year round a temperature of 32° C., that is, the ordinary temperature 
of baths. 


BODIES IMMERSED IN LIQUIDS. 


103. Pressure supported by a body immersed in a liquid.—- 

When a solid is immersed in a liquid, every portion of its surface is sub¬ 
mitted to a perpendicular pressure, which increases with the depth. If 
wre imagine all these pressures decomposed into horizontal and vertical 
pressures, the first set are in equilibrium. The vertical pressures are 
obviously unequal, and will tend to move the body upwards. 

Let us imagine a cube immersed in a mass of water (fig. 62), and that 
four of its edges are vertical. The pressures 
upon the four vertical faces being, clearly, in 
equilibrium, we need only consider the pressures 
exerted on the horizontal faces A and B. The 
first is pressed downwards by a column of water, 
whose base is the face A, and whose height is 
AD, the lower face B is pressed upwards by the 
weight of a column of water whose base is the 
face itself, and -whose height is BD (93). The 
cube, therefore, is urged upwards by a force equal 
to the difference between these two pressures, 
which latter is manifestly equal to the weight 
of a column of water having the same base and 
the same height as this cube. Consequently this 
upward pressure is equal to the weight of the 
volume of water displaced by the immei'sed body. 

We shall readily see from the following reasoning that every body 
immersed in a liquid is pressed upwards by a force equal to the we ight 

F. 3 



Fig. 62. 







82 


ON LIQUIDS. 


[ 104 - 


of the displaced liquid. In a liquid at rest, let us suppose a portion 
of it of any given shape, regular or irregular, to become solidified, 
without either increase or decrease of volume. The liquid thus soli¬ 
dified will remain at rest, and therefore must be acted upon by a force 
equal to its weight and acting vertically upward through its centre of 
gravity; for otherwise motion would ensue. If in the place of the 
solidified water w'e imagine a solid of another substance of exactly 
the same volume and shape, it will necessarily receive the same pressures 
from the surrounding liquid as the solidified portion did; hence, like the 
latter, it will sustain the pressure of a force acting vertically upward 
through the centre of gravity of the displaced liquid, and equal to the 
weight of the displaced liquid. If, as almost invariably happens, the 
liquid is of uniform density, the centre of gravity of the displaced liquid 
means the centre of gravity of the immersed part of the body supposed 
to be of uniform density. This distinction is sometimes of importance ; for 
example, if a sphere is composed of a hemisphere of iron and another of wood, 
its centre of gravity would not coincide with its geometrical centre, but 
if it were placed under water, the centre of gravity of the displaced water 
would be at the geometrical centre, that is, will have the same position 
as the centre of gravity of the sphere, if of uniform density. 

104. Principle of Archimedes.— The preceding principles prove 
that every body immersed in a liquid is submitted to the action of two 
forces ) gravity which tends to lower it, and the buoyancy of the liquid 
which tends to raise it with a force equal to the weight of the liquid 
displaced. The weight of the body is either totally or partially over¬ 
come by this buoyancy, from which it is concluded that a body immersed 
in a liquid loses a part of its weight equal to the weight of the displaced 
liquid. 

This principle, which is the basis of the theory of immersed and 
floating bodies, is called the principle of Archimedes, after the discoverer. 
It is shown experimentally by means of the hydrostatic balance (fig. 63). 
This is an ordinary balance, each pan of which is provided with a hook ; 
the beam can be raised by means of a toothed rack, wdiich is worked by 
a little pinion, C. A catch, D, holds the rack when it has been raised. 
The beam being raised, a hollow copper cylinder, A, is suspended to one 
of the pans, and below this a solid cylinder, B, w^hose volume is exactly 
equal to the capacity of the first cylinder; lastly, an equipoise is placed 
in the other pan. If now the hollow cylinder be filled with water the 
equilibrium is disturbed, but if at the same time the beam is lowered so 
that the solid cylinder B becomes immersed in a vessel of water placed 
beneath it, the equilibrium will be restored. By being immersed in 
water, the cylinder B loses a portion of its weight equal to that of the 
water in the cylinder A. Now as the capacity of the cylinder A is ex- 


BODIES IMMERSED IN LIQUIDS. 


83 


- 105 ] 


actly equal to the volume of the cylinder B, the principle which has 
been before laid down is proved. 

105. Determination of the volume of a body —The principle 
of Archimedes furnishes a method for obtaining the volume of a body of 
any shape, provided it is not soluble in water. The body is suspended 
by a fine thread to the hydrostatic balance, and is weighed first in the 



Tig. 63. 

air, and then in distilled water at 4° C. The loss of weight is the 
weight of the displaced water, from which the volume of the displaced 
water is readily calculated. But this volume is manifestly that of 
the body itself. Suppose, for example, 155 grammes is the loss of 
weight. This is consequently the weight of the displaced water. 
Now it is known that a gramme is the weight of a cubic centimeter 
of water at 4°; consequently, the volume of the body immersed is 155 
cubic centimeters. 





















84 


ON LIQUIDS. 


[ 106 - 


106. Equilibrium of floating bodies. —A body when floating is 
acted on by two forces, namely, its weight, which acts vertically down¬ 
ward through its centre of gravity, and the resultant of the fluid pressures, 
which (103) acts vertically upward through the centre of gravity of the 
fluid displaced ; but if the body is at rest these two forces must be equal, 
and act in opposite directions; whence follow the conditions of equili¬ 
brium, namely:— 

i. The floating body must displace a volume of liquid whose loeight 
equals that of the body. 

ii. The centre of gravity of the floating body must be in the same ver¬ 
tical line with that of the fluid displaced. 

Thus in fig. 64, if C is the centre of gravity of the body and G that 
of the displaced fluid, the line GC must be vertical, since when it is so 
the weight of the body and the fluid pressure will act in opposite 



Fig. 64. Fig. 65. Fig. 66. 


directions along the same line, and will be in equilibrium, if equal. It 
is convenient, with reference to the subject of the present article, to speak 
of the line CG produced as the axis of the body. 

Next let it be enquired whether the equilibrium be stable or unstable. 
Suppose the body to be turned through a small angle (fig. 65) so that 
the axis takes a position inclined to the vertical. The centre of gravity 
of the displaced fluid will no longer be G but some other point G'. And 
since the fluid pressure acts vertically upward through O', its direction 
will cut the axis in some point M', which will generally have different 
positions according as the inclination of the axis to the vertical is greater 
or smaller. If the angle is indefinitely small, M' will have a definite 
position M, which always admits of determination, and is called the 
metacentre. 

If we suppose M to be above C, an inspection of fig. 66 will show that 
when the body has received an indefinitely small displacement the weight 
of the body W and the resultant of the fluid pressures R tends to bring 










BODIES IMMERSED IN LIQUIDS. 


85 


- 107 ] 


the body back to its original position, that is, in this case the equilibrium 
is stable (62). If, on the contrary, M is below C, the forces tend' to cause 
the axis to deviate farther from the vertical, and the equilibrium is un¬ 
stable. Hence the rule, 

iii. The equilibrium of a floating body is stable or unstable according as 
the metacentre is above or below the centre of gravity. 

The determination of the metacentre can rarely be effected except by 
means of a somewhat difficult mathematical process. When, however, 
the form of the immersed part of a body is spherical it can be readily 
determined, for since the fluid pressure at each point converges to the 
centre, and continues to do so when the body is slightly displaced, their 
resultant must in all cases pass through the centre, which is therefore 
the metacentre. To illustrate this: let a spherical body float on the 
surface of a liquid (fig. 67), then its centre 
of gravity and the metacentre both coinciding 
with the geometrical centre C its equili¬ 
brium is neutral (62) ; now suppose a small 
heavy body to be fastened at P the summit 
of the vertical diameter. The centre of gra¬ 
vity will now be at some point G above C. 

Consequently the equilibrium is unstable and 
the sphere, left to itself, will instantly turn 
over and will rest when P is the lower end 
of a vertical diameter. 

On investigating the position of the metacentre of a cylinder, it is 
found that when the ratio of the radius to the height is greater than a 
certain quantity, the position of stable equilibrium is that in which the 
axis is vertical; but if it be less than that quantity, the equilibrium 
is stable when the axis is horizontal. For this reason the stump of 
a tree floats lengthwise, but a thin disc of wood floats flat on the 
water. 

Hence also, if it is required to make a cylinder of moderate length 
float with its axis vertical, it is necessary to load it at the lower end. 
By so doing its centre of gravity is brought below the metacentre. 

107. Cartesian diver.— The different effects of suspension, immersion, 
and floating are reproduced by means of a well-known hydrostatic toy, 
the Cartesian diver (fig. 68). It consists of a glass cylinder nearly full of 
water, on the top of which a brass cap, provided with a piston, is 
hermetically fitted. In the liquid there is a little porcelain figure at¬ 
tached to a hollow glass ball, a, which contains air and water, and 
floats on the surface. In the lower part of this ball there is a little hole 
by which water can enter or escape, according as the air in the in¬ 
terior is more or less compressed. The quantity of water in the globe 




ON LIQUIDS. 


80 


[ 108 - 


is such, that very little more is required to make it siuk. If the piston 
he slightly lowered the air is compressed, and this pressure is 
transmitted to the water of the vessel and the 
air in the bulb. The consequence is, that a 
small quantity of water penetrates into the 
bulb, which therefore becomes heavier and 
sinks. If the pressure is relieved, the air in 
the bulb expands, expels the excess of water 
which had entered it, and the apparatus being 
now lighter, rises to the surface. The experiment 
may also be made, by replacing the brass cap and 
piston by a cover of sheet india rubber, which 
is tightly tied over the mouth. When this is 
pressed by the hand the same effects are pro¬ 
duced. 

108. Swimming- bladder of fishes. —Most 
fishes have an air-bladder below the spine, 
which is called the swimming bladder. The 
fish can compress or dilate this at pleasure 
by means of a muscular effort, and produce 
the same effects as those just described — 
that is, it can either rise or sink in water. 

109. Swimming-.— The human body is 
lighter, on the whole, than an equal volume of 
water; it consequently floats on the surface and 

still better in sea water, which is heavier than fresh water. The difficulty 
in swimming consists, not so much in floating, as in keeping the head above 
water, so as to breathe freely. In man the head is heavier than the 
lower parts, and consequently tends to sink, and hence swimming is an 
art which requires to be learned. With quadrupeds, on the contrary, 
the head, being less heavy than the posterior part of the body, remains 
above water without any effort, and these animals therefore swim 
naturally. 

SPECIFIC GRAVITY—HYDROMETERS. 

110. Determination of specific gravities.— It has been already 
.explained (24) that the specific gravity of a body, whether solid or 
liquid, is the number which expresses the relation of the weight of a 
given volume of this body, to the weight of the same volume of distilled 
water at a temperature of 4°. In order, therefore, to calculate the 
specific gravity of a body, it is sufficient to determine its weight and that 
of an equal volume of water, and then to divide the first weight by the 
second : the quotient is the specific gravity of the body. 

Three methods are commonly used in determining the specific gravities 









SPECIFIC GRAVITY. 


-in] 

of solids and liquids. These are, 1st, the method of the hydrostatic 
balance ; 2nd, that of the hydrometer; and 3rd, the specific gravity flask. 
All three, however, depend on the same principle, that of first ascertain¬ 
ing the weight of a body, and then that of an equal volume of water. 
We shall first apply these methods to determining the specific gravity of 
solids, and then to the specific gravity of liquids. 

111. Specific gravity of solids. —i. Hydrostatic balance .—To obtain 
the specific gravity of a solid by the hydrostatic balance (fig. 63), it is 
first weighed in air, and is then suspended to the hook of the balance 
and weighed in water. The loss of weight which it experiences is, ac¬ 
cording to Archimedes’ principle, the weight of a volume of water equal 
to its own volume; consequently, dividing the weight in air by the loss 
of weight in water, the quotient is the specific gravity required. If P is 
the weight of the body in air, P' its weight in water, and D its specific 
gravity: P — P' being the weight of the displaced water, we have 

D=_‘ P . 
p- p ' 

It may be observed that though the weighing is performed in air, yet, 
strictly speaking, the quantity required is the weight of the body in vacuo, 
and when great accuracy is required, it is necessary to apply to the 
observed weights a correction for the weights 
of the unequal volumes of air displaced by the 
substance, and the weights in the other scale 
pan. It may also be remarked that the water 
in which bodies are weighed is, strictly speak¬ 
ing, distilled water at a standard temperature. 

ii. Nicholson's hydrometer .—This apparatus 
consists of a hollow metallic cylinder B 
(fig. 69), to which is fixed a cone C, loaded 
with lead. The object of the latter is to bring 
the centre of gravity below the metacentre so 
that the cylinder may float with its axis vertical. 

At the top is a stem, terminated by a pan, in 
which is placed the substance whose specific- 
gravity is to be determined. On the stem a 
standard point, o, is marked. 

The apparatus stands partly out of the water, 
and the first step is to ascertain the weight 
which must be plaoed in the pan in order to 
make the hydrometer sink to the standard 
point o. Let this weight be 125 grains, and let sulphur be the sub¬ 
stance whose specific gravity is to be determined. The weights are 
then removed from the pan, and replaced by a piece of sulphur which 
weighs less than 125 grains, and weights added until the hydro- 



Fig. 69. 

















88 


ON LIQUIDS. 


[il2- 


meter is again depressed to the standard o. If, for instance, it has been 
necessary to add 55 grains, the weight of the sulphur is evidently 
the difference between 125 and 55 grains, that is, 70 grains. Having 
thus determined the weight of the sulphur in air, it is now only 
necessary to ascertain the weight of an equal volume of water. To do 
this, the piece of sulphur is placed in the lower pan C at m, as repre¬ 
sented in the figure. The whole weight is not changed, nevertheless 
the hydrometer no longer sinks to the standard ; the sulphur, by immer¬ 
sion, has lost a part of its weight equal to that of the water displaced. 
Weights are added to the upper pan until the hydrometer sinks again 
to the standard. This weight, 34*4 grains for example, represents the 
weight of the volume of water displaced ; that is, of the volume of water 
equal to the volume of the sulphur. It is only necessary, therefore, to 
divide 70 grains, the weight in air, by 34'4 grains, and the quotient 2‘03 
is the specific gravity. 

If the body in question is lighter than water it tends to rise to the 
surface, and will not remain on the lower pan C. To obviate this, a 
small moveable cage of fine wire is adjusted so as to prevent the ascent 
of the body. The experiment is in other respects the same. 

112. Specific gravity flask.— When the specific gravity of a 
substance in a state of powder is required, it can be found most conveni¬ 
ently by means of the specific gravity flask. This instrument is a small 
flask with a large neck fitted with a carefully ground glass stopper. The 
stopper is perforated along its axis, and the bore is continued by means 
of a thin tube which expands into a tube of greater diameter, as shown in 
the figure. On the thin tube is a mark a, and at each weighing the 
flask is filled with water exactly to the mark. This is done by filling 
the flask when wholly under water, and putting in the stopper while it is 
immersed. The flask and the tube are then completely 
filled, and the quantity of water in excess is removed 
by blotting paper. To find the specific gravity proceed 
as follows. Having weighed the powder, place it in one 
of the scale pans, and with it the flask filled exactly to 
a and carefully dried. Then balance it by placing small 
shot, or sand, in the other pan. Next, remove the flask 
and pour the powder into it, and, as before, fill it up 
with water to the mark a. On replacing the flask in 
the scale pan it will no longer balance the shot, since 
the powder has displaced a volume of water equal to 
its own volume. Place weights in the scale pan along 
with the flask until they balance the shot. These 
weights give the weight of the water displaced. Then 
the weight of the powder, and the weight of an equal bulk of water 
being known, its specific gravity is determined as before. 



Fig 70. 


SPECIFIC GRAVITY. 


89 


- 113 ] 


It is important in this determination to remove the layer of air which 
adheres to the powder, and unduly increases the quantity of water 
expelled. This is effected by placing the bottle under the receiver of 
an air-pump, and exhausting. 

113. Bodies soluble in water.— If the body, whose specific gravity 
is to be determined by any of these methods, is soluble in water, the 
determination is made in some liquid in which it is not soluble, such as 
oil, turpentine, or naphtha, the specific gravity of which is known. The 
specific gravity is obtained by multiplying the number obtained in this 
experiment by the specific gravity of the liquid used for the determina¬ 
tion. 

Suppose, for example, a determination of the specific gravity of 
potassium has been made in naphtha. For equal volumes, P represents 
the weight of the potassium, P' that of the naphtha, and P" that of water; 



water. The product of these two fractions is the specific gravity 

of the substance compared with water. 

In determining the specific gravity of porous substances, they are 
varnished before being immersed in water, which renders them imper¬ 
vious to moisture without altering their volume. 

Specific gravity of solids at zero as compared with distilled water at 4° C. 


Zinc, cast . 


Antimony, cast . 


Iron, bar . 
Iron, cast . 
Tin, cast 


Brass. 


Steel, not hammered 


„ cast . 

Lead, cast . 

Silver, cast 
Bismuth, cast 
Copper, drawn wire 


Gold, stamped . 


Platinum, rolled 


fused. 


22 069 Flint glass . 

20-337 Statuary marble 
19-362 Rock crystal 
19*258 St. Gobin glass . 
11-352 China porcelain . 
10-474 St. Sevres porcelain 
9*822 Native sulphur . 
8-878 Anthracite. 

8-788 Compact coal 
8-383 Amber 
7-816 Melting ice 
7-788 Beech 
7-207 Oak . 

7-291 Elm . 

6-861 Yellow pine 
6’712 Common poplar . 


3-329 

2-837 

2-653 

2-488 

2-385 

2-146 

2033 

1-800 

1-329 

1-078 

0-930 

0-852 

0-845 

0-800 

0-657 

0-389 

0-240 


Diamonds . 


3-531 to 3-501 Cork . 






90 


ON LIQUIDS. 


[ 114 - 


1 )= 


114. Specific gravity of liquids. —i. Method of the hydrostatic balance. 

_From the pan of the hydrostatic balance a body is suspended, on which 

the liquid whose specific gravity is to he determined, exerts no chemical 
action; for example, a hall of platinum. This is then successively 
weighed in air, in distilled water, and in the liquid. The loss of weight 
of the body in these two liquids is noted. They represent respectively 
the weights of equal volumes of water, and of the given liquid, and 
consequently it is only necessary to divide the second of them by the 
first to obtain the required specific gravity. 

Let P be the weight of the platinum ball in air, P r its weight in water, 
P" its weight in the given liquid, and let D be the specific gravity 
sought. The weight of the water displaced by the platinum is 
P_P' and that of the second liquid is P— P" from which we get 
P-P" 

P - P' ‘ 

ii. Fahrenheit's hydrometer. — This instrument (fig. 71) resembles 
Nicholson’s hydrometer, but is made of glass, so as to be used in all 
liquids. At its lower extremity, instead of a pan, it is loaded with a 
small bulb containing mercury. There is a standard mark on the stem. 

The weight of the instrument is first accurately determined in air; it is 
then placed in water, and weights added to the scale pan until the mark on 
the stem is level with the water. It follows from the 
first principle of the equilibrium of floating bodies, 
that the weight of the hydrometer, together with 
the weight in the scale pan, is equal to the weight 
of the volume of the displaced water. In the same 
manner, the weight of an equal volume of the given 
liquid is determined, and the specific gravity is found 
by dividing the latter weight by the former. 

Neither Fahrenheit’s nor Nicholson’s hydrometers 
give such accurate results as the hydrostatic balance. 

iii. Specific gravity flash .—This has been already 
described. In determining the specific gravity of a 
liquid, the flask is first weighed empty, and then suc¬ 
cessively, full of water, and of the given liquid. If 
the weight of the flask be subtracted from the two 
weights thus obtained, the result represents the 



Fig. 71. 


weights of equal volumes of the liquid, and of water, from which the 
specific gravity is obtained by division. 

115. On the observation of temperature in ascertaining; specific 
gravities. —-As the volume of a body increases with the temperature, 
and as this increase varies with different substances, the specific gravity 
of any given body is'not exactly the same at different temperatures; and, 






SPECIFIC GRAVITY OF LIQUIDS. 


91 


- 116 ] 


consequently, a certain fixed temperature is chosen for these determina¬ 
tions. That of water, for example, has been made at 4° C., for at this 
point it has the greatest density. The specific gravities of other bodies 
are assumed to be taken at zero; but as this is not always possible, 
certain corrections must be made, which we shall consider in the Book 
on Heat. 


Specific gravities of liquids at zero, compared with that of water at 4° C. 

as unity. 


Mercury 

. 13*598 

Distilled water at 4° C. 

. 1*000 

Sulphuric acid . 

. 1*841 

„ „ at 0° C. 

. 0*999 

Hydrochloric acid 

. 1*240 

Olive oil . 

. 0*915 

Nitric acid . 

. 1*042 

Oil of turpentine 

. 0*870 

Milk .... 

. 1*030 

Naphtha . 

. 0*847 

Sea water . 

. 1*026 

Absolute alcohol 

. 0*803 

Claret 

. 0*994 

Ether 

. 0*723 


116. Use of tables of specific gravities.— Tables of specific gravity 
admit of numerous applications. In mineralogy the specific gravity 
of a mineral is often a highly distinctive character. By means of 
tables of specific gravities the weight of a body may be calculated when its 
volume is known, and conversely the volume when its weight is known. 

With a view to explaining the last-mentioned use of these tables, 
it will be well to premise a statement of the connection existing between 
the British units of length, capacity, and weight. It will manifestly 
be sufficient for this purpose to define that which exists between the yard, 
gallon, and pound avoirdupois, since other measures stand to these in 
well-known relations. The yard, consisting of 36 inches, may be 
regarded as the primary'unit. Though it is essentially an arbitrary 
standard, it is determined by this, that the simple pendulum which 
makes an oscillation, in a mean second at London on the sea level, is 
39T375 inches long. The gallon contains 277*274 cubic inches. A gallon 
of distilled water at the standard temperature weighs 10 lbs. avoirdu¬ 
pois or 70,000 grains troy; or, which comes to the same thing, one 
cubic inch of water weighs 252*5 grains. 

On the French system the meter is the primary unit, and is so chosen 
that 10,000,000 meters are the length of a quadrant of the meridian 
from either pole to the equator. The meter contains 10 decimeters, or 
100 centimeters, Or 1,000 millimeters, its length equals 1*0936 yards. 
The unit of the measure of capacity is the litre or cubic decimeter. 
The unit of weight is the gramme, which is the weight of a cubic 
centimeter of distilled water at 4° C. The kilogramme contains 1,000 
grammes, or is the weight of a decimeter of distilled water at 4° C. 
The gramme equals 15*443 grains. 



92 


ON LIQUIDS. 


[ 117 - 


If V is the number of cubic centimeters (or decimeters) in a certain 
quantity of distilled water at 4° C., and P its weight in grammes (or 
kilogrammes), it is plain that P=V. Now consider a substance whose 
specific gravity is D, every cubic centimeter of this substance will weigh 
as much as D cubic centimeters of water, and therefore V centimeters 
of this substance will weigh as much as DV centimeters of water. 
Hence if P is the weight of the substance in grammes we have 
P=DV. If, however, V is the volume in cubic inches, and P the 
weight in grains, we shall have P=252’5 DV. 

As an example we may calculate the internal diameter of a glass 
tube. Mercury is introduced and the length and weight of the column 
at 4° C. are accurately determined. As the column is cylindrical we 
have V=irr 2 /, where r is the radius, and l the length of the column in 
centimeters. Hence if D is the specific gravity of mercury, and P the 
weight of the column in grammes, we have P—7rr-/D, and therefore 



If r and l are in inches and P in grains, we shall have P=252*5rr ! /D 
and therefore 



In a similar manner the diameter of very fine metallic wires can be 
calculated. 

117. Hydrometers with variable volume.— The hydrometers of 
Nicholson and Fahrenheit are called hydrometers of constant volume, but 
variable weight, because they are always immersed to the same extent, 
but carry different weights. There are also hydrometers of variable 
volume but of constant weight. These instruments, known under the 
different names of acidometer, alcoholometer, lactometer, and saccharometer , 
are not used to determine the specific gravity of the liquids, but to 
show whether the acids, alcohols, solutions of sugar, etc., are more or 
less concentrated, 

118. Beaume’s hydrometer.— This, which was the first of these 
instruments, may serve as a type of them. It consists of a glass tube 
(fig. 72) loaded at its lower end with mercury, and with a bulb blown 
in the middle. The stem, the external diameter of which is as regular 
as possible, is hollow, and the scale is marked upon it. 

The graduation of the instrument differs according as the liquid, for 
which it is to be used, is heavier or lighter than water. In the first 
case, it is so constructed that it sinks in water nearly to the top of 
the stem, to a point A, which is marked zero. A solution of fifteen 
parts of salt in eightv-five parts of water is made, and the instrument 





HYDROMETERS. 


93 


- 119 ] 

immersed in it. It sinks to a certain point on tlie stem, B, which is 
marked 15; the distance between A and B is divided into 15 equal 
parts, and the graduation continued to the bottom 
of the stem. Sometimes the graduation is on a 
piece of paper in the interior of the stem. 

The hydrometer thus graduated only serves for 
liquids of a greater specific gravity than water, such 
as acids and saline solutions. For liquids lighter 
than water a different plan must be adopted. 

Beaume took for zero, the point to which the appar¬ 
atus sank in a solution of 10 parts of salt in 90 of 
water, and for 10° he took the level in distilled water. 

This distance he divided into 10°, and continued the 
division to the top of the scale. 

The graduation of these hydrometers is entirely 
conventional, and they give neither the densities of 
the liquids, nor the quantities dissolved. But they 
are very useful in making mixtures or solutions in 
given proportions; the results they give being suffi¬ 
ciently near in the majority of cases. For instance, it is found that a 
well-made syrup marks 35° on Beaume’s hydrometer, from which a 
manufacturer can readily judge whether a syrup which is being evapo¬ 
rated has reached the proper degree of concentration. 

119. Gay-I*ussac’s alcoholometer. —This instrument is used to 
determine the strength of spirituous liquors; that is, the proportion of 
pure alcohol which they contain. It differs from Beaume’s hydrometer 
in the graduation. 

Mixtures of absolute alcohol and distilled water are made, containing 
5, 10, 20, 30, etc., per cent, of the former. The alcoholometer is so con¬ 
structed that when placed in pure distilled water, the bottom of its 
stem is level with the water, and this point is zero. It is next placed 
in absolute alcohol, which marks 100°, and then successively in mixtures 
of different strengths, containing 10, 20, 30, etc., per cent. The divisions 
thus obtained are not exactly equal, but their difference is not great,, and 
they are subdivided into ten divisions, each of which marks one per cent, 
of absolute alcohol in a liquid. Thus a brandy in which the alcoholo¬ 
meter stood at 48, would contain 48 per cent, of absolute alcohol, and 
the rest would be water. 

All these determinations are made at 15° C., and for that temperature 
only are the indications correct. For, other things being the same, if 
the temperature rises the liquid expands, and the alcoholometer will 
sink, and the contrary, if the temperature falls. To obviate this error 
Gay-Lussac constructed a table which for each percentage of alcohol 










94 


ON LIQUIDS. 


[ 120 - 


gives the reading of the instrument for each degree of temperature from 
0° up to 30°. When the exact analysis of an alcoholic mixture is to he 
made, the temperature of the liquid is first determined, and then the 
point to which the alcoholometer sinks in it. The number in the table 
corresponding to these data indicates the percentage of alcohol. From 
its giving the percentage of alcohol, this is often called the centesimal 
alcoholometer. 

120. Salimeters. — Salimeters, or instruments for indicating the per¬ 
centage of salt contained in a solution, are made on the principle of the 
centesimal alcoholometer. They are graduated by immersing them in 
pure water, which gives the zero, and then in solutions containing dif¬ 
ferent percentages, 5, 10, 20, etc., of the salt, and marking on the scale 
the corresponding points. These instruments are so far objectionable, 
that every salt requires a special instrument. Thus one graduated for 
common salt would give totally false indications in a solution of nitre. 

Lactometers and vinometers are similar instruments, and are used for 
measuring the quantity of water which is introduced into milk or wine 
for the purpose of adulteration. But their use is limited, because the 
density of these liquids is very variable, even when they are perfectly 
natural, and an apparent fraud may be really due to a bad natural quality 
of wine or milk. TJrinometers , which are of extensive use in medicine, 
are based on the same principle. 

121. Densimeter.- The densimeter is an apparatus for indicating the 
specific gravity of a liquid. Gay-Lussac’s densimeter has the same 

construction as Beaume’s hydrometer, but is 
graduated in a different manner. Rosseau’s den¬ 
simeter (fig. 73) is of great use in many scien¬ 
tific investigations, in determining the specific 
gravity of a small quantity of a liquid. It has 
the same form as Beaume’s hydrometer, but on the 
upper part of the stem there is a small tube, in 
which is placed'the substance to be determined. 
A mark on the side of the tube indicates a measure 
of a cubic centimeter. / 

The instrument is so constructed that it sinks 
in distilled water to a point, B, just at the bottom 
of the stem. It is then filled with distilled water 
to the height measured on the tube, which indi¬ 
cates a cubic centimeter, and the point to which 
it now sinks is 20°. The interval between 0 and 
20 is divided into 20 equal parts, and this gradua¬ 
tion is continued to the top of the scale. As this is of uniform bore 
each division corresponds to ~ gramme or O'Oo. 



Fig. 73. 










122 j 


CAPILLARITY. 


95 


To obtain the density of any liquid, bile for example, the tube is filled 
Avith it up to the mark A; if the densimeter sinks to 20£ divisions, its 
weight is 0 05 x 20*5=1*025; that is to say, that with equal volumes 
the weight of water being 1, that of bile is 1-025. The specific gravity 
of bile is therefore 1-025. 


CHAPTER II. 

CAPILLARITY, ENDOSMOSE, EFFUSION, ABSORPTION, AND IMBIBITION. 

122. Capillary phenomena. —When solid bodies are placed in con¬ 
tact with liquids, a class of phenomena is produced called capillary 
phenomena , because they are best seen in tubes whose diameters are 
comparable with the diameter of a hair. These phenomena are treated 
of in physics imder the head of capillarity or capillary attraction : the 
latter expression is also applied to the force which produces the pheno¬ 
mena. 

The phenomena of capillarity are very various, but may all be referred 
to the mutual attraction of the liquid molecules for each other, and to 
the attraction between these molecules and solid bodies. The following- 
are some of these phenomena :— 

When a body is placed in a liquid which wets it, for example a glass 



Fig. 74. Fig. 75. Fig. 76. Fig. 77. 


rod in water, the liquid, as if not subject to the laws of gravitation, is 
raised upwards against the sides of the solid, and its surface, instead of 
being horizontal, becomes slightly concave (fig. 74). If, on the contrary, 
the solid is one which is not moistened by the liquid, as glass by mercury, 
the liquid is depressed against the sides of the solid, and assumes a convex 
shape, as represented in fig. 75. The surface of the liquid exhibits 
the same concavity or convexity against the sides of a vessel in which 
it is contained, according as the sides are or are not moistened by the 
liquid. 





















96 


ON LIQUIDS. 


[ 123 - 


These phenomena are much more apparent when a tube of small 
diameter is placed in a liquid. And according as the tubes are or are 
not moistened by the liquid, an ascent or a depression of the liquid is 
produced, which is greater in proportion as the diameter is less, figs. 76 
and 77. 

When the tubes are moistened by the liquid, its surface assumes the 
form of a concave hemispherical segment, called the concave meniscus 
(fig. 76) ; when the tubes are not moistened, there is a convex meniscus 
(fig. 77;. 

123. Laws of the ascent and depression in capillary tubes.— 

Gay-Lussac has shown experimentally that t)re elevation and depression 
of liquids in capillary tubes are governed by the three following laws:— 

I. When a capillary tube is placed in a liquid , the liquid is raised or 
depressed according as it does or does not moisten the tube. 

II. For the same liquid the elevation varies inversely as the diametei' of 
the tube , when the diameter does not exceed two millimeters. 

III. The elevation varies ivith the nature of the liquid , and with the tem¬ 
perature, but is independent of the nature and thickness of the tube. 

These laws hold good in vacuo as well as in air. 

When liquids are in tubes which they do not moisten, the depression 
is in the inverse ratio of the diameter of the tubes; but for tubes of the 
same diameter the depression depends on the substance of the tubes. 
For instance, in an iron tube 1 millimeter in diameter, the depression of 
mercury is 1*226 millimeter; but in a platinum tube of the same diameter 
the depression is 0*655 millimeter. Moreover the depression depends on 
the height of the convex meniscus of the mercury, and this height varies 
for the same tube, according as the meniscus is formed during an ascend¬ 
ing or descending motion. of the mercurial column in the tube. These 
results undergo modification if the mercury is impure. 

124. Ascent and depression between parallel or inclined 
surfaces. —When two bodies of any given shape are dipped in water, 
analogous capillary phenomena are produced, provided the bodies are 
sufficiently near. If, for example, two parallel glass plates are immersed 
in water, at a very small distance from each other, water will rise between 
the two plates in the inverse ratio of the distance which separates them. 
The height of the ascent for any given distance is half what it would be 
in a tube whose diameter is equal to the distance between the plates. 

If the parallel plates are immersed in mercury, a corresponding de¬ 
pression is produced, subject to the same laws. 

If two glass plates AB and AC with their planes vertical and in¬ 
clined to one another at a small angle as represented in fig. 78, have 
their ends dipped into a liquid which wets them, the liquid will rise 
between them. The elevation will be greatest at the line of contact of 


CAPILLARITY. 


97 


- 126 ] 

plates and from thence gradually less, the surface taking the form of an 
equilateral hyperbola, whose asymptotes are respectively the line of 
intersection of the plates, and the line in which the plates cut the 
horizontal surface of the water. 

If a drop of water be placed within a conical glass tube whose angle 
is small and axis horizontal it will have a concave meniscus at each end 
(fig. 79) and will tend to move towards the vertex. But if the drop he 
of mercury it will have a convex meniscus at each end (fig. 80) and will 
tend to move from the vertex. 




Fig. 79. 



Fig. 80. 


125. Attraction and repulsion produced by capillarity. —The 

attractions and repulsions observed between bodies floating on the surface 
of liquids are due to capillarity, and are subject to the following laws:— 

i. When two floating balls both moistened by the liquid, for ex¬ 
ample, cork upon water, are so near that the liquid surface between 
them is not level, an attraction takes place. 

ii. The same effect is produced when neither of the balls is moistened, 
as is the case with balls of wax on water. 

. iii. Lastly, if one of the balls is moistened and the other not, as a ball 
of cork and a ball of wax in water, they repel each other If the curved 
surfaces of the liquid in their respective neighbourhoods intersect. 

As all these capillary phenomena depend on the concave or convex 
curvature which the liquid assumes in contact with the solid, a short 
explanation of the cause which determines the form of this curvature is 
necessary. 

126. Cause of the curvature of liquid surfaces in contact 

with solids.— The form of the surface of a liquid in contact with a solid 
depends on the relation between the attraction of the solid for the 
liquid, and of the mutual attraction between the molecules of the liquid. 

Let ?n be a liquid molecule (fig. 81) in contact with a solid. This 
molecule is acted upon by three forces: by gravity, which attracts it in 
the direction of the vertical mV by the attraction of the liquid F, 

v 










98 


ON LIQUIDS. 


[ 127 - 


which acts in the direction mF; and by the attraction of the plate n, 
which is exerted in the direction mn. According to the relative inten¬ 
sities of these forces, their resultant can take three positions:— 

i. The resultant is in the direction of the vertical mR (fig. 81). In 
this case the surface m is plane and horizontal; for, from the condition 



of the equilibrium of liquids, the surface must be perpendicular to the 
force which acts upon the molecules. 

ii. If the force n increases or F diminishes, the resultant R is within 
the angle nmP (fig. 82): in this case the surface takes a direction per¬ 
pendicular to mil, and becomes concave. 

iii. If the force F increases, or n diminishes, the resultant R takes 
the direction «iR (fig. 83) within the angle PmF, and the surface be¬ 
coming perpendicular to this direction is convex. 




Fig. 85. 


127. Influence of the curvature on capillary phenomena.— 

The elevation or depression of a liquid in a capillary tube depends 'oil 
the concavity or convexity of the meniscus. In a concave meniscus 
ahcd (%• 84> b the liquid molecules are sustained in equilibrium by the 
forces acting on them, and the} 7- exercise no downward pressure on the in¬ 
ferior layers. On the contrary, in virtue of the molecular attraction they 
act on the nearest inferior layers, from which it follows that the pressure 
on any layer, mn, in the interior of the tube, is less than if there were 
no meniscus. The consequence is, that the liquid ought to rise in the 
tube until the internal pressure on the layer, mn, is equal to the pressure 
oj), which acts externally on a point, p, of the same layer. 

























































CAPILLARITY. 


99 


- 128 ] 

Where the meniscus is convex (fig. 85) equilibrium exists in virtue 
of the molecular forces acting on the liquid ,• but as the molecules which 
would occupy the space ghik, if there were no molecular action, do not 
exist, they exercise no attraction on the lower layers. Consequently the 
pressure on any layer mn, in the interior of the tube, is greater than if 
the space ghik were filled, for the molecular forces are more powerful 
than gravity. The liquid ought, therefore, to sink in the tube until the 
internal pressure on a layer, mn, is equal to the external pressure on any 
point, p, of this layer. 

The theory of capillarity, one of the most difficult in physics, can only 
be treated completely by mathematical analysis. It has engaged the 
attention of the most eminent mathematicians, particularly Clairaut, 
Laplace, and Poisson. As we have seen, the theory accounts for the eleva¬ 
tion and depression of liquids not only in tubes, but also between parallel 
and inclined plates. It also explains the attractions and repulsions ob¬ 
served between floating bodies. 

128. Various capillary phenomena. —The following facts are 
among the many which are caused by capillarity:— 

When a capillary tube is immersed in a liquid which moistens it, and 
is then carefully removed, the column of liquid in the tube is seen to 
be longer than while the tube was immersed in the liquid. This arises 
from the fact that a drop adheres to the lower extremity of the tube, and 
forms a concave meniscus, which concurs with that of the upper meniscus 
to form a longer column (127). 

For the same reason a liquid does not overflow in a capillary tube, 
although the latter may be shorter than the liquid column which would 
otherwise be formed in it. For when the liquid reaches the top of the 
tube, its upper surface, though previously concave, becomes Convex, and, 
as the downward pressure becomes greater than if the surface w .re plane, 
the ascending motion ceases. 

Insects can often move on the surface of water without sinking. This 
is a capillary phenomenon caused by the fact, that as their feet are not 
wetted by the water, a depression is produced which keeps them up in 
spite of their weight. Similarly a sewing needle gently placed on water, 
does not sink, because its surface, being covered with an oily layer, does 
not become wetted. But if washed in alcohol, or in potash, it at once 
sinks to the bottom. 

It is from capillarity the sap rises in plants, that oil ascends in the 
wicks of lamps, that water rises in wood, sponge, bibulous paper, sugar, 
sand, and in all bodies which possess pores of a perceptible size. 

In the next section, under the heads of endosmose, absorption, and 
imbibition, we shall become acquainted with some new phenomena which 
greatly resemble capillarity,, and are often confounded with it. 

f 2 



100 


ON LIQUIDS. 


[ 129 - 


END0SM0SE, EFFUSION, ABSORPTION, AND IMBIBITION. 

129. Endosmosc and exosmose.— When two different liquids 
are separated by a thin porous partition, either inorganic or organic, a 
current sets in from each liquid to the other; to these currents the 
names endosmose and exosmose are respectively given. These terms, which 
signify impulse from within , and impulse from without, were first introduced 
by M. Dutrochet, who first drew attention to these phenomena. They 
may be well illustrated by means of the endosmometer. This consists of 
a long tube, at the end of which a membranous bag is firmly bound 
(fig. 86). The bag is then filled with a strong syrup, or some other 
solution denser than water, such as milk or albumen, and is immersed in 
water. The liquid is found gradually to rise in the tube, to a height 
which may attain several inches: at the same time, the level of the 
liquid in which the endosmometer is immersed becomes lower. It 
follows, therefore, that some of the external liquid has passed through 
the membrane and has mixed with the internal liquid. The external 

liquid moreover is found to contain 
some of the internal liquid. Hence 
two currents have been produced in 
opposite directions. The flow of the 
liquid towards that which increases 
in volume is endosmose , and the current 
in the opposite direction is exosmose. 
If water is placed in the bag, and im¬ 
mersed in syrup, endosmose is pro¬ 
duced from the water towards the 
syrup, and the liquid in the interior dimi¬ 
nishes in volume while the level of the 
exterior is raised. 

The height of the ascent in the en¬ 
dosmometer varies with different liquids. 
Of all vegetable substances, sugar is 
that which, for the same density, has 
the greatest power of endosmose, while 
albumen has the highest power of all 
animal substances. In general, it may 
be said that endosmose takes place 
towards the denser liquid. Alcohol 
Tig. 86. an( i ether form an exception to this : 

they behave like liquids which are 
denser than water. With acids, according as they are more or less 














- 130 ] 


END0SM0SE AND EXOSMOSE. 


101 


dilute, tlie endosmose is from the water towards the acid, or from the acid 
towards water. 

According to Dutrochet, it is necessary for the production of endos¬ 
mose : i. that the liquids be different but capable of mixing, as alcohol 
and water; there is no endosmose, for instance, with water and oil ; 
ii. that the liquids be of different densities; and iii. that the membrane 
must be permeable to at least one of the substances. 

The current through thin inorganic plates is feeble, but continuous, 
while organic membranes are rapidly decomposed, and endosmose then 
ceases. 

The well-known fact that dilute alcohol kept in a porous vessel 
becomes concentrated, depends on endosmose. If a mixture of alcohol 
and water be kept for some time in a bladder, the volume diminishes, 
but it becomes much more concentrated. The reason, doubtless, is 
that the bladder permits the endosmose of water rather than that of 
alcohol. 

Dutrochet’s method is not adapted for quantitative measurements, for 
it does not take into account the hydrostatic pressure produced by the 
column. Jolly has examined the endosmose of various liquids by 
weighing the bodies diffused. He calls the endosmotic equivalent of a, 
substance the number which expresses how many parts by weight of 
water pass through the bladder in exchange for one part by weight of 
the substance. The following are some of the endosmotic equivalents 
which he determined:— 


Chloride of sodium . 4*3 Caustic potass . . . 215*0 

Sulphate of magnesium . 11*7 Sulphuric acid . . 0*4 

,, copper . 9*5 Alcohol .... 4*2 

Sugar .... 7*1 

He also found that the endosmotic equivalent increases with the tempera¬ 
ture ; and that the quantities of substances which pass in equal times 
through the bladder are proportional to the strength of the solution. 

130. Diffusion of liquids. —If oil be poured on water no tendency to 
intermix is observed, and even if the two liquids be violently agitated 
together, on allowing them to stand, two separate layers are formed. 
With alcohol and water the case is different; if alcohol, which is speci¬ 
fically lighter, be poured upon water, the liquids gradually intermix, they 


diffuse into one another. 

The laws of this diffusion, in which no porous diaphragm intervenes, 
have been completely investigated by Graham.. The method, by which 
his latest experiments were made, was the following. In a glass vessel 
containing about 700 cubic centimetres of distilled water, about 100 cubic 
centimetres of the solution to be examined was carefully added by means 


102 


ON LIQUIDS. 


[ 130 - 


of a capillary tube, so as to form a layer on the bottom. After a certain 
interval of time, successive layers were carefully drawn off by a syphon, 
and their contents examined. 

The general results of these investigations may be thus stated : 

i. When solutions of the same substance, but of different strengths, are 
taken, the quantities diffused in equal times are proportional to the 
strengths of the solutions. 

ii. In the case of solutions containing equal weights of different sub¬ 
stances, the quantities diffused vary with the nature of the substances. 
Saline substances may be divided into a number of equidiffusive groups, 
the rates of diffusion of each group being connected with the others by a 
simple numerical relation. 

iii. The quantity diffused varies with the temperature. Thus taking 
the rate of diffusion of hydrochloric acid at 15° C. as unity; at 49° C. it 
is 2*18. 

iv. If two substances which do not combine be mixed in solution, 
they may be partially separated by diffusion, the more diffusive one 
passing out most rapidly. In some cases chemical decomposition even 
may be effected by diffusion. Thus bisulphate of potassium is decomposed 
into free sulphuric acid and sulphate of potassium. 

v. If liquids be dilute a substance will diffuse into water, containing an¬ 
other substance dissolved as into pure water; but the rate is materially 
reduced if_a portion of the diffusing substance be already present. 

The following table gives the approximate times of equal diffusion :— 

Hydrochloric acid . . 1-0 Sulphate of magnesium . 7-0 

Chloride of sodium . 2-3 Albumen .... 49-0 

Sugar . . . . 7*0 Caramel . . . . 98-0 

It will be seen from the above table that the difference between the 
rates of diffusion is very great. Thus sulphate of magnesium, one of the 
least diffusible saline substances, diffuses seven times as rapidly as albumen 
and 14 times as rapidly as caramel. These last substances, like hydrated 
silicic acid, starch, dextrine, gum, etc., constitute a class of substances 
which are characterised by their incapacity for taking the crystalline 
form, and by the mucilaginous character of their hydrates. Considering 
gelatine as the type of this class, Graham has proposed to call them colloids 
( Ko\\r), glue), in contradistinction to the far more easily diffusible 
crystalloid substances. 

Graham has proposed a method of separating bodies based on their 
unequal diffusibility, which he calls dialysis. His dialyser consists of a 
ring of gutta percha over which is stretched while wet a sheet of parch¬ 
ment paper, forming thus a vessel about two inches high and ten 
inches in diameter, the bottom of which is of parchment paper. After 


ENDOSMOSE AND EXOSMOSE. 


103 


- 131 ] 

pouring in the mixed solution to he dialysed, the whole is floated on a 
vessel containing a very large quantity of water. In the course of one 
or two days a more or less complete separation will have been effected. 
Thus solution of arsenious acid mixed with various kinds of food readily 
diffuses out. 

The process has received important applications to laboratory and phar¬ 
maceutical purposes. 

For further information on this subject the student is referred to a 
very complete article on the diffusion of liquids in the third volume 
of Watt’s Dictionary of Chemistry. 

131. Endosmose of gases.— The phenomena of endosmose are seen 
in a high degree in the case of gases. When two different gases are 
separated by a porous diaphragm, an exchange takes place between 
them, and ultimately the composition of the gas on both sides of the 
diaphragm is the same; but the rapidity with which different gases 
diffuse into each other under these circumstances varies considerably. 
The laws regulating this phenomenon have been investigated by Graham. 
Numerous experiments illustrate it, two of the most interesting of which 
are the following :— 

A glass cylinder closed at one end is filled with carbonic acid gas, its 
open end tied over with a bladder, and the whole placed under a jar 



of hydrogen. Diffusion takes place between them through the porous 
diaphragm, and after the lapse of a certain time hydrogen has passed 
through the bladder into the cylindrical vessel in much greater quantity 
than the carbonic acid which has passed out, so that the bladder becomes 
very much distended outwards (fig. 87). If the cylinder be filled with 
hydrogen and the bell-jar with carbonic acid, the reverse phenomenon 
will be produced—the bladder will be distended inwards (fig. 88). 

A tube about 12 inches long, closed at one end by a plug of dry plaster 
of Paris, is filled with dry hydrogen, and its open end then immersed in 
a mercury bath. Endosmose of the hydrogen towards the air takes place 







104 ON LIQUIDS. [ 133 - 

so rapidly that a partial vacuum is produced and mercury rises in the 
tube to a height of several inches (fig. 89). If several such tubes are 
filled with different gases, and allowed to diffuse into the air in a similar 
manner, in the same time, different quantities of the various gases will 
diffuse, and Graham found that the law regulating 
these diffusions is, that the force of diffusion is 
inversely as the square roots of the densities of gases. 
Thus, if two vessels of equal capacity, containing 
oxygen and hydrogen, be separated by a porous 
plug, diffusion takes place, and after the lapse of 
some time, for every one part of oxygen which has 
passed into the hydrogen, four parts of hydrogen 
have passed into the oxygen. Now the density of 
hydrogen being 1, that of oxygen is 16, hence 
the force of diffusion is inversely as the square 
roots of these numbers. It is four times as great 
in the one which has the density of the other. 

132. Effusion and Transpiration of Gases.— 
Effusion is the term applied to the phenomenon 
of the passage of gases into vacuum, through a 
minute aperture not much more or less than 0-013 millimeter in dia¬ 
meter, in a thin plate of metal or of glass. Within the limits of ex¬ 
perimental errors, the rates of effusion of different gases coincide with 
those of their diffusion. 

If, however, the gases issue through long, fine capillary tubes into a 
vacuum, the rate of efflux, or the velocity of transpiration , is independent 
of the rate of diffusion. 

i. For the same gas , the rate of transpiration increases , other things being 
equal , directly as the pressure ; that is, equal volumes of air of different 
densities require times inversely proportional to their densities. 

ii. With tubes of equal diameters , the volume transpired in equal times 
is inversely as the length of the tube. 

iii. As the temperature rises the transpiration becomes sloiver. 

iv. The rate of transpiration is independent of the material of the tube. 

133. Absorption and imbibition. —The words absorption and im¬ 
bibition are used almost promiscuously in physics; they indicate the 
penetration of a liquid or a gas into a porous body. Absorption is used 
both for liquids and gases, while imbibition is restricted to liquids. 

In physiology an important distinction is made between the two words: 
absorption means the penetration of a foreign' substance into the tissues 
of a living body, while imbibition refers to penetration into bodies de¬ 
prived of life, whether organic or not. 

134. Absorption of gases. —The surfaces of all solid bodies exert 



Fig. 89. 




ABSORPTION. 


105 


- 136 ] 

an attraction on the molecules of gases with which they are in contact, 
of such a nature, that they become covered with a more or less thick 
layer of condensed gas. When a porous body, which consequently presents 
an immensely increased surface in proportion to its size, is placed in a gas 
over mercury the great diminution of volume which ensues indicates that 
considerable quantities of gas are absorbed. 

Now, although there is no absorption such as arises from chemical 
combinations between the solid and gas (as with phosphorus and 
oxygen), still the quantity of gas absorbed is not entirely dependent on the 
physical conditions of the solid body; it is influenced in some measure by 
the chemical nature both of the solid and the gas. Of all bodies boxwood 
charcoal has the greatest absorptive power. One volume of this sub¬ 
stance at the ordinary temperature and pressure absorbs the following 
quantities of gas:— 


Ammonia . 

90 vol. 

Carbonic oxide . 

9*4 vol. 

Hydrochloric acid 

85 „ 

Oxygen 

9-2 „ 

Sulphurous „ 

65 „ 

Nitrogen . 

7-5 „ 

Sulphuretted hydrogen 
Carbonic acid 

55 „ 

35 „ 

Hydrogen . 

1-75 „ 


The absorptive power of pine charcoal is half as much as that of 
boxwood. The charcoal made from corkwood, which is very porous, is 
not absorbent; neither is graphite. Platinum, in the finely divided 
form known as platinum sponge, is said to absorb 250 times its volume 
of oxygen gas. Many other porous substances, such as meerschaum, 
gypsum, silk, etc., are also highly absorbent. 

135. Absorption in plants. —Absorption takes place in all parts of 
the plant, but more especially in the rootlets and by the leaves. These 
organs absorb, in the form of water, carbonic acid, and ammonia, the 
oxygen, hydrogen, carbon, and nitrogen necessary for the growth of the 
plants. 

Liquids, and the salts which they hold in solution, are absorbed by 
the rootlets, by a double process of capillarity and endosmose. The sap, 
which is then elaborated by the plant, increasing in density towards the 
higher part, owes its ascending direction to endosmose. The ascent of 
the sap is also promoted by the vacuum which the exhalations through 
the leaves tend to produce. Capillary action can only raise the liquid in 
the lower cells; it cannot produce a current. 

130. Absorption in animals. —In the lower animal's whose tissues 
are formed only of cellules, nutrition is accomplished as in plants by ab¬ 
sorption and endosmose. The absorption by which some of these animals 
are nourished is in reality endosmose. 

In the higher animals also absorption is met with. Madder ad- 

f 3 


106 


ON LIQUIDS. 


[ 136 - 


ministered to an animal penetrates its bones and colours them red. If a 
liquid is in contact with a cutaneous surface from which the epidermis 
has been removed, or with a mucous membrane, both which are very 
vascular, the liquid passes into the vessels by endosmose ; this constitutes 
absorption. 

The more liquid a substance, the more readily is it absorbed. At the 
same time a liquid must moisten a membrane in order to be absorbed. 
Fatty substances, which do not moisten surfaces, are not absorbed. But 
M. Bernard has found that when they are made into an emulsion with 
pancreatic juice, absorption readily takes place. And Dr. Loze has 
recently observed that cod-liver oil, when made into an emulsion, has a 
more energetic action, which doubtless arises from its being more com¬ 
pletely absorbed. 

Like endosmose, absorption is promoted by heat, and also by depletion. 
After copious perspiration or loss of blood it also increases. 


- 137 ] 


PROPERTIES OF GASES. 


107 


BOOK IV. 

ON GASES. 


CHAPTER I. 

PROPERTIES OF GASES. ATMOSPHERE. BAROMETERS. 

137. Physical properties of g-ases. — Gases are bodies whose 
molecules are in a constant state of repulsion, in virtue of which they 
possess the most perfect mobility, and are continually tending to occupy 
a greater space. This property of gases is known by the names expan¬ 
sibility, tension, or elastic force , from which they are often called elastic 
fluids. 

Gases and liquids have several properties in common, and some in 
which they seem to differ are in reality only different degrees of the 
same property. Thus, in both, the particles are capable of moving; in 
gases quite freely ; in liquids not quite freely, owing to a certain } degree of 
viscosity. Both are compressible, though in very different degrees ; if a 
liquid and a gas both exist under a pressure of one atmosphere, and then 
the pressure be doubled, the water is compressed by about the zobbbb 
part, while the gas is compressed by one half. In density there is a great 
difference: water, which is the type of liquids, is about 800 times as 
heavy as air, the type of gaseous bodies, while under a pressure of one 
atmosphere. The property by which gases are distinguished from liquids 
is their tendency to indefinite expansion. 

Matter assumes the solid, liquid, or gaseous form according to the rela¬ 
tive strength of the cohesive and repulsive forces exerted between their 
particles. In liquids these forces balance; in gases repulsion preponde¬ 
rates. 

By the aid of pressure and of very low temperatures, the force of 
cohesion may be so far increased in many gases that they are converted 
into liquids, and there is every reason for believing that with sufficient 
pressure and cold they might all be liquefied. On the other hand, heat, 
which increases the force of repulsion, converts liquids, such as water, 
alcohol, and ether, into the aeriform state in which they obey all the 



108 


ON GASES. 


[ 138 - 

laws of gases. This aeriform state of liquids is known by the name of 
vapour, while gases are bodies which, under ordinary temperature and 
pressure, remain in the aeriform state. 

In describing the properties of gases we shall, for obvious reasons, have 
exclusive reference to atmospheric air as their type. 

138. Expansibility of gases. — This property of gases, their ten¬ 
dency to assume continually a greater volume, is exhibited by means of 
the following experiment. A bladder closed by a stop-cock and about 
half full of air is placed under the receiver of the air pump (fig. 90), 

and a vacuum is produced, on which the 
bladder immediately distends. This 
arises from the fact that the molecules 
of air repel each other and press against 
the sides of the bladder. Under ordi¬ 
nary conditions this internal pressure is 
counterbalanced by the air in the re¬ 
ceiver, which exerts an equal and con¬ 
trary pressure. But when this pressure 
is removed by exhausting the receiver, 
the internal pressure becomes evident. 
When air is admitted into the receiver 
the bladder resumes its original form. 

139. Compressibility of gases.— 
The compressibility of gases is rea¬ 
dily shown by the pneumatic syringe 
(fig. 91). This consists of a stout glass 
Fig. 90. tube closed at one end, and provided 

with a tight-fitting solid piston. When 
the rod of the piston is pressed, it moves down in the tube, and the air 
becomes compressed into a smaller volume ; but, as soon as the force is 



Fig. 91. 



removed, the air regains its original volume, and the piston rises to its 
former position. 











WEIGHT OF GASES. 


109 


- 141 ] 



140. Weight of gases.— From their extreme fluidity and expan¬ 
sibility, gases seem to be uninfluenced by the force of gravity; they 
nevertheless possess weight, like solids and liquids. To show this, a glass 
globe of 3 or 4 quarts capacity is taken (fig. 92), the neck of which is 
provided with a stopcock, which hermetically closes it, 

and by which it can be screwed to the plate of the air 
pump. The globe is then exhausted, and its weight 
determined by means of a delicate balance. Air is now 
allowed to enter, and the globe again weighed. The 
weight in the second case will be found to be greater 
than before, and if the capacity of the vessel is known, 
the increase will obviously be the weight of that volume 
of air. 

By a modification of this method, and with the adop¬ 
tion of certain precautions, the weight of air and of other 
gases has been determined: 100 cubic inches of dry air 
under the ordinary atmospheric pressure of 30 in. and 
at the temperature ot 16° C., weigh 31 grains; the same 
volume of carbonic acid gas under the same circum- J 
stances weighs 47-25 grains ; 100 cubic inches of hydro- \ 
gen, the lightest of all gases, weigh 2T4 grains ; and 100 
cubic inches of hydriodic acid gas weigh 146 grains. 

The ratio of the density of air at 0° C. and 30 inches 
pressure to that of water at 0° C. is found to be 0-001296. In other 
words, the latter is 771 times as heavy as the former. 

141. Pressures exerted by gases.— Gases exert on their own mole¬ 
cules and on the sides of vessels which contain them, pressures which 
may be regarded from two points of view. First, we may neglect the 
weight of the gas; secondly, we may take account of its weight. If we 
neglect the weight of any gaseous mass at' rest, and only consider 
its expansive force, it will be seen that the pressures due to this force act 
with the same intensity on all points, both of the mass itself and of the 
vessel in which it is contained. For it is a necessary consequence of the 
elasticity and perfect fluidity of gases, that the repulsive force between 
the molecules is the same at all points, and acts equally in all directions. 
This principle of the equality of the pressure of gases in all directions 
may be shown experimentally by means of an apparatus resembling that 
by which the same principle is demonstrated for liquids (fig. 49). 

If we consider the weight of any gas we shall see that it gives rise to 
pressures which obey the same laws as those produced by the weight of 
liquids. Let us imagine a cylinder, with its axis vertical, several miles 
high, closed at both ends and full of air. Let us consider any small 
portion of the air enclosed between two horizontal planes. This portion 


Fig. 92. 


110 


ON GASES. 


[ 142 - 

must sustain the weight of all the air above it, and transmit that weight 
to the air beneath it, and likewise to the curved surface of the cylinder 
which contains it; and at each point in a direction at right angles to the 
surface. Thus the pressure increases from the top of the column to the 
base; at any given layer, it acts equally on equal surfaces, and at right 
angles to them, whether they are horizontal, vertical, or inclined. The 
pressure acts on the sides of the vessel, and on any small surface it is 
equal to the weight of a column of gas, whose base is this surface, and 
whose height its distance from the summit of the column. The pressure 
is also independent of the shape and dimensions of the supposed cylinder, 
provided the height remains the same. 

For a small quantity of gas the pressures due to its weight are quite 
insignificant, and may be neglected; but for large quantities, like the 
atmosphere, the pressures are considerable, and must be allowed for. 

142. The atmosphere. Its composition.— The atmosphere is the 
layer of air which surrounds our globe in every part. It partakes of the 
rotatory motion of the globe, and would remain fixed relatively to terres¬ 
trial objects, but for local circumstances, which produce winds, and are 
constantly disturbing its equilibrium. 

Air was regarded by the ancients as one of the four elements. Modern 
chemistry, however, has shown that it is a mixture of oxygen and nitro¬ 
gen gases in the proportion of 20-8 volumes of the former to 79*2 volumes 
of the latter. By weight it consists of 23 parts of oxygen to 77 parts of 
nitrogen. 

The atmosphere also contains a quantity of aqueous vapour, which 
varies with the temperature, the season, the locality, and the direction of 
the winds. It further contains a small quantity of ammoniacal gas, and 
from 3 to 6 parts in 10,000 of its volume of carbonic acid. 

The carbonic acid arises from the respiration of animals, from the pro¬ 
cesses of combustion, and from the decomposition of organic substances. 
M. Bousingault has estimated that in Paris the following quantities of 
carbonic acid are produced every 24 hours : 

By the population and by animals . 11,895,000 cubic feet 
By processes of combustion . . . 92,101,000 „ 

103,996,000 „ 

Notwithstanding this enormous continual production of carbonic acid 
on the surface of the globe, the composition of the atmosphere does not 
vary j for plants in the process of vegetation decompose the carbonic 
acid, assimilating the carbon, and restoring to the atmosphere the oxygen 
which is being continually consumed in the processes of respiration and 
combustion. 

143. Atmospheric pressure.— If we neglect the perturbations to 



THE ATMOSPHERE. 


Ill 


- 144 ] 

which the atmosphere is subject, as being inconsiderable, we may consider 
it as a fluid sea of a certain depth, surrounding the earth on all sides, and 
exercising the same pressure as if it were a liquid of very small density. 
Consequently the pressure on the unit of area is constant at a given level, 
being equal to the weight of the column of atmosphere above that level 
whose horizontal section is the unit of area. It will act at right angles 
to the surface, whatever be its position. It will diminish as we ascend, 
and increase as we descend from that level. Consequently, at the same 
height the atmospheric pressures on unequal plane surfaces will be pro¬ 
portional to the areas of those surfaces, provided they be small in propor¬ 
tion to the height of the atmosphere. 

In virtue of the expansive force of the air, it might be supposed that 
the molecules would expand indefinitely into the planetary spaces. But, 
in proportion as the air expands, its expansive force decreases, and is 
further weakened by the low temperature of the upper regions of the 
atmosphere, so that, at a certain height, an equilibrium is established 
between the expansive force which separates the molecules, and the 
action of gravity which draws them towards the centre of the earth. It 
is therefore concluded that the atmosphere is limited. 

From the weight of the atmosphere, and its decrease in density, and 
from the observation of certain phenomena of twilight, its height has 
been estimated at from 30 to 40 miles. Above that height the air is 
extremely rarefied, and at a height of 60 miles it is assumed that there is 
a perfect vacuum. From certain observations 
recently made in the tropical zone, and par¬ 
ticularly at Rio Janeiro, on the twilight arc, 

M. Liais estimates the height of the atmo¬ 
sphere at between 198 and 212 miles, con¬ 
siderably higher, therefore, than what has 
hitherto been believed. 

As it has been previously stated that 100 
cubic inches of air weigh 31 grains, it will 
readily be conceived that the whole atmo¬ 
sphere exercises a considerable pressure on 
the surface of the earth. The existence of 
this pressure is shown by the following ex¬ 
periments. 

144. Crushing force of the atmosphere. 

—On one end of a stout glass cylinder, about 
5 inches high, and open at both ends, a piece 
of bladder is tied quite air-tight. The other 
end, the edge of which is ground and well 
plate of the air pump (fig. 93). As soon as a vacuum is produced in 



Fig. 93. 

greased, is pressed on the 








112 


ON GASES. 


[ 145 - 

the vessel, by working the air pump, the bladder is depressed by the 
weight of the atmosphere above it, and finally bursts with a loud report 
caused by the sudden entrance of the air. 

145. ESag'deburg' hemispheres.— The preceding experiment only 
serves to illustrate the downward pressure of the atmosphere. By means 
of the Magdeburg hemispheres (figs. 94 and 95), the invention of which is 



Fig. 94. Fig. 9o. 


due to Otto von Guericke, burgomaster of Magdeburg, it can be shown that 
the pressure acts in all directions. This apparatus consists of two hollow 
brass hemispheres of 4 to 4i- inches diameter, the edges of which are 
made to fit tightly, and are well greased. One of the hemispheres is 
provided with a stopcock, by which it can be screwed on the air pump, 
and on the other there is a handle. As long as the hemispheres contain 
air they can be separated without any difficulty, for the external pressure 
of the atmosphere is counterbalanced by the elastic force of the air in 
the interior. But when the air in the interior is pumped out by means 
of the air pump, the hemispheres cannot be separated without a power¬ 
ful effort; and as this is the case in whatever position they are held, it 
follows that the atmospheric pressure is transmitted in all directions. 

DETERMINATION OF THE ATMOSPHERIC PRESSURE. BAROMETERS. 

146. Torricelli’s experiment. —The above experiments demonstrate 
the existence of the atmospheric pressure, but they give no indications 




113 


-147] DETERMINATION OF THE ATMOSPHERIC PRESSURE. 

as to its amount. The following experiment, which was first made in 
1643 by Torricelli, a pupil of Galileo, gives an exact measure of the 
weight of the atmosphere. 

A glass tube is taken, about a yard 
long and a quarter of an inch internal 
diameter (fig. 96). It is sealed at one 
end, and is quite filled with mercury. 

The aperture C being closed by the 
thumb, the tube is inverted, the open 
end placed in a small mercury trough, 
and the thumb removed. The tube 
being in a vertical position, the column 
of mercury sinks, and after oscillating 
some time, it finally comes to rest at a 
height A, which at the level of the 
sea is about 30 inches above the mer¬ 
cury in the trough. The mercury is 
raised in the tube by the pressure of 
the atmosphere on the mercury in 
the trough. There is no contrary 
pressure on the mercury in the tube, 
because it is closed. But if the end 
of the tube be opened, the atmo¬ 
sphere will press equally inside and 
outside the tube, and the mercury will 
sink to the level of that in the trough. 

It has been shown in hydrostatics (98) 
that the heights of two columns of 
liquid in communication with each 
other are inversely as their densities, and hence it follows, that the pressure 
of the atmosphere is equal to that of a column of mercury, the height of 
which is 30 inches. If, however, the weight of the atmosphere diminishes, 
the height of the column which it can sustain must also diminish. 

147. Pascal’s experiments. —Pascal, who wished to prove that the 
force which sustained the mercury in the tube was really the pressure of 
the atmosphere, made the following experiments, i. If it were the 
case, the column of mercury ought to descend in proportion as we ascend 
in the atmosphere. He accordingly requested one of his relations to 
repeat Torricelli’s experiment on the summit of the Puy de Dome in 
Auvergne. This was done, and it was found that the mercurial column 
was about 3 inches lower, thus proving that it is really the weight of 
the atmosphere which supports the mercury, since, when this weight 
diminishes, the height of the column also diminishes, ii. Pascal re- 



Fig. 96. 















114 


ON GASES. 


[ 148 - 

peated Torricelli’s experiment at Rouen, in 1646, -with other liquids. He 
took a tube closed at one end, nearly 50 feet long, and having filled it 
with water, placed it vertically in a vessel of water, and found that the 
water stood in the tube at a height of 34 feet j that is, 13-6 times as 
high as mercury. But since mercury is 13*6 times as heavy as water, 
the weight of the column of water was exactly equal to that of the 
column of mercury in Torricelli’s experiment, and it was consequently 
the same force, the pressure of the atmosphere, which successively sup¬ 
ported the two liquids. Pascal’s other experiments with oil and with 
wine gave similar results. 

148. Amount of tlie atmospheric pressure. —Let us assume that 
the tube in the above experiment is a cylinder, the section of which is 
equal to a square inch, then since the height of the mercurial column in 
round numbers is 30 inches, the column will contain 30 cubic inches, 
and as a cubic inch of mercury weighs 3433 5 grains=0'49 of a pound, the 
pressure of such a column on a square inch of surface is equal to 14*7 
pounds. In round numbers the pressure of the atmosphere is taken at 
15 pounds on the square inch. A surface of a foot square contains 144 
square inches, and therefore the pressure upon it is equal to 2,160 pounds, 
or nearly a ton. 

A gas or a liquid which acts in such a manner that a square inch of 
surface is exposed to a pressure, 15 pounds, is called a pressure of one 
atmosphere . If, for instance, the elastic force of the steam of a boiler is so 
great that each square inch of the internal surface is exposed to a pressure 
of 90 pounds (=6 X 15) we say it was under a pressure of six atmospheres. 

The surface of the body of a man of middle size is about 16 square 
feet; the pressure, therefore, which a man supports on the surface of his 
body is 37,560 pounds, or upwards of 16 tons. Such an enormous 
pressure might seem impossible to be borne ; but it must be remembered 
that in all directions there are equal and contrary pressures which 
counterbalance one another. It might also be supposed that the effect of 
this force, acting in all directions, would be to press the body together 
and crush it. But the solid parts of the skeleton could resist a far greater 
pressure; and as to the air and liquids contained in the organs and vessels, 
the air has the same density as the external air, and cannot be further 
compressed by the atmospheric pressure ; and from what has been said 
about liquids (88) it is clear that they are virtually incompressible. 
When the external pressure is removed from any part of the body, 
either by means of a cupping vessel or by the air pump, the pressure 
from within is seen by the distension of the surface. 

149. Different kinds of barometers.— The instruments used for 
measuring the atmospheric pressure are called barometers. In ordinary 
barometers, the pressure is measured by the height of a column of 


BAROMETERS. 


115 


- 151 ] 


mercury, as in Torricelli’s experiment; tlie barometers which we are 
about to describe are of this kind. But there are barometers without 
any liquid, one of which, the aneroid, is remarkable for its simplicity and 
portability. 

150. Cistern barometer.— The cistern barometer consists of a straight 
glass tube closed at one end, about 33 inches long, filled with mercury, and 
dipping into a cistern containing the same metal. In order to render the 
barometer more portable, and the variations of the level in the cistern 
less perceptible when the mercury rises or falls in the tube, 

several different forms have been constructed. Fig. 97 re¬ 
presents one form of the cistern barometer. The apparatus 
is fixed to a mahogany stand, on the upper part of which 
there is a scale graduated in millimeters or inches from the 
level of the mercury in the cistern; a moveable index, i, 
shows on the scale the level of the mercury. A thermo¬ 
meter on the side of the tube indicates the temperature. 

There is one fault to which this barometer is liable, in 
common with all others of the same kind. The zero of 
the scale does not always correspond to the level of the 
mercury in the cistern. For as the atmospheric pressure 
is not always the same, the height of the mercurial column 
varies: sometimes mercury is forced from the cistern into 
the tube, and sometimes from the tube into the cistern, 
so that, in the majority of cases, the graduation of the 
barometer does not indicate the true height. If the dia¬ 
meter of the cistern is large, relatively to that of the tube, 
the error from this source is lessened. The height of the 
barometer is the distance between the levels of the mer¬ 
cury in the tube and in the cistern. As the pressure 
which the mercury exerts by its weight at the base of 
the tube is independent of the form of the tube and of 
its diameter (98), provided it is not capillary, the height 
of the barometer is independent of the diameter of the 
tube, and of its shape, but is inversely as the density of 
the liquid. With mercury the mean height at the level 
of the sea is 29-92, or in round numbers 30, inches ; in a 
water barometer it would be about 33 ‘7 feet. 

151. Fortin’s barometer. — Fortin's barometer differs 
from that just described, in the shape of the cistern. The 
base of the cistern is made of leather, and can be raised 
or lowered by means of a screw; this has the advantage, Fig. 97. 
that a constant level can be obtained, and also that the instrument is 
made more portable. For in travelling, it is only necessary to raise the 
























116 


ON GASES. 


[ 152 - 


leather until the mercury, which rises with it, quite fills the cistern ; the 
barometer may then be inclined, and even inverted, without any fear that 
a bubble of air may enter, or that the shock of the mercury may crack 
the tube. 

Fig. 98 represents the arrangement of the barometer, the tube of 
which is placed in a brass case. At the top of this case, there are two 
longitudinal apertures, on opposite sides, so that the level of the 
mercury, B, is seen. The scale on the case is graduated in millimeters. 
An index A moved by the hand, gives, by means of a vernier, the 
height of the mercury to ~ of a millimeter. At the 
bottom of the case there is the cistern b, containing 
mercury, O. 

Fig. 99 shows the details of the cistern on a larger 
scale. It consists of a glass cylinder ei, which allows the 
mercury to be seen; the bottom of the cylinder is closed 
with leather, mn, which is raised or lowered by means of a 
screw, C. This screw works in the bottom of a brass 
P cylinder, G, which is fastened on the glass cylinder. At 

the top of the cistern there is a small ivory pointer, a, 
the point of which exactly corresponds to the zero on the 
scale. The upper part of the cistern is closed by buckskin, 
d , which is fastened to the barometer tube, E, and to a tubu- 
lure in the brass plate, which covers the cistern. The 
atmospheric pressure is transmitted through the pores of 
this leather. In using this barometer, the 
mercury is first made level with the point a , 
which is effected by turning the screw C 
either in one direction or the other. In this 
manner the distance of the top, B, of the 
b column of mercury from the ivory point a, 
gives exactly the height of the barometer. 

, 152. Gajr-Iussac’s syphon barometer. 

—The syphon barometer is a bent glass tube, 
one of the branches of which is much longer 
than the other. The longer branch, which is 
closed at the top, is filled with mercury as in 
the cistern barometer, while the shorter branch, 
which is open, serves as a cistern. The differ¬ 
ence between the two levels is the height of 
the barometer. 

Fig. 100 represents the syphon barometer as 




Fig. 99. 


Fig. 98. 

modified by Gay-Lussac. In order to render it more available for 
travelling, by preventing the entrance of air, he joined the two branches 






























BAROMETERS. 


117 


- 153 ] 



by a capillary tube; 'when the instrument is inverted, the tube always 
remains full in virtue of its capillarity, and air cannot penetrate into the 
longer branch. A sudden shock, however, might separate the mercury 
and admit some air. To avoid this M. Bunten has introduced an 
ingenious modification into the apparatus. The longer branch is drawn 
out to a fine point, and is joined to a tube K of the form represented in 
figure 101. By this arrangement, if air passes through the capillary tube, 
it cannot penetrate the drawn-out extremity of the longer branch, but 
lodges in the upper part of the enlargement K. In this position it does 
not affect the observations, since the vacuum is always 
at the upper part of the tube; it is moreover easily re¬ 
moved. 

In Gay-Lussac’s barometer the shorter branch is 
closed, but there is a lateral capillary aperture a, through 
which the atmospheric pressure is transmitted. 

The barometric height is determined by means of 
two scales, which have a common zero at 0, towards 
the middle of the longer branch, and are graduated in 
contrary directions, the one from O to E, and the other 
from 0 to B, either on the tube itself, or on brass rules 
fixed parallel to the tube. Two sliding verniers, m 
and n, indicate ~ of a millimeter. The total height 
of the barometer AB, is the sum of the distances from 
0 to A and from 0 to B. 

153. Precautions in reference to barometers.— 

In constructing barometers, mercury is chosen in pre¬ 
ference to any other liquid. For being the densest of 
all liquids it stands at the least height. When the 
mercurial barometer stands at 30 inches, the 
water barometer would stand at about 34 feet. 

It also deserves preference because it does not 
moisten the glass. It is necessary that the 
mercury be pure and free from oxide ; other¬ 
wise it adheres to the glass and tarnishes it. 

Moreover if it is impure its density is changed, 
and the height of the barometer is too great 
or too small. Mercury is purified, before being 
used for barometers, by treatment with dilute 
nitric acid, and by distillation. 

The space at the top of the tube (figs. 96 
and 97), which is ^.called the Torricellian 
vacuum, must be quite free from air and 




Fig. 100. * Fig. 101. 


from aqueous vapour, for otherwise either would depress the mercurial 




























118 


ON GASES. 


[ 154 - 

column by its elastic force. To obtain this result, a small quantity of 
pure mercury is placed in the tube and boiled for some time. It is then 
allowed to cool, and a further quantity, previously warmed, added, which 
is boiled, and so on, until the tube is quite full; in this manner the 
moist ure and the air which adhere to the sides of the tube pass off with 
the mercurial vapour. 

A barometer is free from air and moisture if, when it is inclined, the 
mercury strikes with a sharp metallic sound against the top of the tube. 
If there is air or moisture in it, the sound is deadened. 

154. Correction for capillarity. —In cistern barometers there is 
always a certain depression of the mercurial column due to capillarity, 
unless the internal diameter of the tube exceeds 08 inch. To make 
the correction due to this depression, it is not enough to know the 
diameter of the tube, we must also know the height of 
the meniscus od (fig. 102), which varies according as the 
meniscus has been formed during an ascending or de¬ 
scending motion of the mercury in the tube. Conse¬ 
quently the height of the meniscus must be determined 
by bringing the pointer to the level ab, and then to the 
level d , when the difference of the readings will give the 
height od required. These two terms, namely, the in¬ 
ternal diameter of the tube, and the height of the meniscus, 
being known, the resulting correction can be taken out 
of the following table, which follows the arrangement frequently adopted 
for a multiplication table:— 

--—~i 


Internal Height of Sagitta of Meniscus in inches. 

Diameter 


in inches. 

o-oio 

0-015 

0-020 

0-025 

0-030 

0-035 

0-040 

0-157 

00293 

0-0431 

0-0555 

0-0677 

0-0780 

0-0870 

0-0948 

0-236 

00119 

0-0176 

00231 

0-0294 

0-0342 

0-0398 

0-0432 

0-315 

0-0060 

0-0088 

0-0118 

0-0144 

0-0175 

00196 

00221 

0-394 

0-0039 

0-0048 

0-0063 

0-0078 

0-0095 

0-0110 

0-0125 

0-472 

0-0020 

0-0029 

0-0036 

0-0045 

0-0053 

00063 

0*0073 

0-550 

0-0010 

0-0017 

i 

0-0024 

0-0029 

00034 

0-0039 

00044 


In Gay-Lussac's barometer the two tubes are made of the same dia¬ 
meter, so that the error caused by the depression in the one tube very 
nearly corrects that caused by the depression in the other. As, however, 
the meniscus in the one tube is formed by a column of mercury with an 
ascending motion, while that in the other by a column with a descending 
motion, their heights will not be the same, and the reciprocal correction 
will not be quite exact. 



Fig. 102. 





























BAROMETERS. 


119 


- 156 ] 

155. Correction for temperature. — In all observations with 
barometers, whatever be their construction, a correction must be made 
for temperature. Mercury contracts and expands with differfent tempera¬ 
tures ; hence its density changes, and consequently the barometric height, 
for this height is in the inverse ratio of the density of the mercury; 
so that for different atmospheric pressures the mercurial column might 
have the same height. Accordingly, in each observation, the height 
observed must be reduced to a determinate temperature; the choice of 
this is quite arbitrary, but that of melting ice is always adopted. It 
will be seen, in the Book on Heat, how this correction is made. 

By the aid of tables which have been prepared for this purpose, the 
height of the barometer is readily reduced to zero Centigrade. 

156. Variations in the height of the barometer. —When the baro¬ 
meter is observed for several days, its height is found to vary in the same 
place, not only from one day to another, but also during the same day. 

The extent of these variations, that is, the difference between the 
greatest and the least height, is different in different places. It increases 
from the equator towards the poles. Except under extraordinary cir¬ 
cumstances, the greatest variations do not exceed 6 millimeters under 
the equator, 30 under the tropic of Cancer, 40 in France, and 60 at 25 
degrees from the pole. The greatest variations are observed in winter. 

The mean daily height is the height obtained by dividing the^sum of 
24 successive hourly observations by 24. In our latitudes, the barometric 
height at noon corresponds to the mean daily height. 

The mean monthly height is obtained by adding together the mean 
daily heights for a month, and dividing by 30. 

The mean yearly height is similarly obtained. 

Under the equator, the mean annual height at the level of the sea is 
0 m, 758, or 29'84 inches. It increases from the equator, and between the 
latitudes 30° and 40° it attains a maximum of 0 m, 763, or 30’04 inches. 
In lower latitudes it decreases, and in Paris it does not exceed 0 ra, 7568. 

The general mean at the level of the sea is 0 m, 761 or 2996 inches. 

The mean monthly height is greater in winter than in summer, in 
consequence of the cooler atmosphere. 

Two kinds o:' variations are observed in the barometer: 1st, the acci¬ 
dental variations , which present no regularity; they depend on the seasons, 
the direction of the winds, and the geographical position, and are common 
in our climates: 2nd, the daily variations, which are produced periodically 
at certain hours of the day. 

At the equator, and between the tropics, no accidental variations are 
observed; but the daily variations take place with such regularity that a 
barometer may serve to a certain extent as a clock. The barometer sinks 
from midday till towards four o’clock; it then rises, and reaches its 


120 


ON GASES. 


[157- 

maximum at about ten o’clock in the evening. It then again sinks, and 
reaches a second minimum towards four o’clock in the morning, and a 
second maximum at ten o’clock. 

In the temperate zones there are also daily variations, but they are 
detected with difficulty, since they occur in conjunction with accidental 
variations. 

The hours of the maxima and minima appear to be the same in all 
qlimates, whatever be the latitude; they merely vary a little with the 
seasons. 

157. Causes of barometric variations. —It is observed that the 
course of the barometer is generally in the opposite direction to that of 
the thermometer; that is, that when the temperature rises the barometer 
falls, and vice versa ; which indicates that the barometric variations at 
any given place are produced by the expansion or contraction of the air, 
and therefore by its change in density. If the temperature were the same 
throughout the whole extent of the atmosphere, no currents would be 
produced, and, at the same height, the atmospheric pressure would be 
everywhere the same. But when any portion of the atmosphere becomes 
warmer than the neighbouring parts, its specific gravity is diminished, 
and it rises and passes away through the upper regions of the atmosphere, 
whence it follows that the pressure is diminished, and the barometer falls. 
If any portion of the atmosphere retains its temperature, while the 
neighbouring parts become cooler, the same effect is produced; for in 
this case, too, the density of the first-mentioned portion is less than that 
of the others. Hence, also, it usually happens that an extraordinary fall 
of the barometer at one place is counterbalanced by an extraordinary rise 
at another place. With reference to the daily variations, they appear to 
result from the expansions and contractions which are periodically pro¬ 
duced in the atmosphere by the heat of the sun during the rotation of 
the earth. 

158. Relation of barometric variations to the state of the 
weather. —It has been observed that, in our climate, the barometer in 
fine weather is generally above 30 inches, and is below this point when 
there is rain, snow, wind, or storm, and also, that for any given number 
of days at which the barometer stands at 30 inches, there are as many 
fine as rainy days. From this coincidence between the height of the 
barometer and the state of the weather, the following indications have 
been marked on the barometer, counting by thirds of an inch above and 
below 30 inches: 


Height. 

31 inches . 


m » 
„ 


State of the weather. 
. Very dry. 

. Settled weather. 

. Fine weather. 


- 159 ] 


BAROMETERS. 


121 


Height State of the weather. 

30 inches ....... Variable. 

29§ Pain or wind. 

29£ „ ...... Much rain. 

29 „ ...... Tempest. 

In using the barometer as an indicator of the state of the weather, we 
must not forget that it really only serves to measure the weight of the 
atmosphere, and that it only rises or 
falls as this weight increases or dimi¬ 
nishes ; and although a change of 
weather frequently coincides with a 
change in the pressure, they are not 
necessarily connected. This coincidence 
arises from meteorological conditions 
peculiar to our climate, and does not 
always occur. That a fall in the baro¬ 
meter usually precedes rain in our 
latitudes, is caused by the position of 
Europe. The south-west winds, which 
a# hot and consequently light, make 
the barometer sink; but at the same 
time, as they become charged with 
aqueous vapour in crossing the ocean, 
they bring us rain. The winds of the 
north and north-east, on the contrary, 
being colder and denser, make the baro¬ 
meter rise; and as they only reach us 
after having passed over vast continents 
they are generally dry. 

When the barometer rises or sinks 
slowly, that is, for two or three days, 
towards fine weather or towards rain, 
it has been found from a great number 
of observations that the indications 
are then extremely probable. Sudden 
variations in either direction indicate 
bad weather or wind. 

159. Wheel barometer. —The wheel barometer , which was invented by 
Hooke, is a syphon barometer, and is especially intended to indicate good 
andbad weather (fig. 103). In the shorter leg of the syphon there is a 
float, which rises and falls with the mercury (fig. 104). A string 
attached to this float passes round a pulley, O, and at the other end there 
is a weight, P, somewhat lighter than the float. A needle fixed to the 



Fig. 103. 


Fig. 104. 










122 


ON GASES. 


[ 160 - 

pulley moves round a graduated circle, on wiiicli is marked variable, rain, 
Jine weather, etc. When the pressure varies the float sinks or rises, and 
moves the needle round to the corresponding points on the scale. 

The barometers ordinarily met with in houses, and which are called 
weather glasses, are of this kind. They are, however, of little use, for two 
reasons. The first is, that they are neither very delicate nor precise in 
their indications. The second, which applies equally to all barometers, 
is, that those commonly in use in this country are made in London, and 
the indications, if they are of any value, are only so for a place of the 
same level and of the same climatic conditions as London. Thus a baro¬ 
meter standing at a certain height in London would indicate a certain 
state of weather, but if removed to Shooter’s Hill it would stand half an 
inch lower, and would indicate a different state of weather. As the 
pressure differs with the level and with geographical conditions, it is 
necessary to take these into account if exact data are wanted. 

160. Determination of heights by the barometer. —Since the atmo¬ 
spheric pressure decreases as we ascend, it is obvious that the barometer 
will keep on falling as it is taken to a greater and greater height—a 
fact which suggests a very useful method of determining the difference 
between the elevations of two stations, such as the base and summit of 
a mountain. The method may be explained as follows. 

It will be seen in the next chapter that if the temperature of an 
enclosed portion of air continues constant, its volume will vary inversely 
as the pressure per square inch. That is to say, if we double the pressure 
we shall halve the volume. This fact is commonly called Boyle 
and Mariotte’s law. But if we halve the volume we manifestly 
double the quantity of air in each cubic inch, or double the 
density of the air, and so on in any proportion. Consequently, 
the law is equivalent to this :—That for a constant temperature 
--Q the density of air is proportional to the pressure per square inch 
- P which it sustains. 

Now suppose A and B (fig. 105) to represent two stations, and 
that it is required to determine the vertical height of B above A; 
it being borne in mind that A and B are not necessarily in the 
same vertical line. Take P any point in AB, and Q a point at a 
small distance above P. Suppose the pressure per square inch of 
the atmosphere at P to be denoted by p, and at Q let it b( 
Pig. diminished by a quantity denoted by dp. It is plain that this 
diminution equals the weight of the column of air between I 
and Q, whose section is one square inch. But, since the density of tk 
air is directly proportional to p, the weight of a cubic inch of air wL 
equal kpg , where k denotes a certain quantity to be determined here¬ 
after, and g the accelerating force of gravity (70). Hence, if we denote 





- 160 ] DETERMINATION OF HEIGHTS BY THE BAROMETER. 


123 


PQ in inches by dx, the pressure will be diminished by kpg.dx , and we 
may represent this fact algebraically by the equation 
kpg.dx = — dp 

By a well-known algebraical process this leads to the conclusion that 


kgX = log 

where X denotes the height of AB, and P and P x the atmospheric pressures 
at A and B respectively, the logarithms being of the kind called 1 Napierian 
logarithms.’ Now, if H and H x are the heights of the barometer at A 
and B respectively, the temperature of the mercury being the same at 
both stations, their ratio equals that of P to P p and therefore 


X = 


1 i H 

b/ k « h ; 


It remains to determine k and g. 

(1) Since the force of gravity is different for places in different 
latitudes, g will depend upon the latitude (73). It is found that if g is 
the accelerating force of gravity in latitude <p, and f that force in latitude 
4o°, then 

f 

9 ~ 1+0-0025G cos 2<p 


where f has a definite numerical value. 

(2) From what has been stated above it will be seen that if p is the 
density of air at a temperature of t° C., under Q the pressure exerted by 
29-92 inches of mercury, we shall have 

kQ — p 

But it appears that if p 0 is the density of air under the same pressure Q 
at 0° C., we shall have 

„ _ Po 

p ~ 1 +at 

Where a has a definite numerical value. Therefore 

Now if a is the density of mercury, and if the latitude is 45°, we shall 
have 

Q = 29-92.0 -fs 


hnd therefore 

‘ i.f-t 5 _ 1 

< K J — „ • 29'92(l+o<) 

sT 0 w p 0 —o- is the ratio which the density of dry air at a temperature 0° 
in latitude 45° under a pressure of 29*92 inches of mercury, bears to 
the density of mercury at 0° C., and therefore p 0 +<r is a determinate 
number. Substituting 

a 2 





124 


ON GASES. 


[ 160 - 


X = 29 92 in. . y (1+0*00256 cos 2$) (1 + at) log -jgr 

The value of a is 0-003665, which is nearly equal to T ^. If we sub¬ 
stitute the proper values for <r-^-p 0 , and change the logarithms into common 
logarithms, and instead of t use the mean of T and T p the temperatures 
at the upper and lower stations, it will be found that 

2fT+T ) jj 

X (in feet) = 60346 (1 + 0*00256 cos 2^) ( 1+ ^q 1 -) log g- 

which is La Place’s barometric formula. In using it, it must be remem¬ 
bered that T and Tj are the temperatures on the Centigrade thermometer, 
and that II and are the heights of the barometer reduced to 0° C. 
Thus if h is the measured height of the barometer at the lower station 
we have 

H = 7t( 1 - gAj) 

If the height to be measured is not great, one observer is enough. For 
greater heights the ascent takes some time, and in the interval the pres¬ 
sure may vary. Consequently in this case there must be two observers, 
one at each station, who make simultaneous observations. 

Let us take the following example of the above formula:—Suppose 
that in latitude 65° N. at the lower of two stations the height of the 
barometer were 30*025 inches, and the temperature of air and mercury 
17°*32 C., while at the upper the height of the barometer was 28*230 
inches, and the temperature of air and mercury was 10°*55 C. Determine 
the height of the upper station above the lower. 

(1) Find H and T1 1 : viz. 

H = 30025(l - ^jjg)= 29 945 

Hj = 28-23o( 1 - 28-185 

V 6500/ 

Hence log ~ = 1*4763243-1*4500155 = 0*02562688 

(2) Find 1 +~' ( 1000 I ) viz * 1,05574 

(3) Find 1 +0*00256 cos 2<p 

Since 0*00256 cos 130°= - 0*00256 cos 50° 

= -0*001824 

therefore 1 + 0*00256 cos 2<p— 0*998355 

Hence the required height in feet equals 

60316 x 0*998355 x 1*05574 x 0*02562688 = 1671 
It may be easily proved that if H and H x do not greatly differ the 

Napierian logarithm of ^ equals 2g=-5l. if f or instance H equals 30 







- 161 ] 


BOYLE AND MARIOTTE S LAW. 


125 


inches, and H 1 equals 29 inches, the resulting error would not exceed the 
5000 P a1 '^ t ^ ie whole. Accordingly for heights not exceeding 2000 ft. 
we may without much error use the formula, 

[-H, 


X (in feet) = 52500 (l + 2 A+£2) 


H+Hj 


CHAPTER II. 

MEASUREMENT OF THE ELASTIC FORCE OF GASES. 

161. Boyle and Mariotte’s law.— The law of the compressibility 
of gases was discovered by Boyle and Mariotte 
independently. In consequence it is in England 
commonly called Boyle’s law, and, on the con¬ 
tinent, Mariotte’s law. It is as follows: ‘ The 

temperature remaining the same , the volume of a 
given quantity of gas is inversely as the pressure 
which it hears.’ 

This law is verified by means of an apparatus 
called Mariotte’s tube (fig. 106). It consists of a 
long glass tube fixed to a vertical support; it is 
open at the upper part, and the other end, which 
is* bent into a short vertical leg, is closed. On 
the shorter leg there is a scale, which indicates 
equal capacities ; the scale against the long leg 
gives the heights. The zero of both scales is in 
the same horizontal line. 

A small quantity of mercury is poured into the 
tube, so that its level in both branches is at zero, 
which is effected without much difficulty. The 
air in the short leg is thus under the ordinary 
atmospheric pressure. Mercury is then poured 
into the longer tube until the volume of the air in 
the smaller tube is reduced to one half ; that is 
until it is reduced from 10 to 5, as shown in the 
figure. If the height of the mercurial column, 

OA, be measured, it will be found exactly equal 
to the height of the barometer at the time of the 
experiment. The pressure of the column CA is 
therefore equal to an atmosphere, which, with the 
atmospheric pressure acting on the surface of the 
column at C, makes two atmospheres. Accordingly, by doubling the 
pressure, the volume of the gas has been diminished to one half. 


1 i 

<: 

I 


-t 




f 


■ 20 

i-rrOU 

10 



•J- 

L 


106 . 

















126 


ON GASES. 


[l 61 - 

If mercury be poured into the longer branch until the volume of the 
air is reduced to one-third its original volume, it will be found that the 
distance between the level of the two tubes is equal to two barometric 
columns. The pressure is now three atmospheres, while the volume is 

reduced to one-third. Dulong and Petit 
have verified the law for air up to 27 atmo¬ 
spheres, by means of an apparatus analogous 
to that which has been described. 

The law also holds good in the case of 
pressures of less than one atmosphere. To 
establish this, mercury is poured into a 
graduated tube until it is about two-thirds 
full, the rest being air. It is then inverted 
in a deep trough containing mercury (fig. 
107), and lowered until the levels of the 
mercury inside and outside the tube are the 
same, and the volume noted. The tube is 
then raised, as represented in the figure, until 
the volume of the air is doubled. The 
height of the mercury in the tube, above the 
mercury in the trough, is then found to be 
exactly half the height of the barometric 
column. Accordingly, for half the pressure 
the volume has been doubled. 

In the experiment with Mariotte’s tu]}e, as 
the quantity of air remains the same, its 
density must obviously increase as its volume 
diminishes, and vice versa. The law may thus 
be enunciated : 1 For the same temperature the 
density of a gas is proportional to its pressure ' 
Hence, as water is 770 times as heavy as air, 
under a pressure of 770 atmospheres, air 
would be as dense as water. 

Until within the last few years Boyle’s law was supposed to be 
absolutely true for all gases at all pressures, but Despretz, who ex¬ 
amined the compressibility of gases, obtained results incompatible with 
the law. He took two graduated glass tubes of the same length, and 
filled one with dir and the other with the gas to be examined. These 
tubes were placed in the same mercury trough, and the whole apparatus 
immersed in a strong glass cylinder filled with water. By means of a 
piston moved by a screw which worked in a cap at the top of a cylinder, 
the liquid could be subjected to an increasing pressure, and it could be 
seen whether the compression of the two gases was the same or not. 








BOYLE. AND MARIOTTE’s LAW. | ->7 

The apparatus resembled that used for examining the compressibility 
ot liquids (fig. 47). In this manner Despretz found that carbonic acid 
sulphuretted hydrogen, ammonia, and cyanogen, are more compressible 
than air: hydrogen, which has the same compressibility as air up to 15 
atmospheres, is then less compressible. From these experiments it was 
concluded that the law of Boyle and Mariotte was not general. 



I 11 some experiments on the elastic force of vapours, Dulong and 
Arago had occasion to test the accuracy of Boyle and Mariotte’s law. 
lhe method adopted was exactly that of Mariotte, but the apparatus had 
gigantic dimensions. 













































128 


ON GASES. 


[ 161 - 

The gas to be compressed was contained in a strong glass tube, GF 
(fig. 108), about six feet long and closed at the top, G. The pressure 
was produced by a column of mercury, which could be increased to 
a height of 65 feet, contained in a long vertical tube, KL, formed of a 
number of tubes firmly joined by good screws, so as to be perfectly tight. 

The tubes KL and GF were hermetically fixed in a horizontal iron 
pipe, DE, which formed part of a mercurial reservoir, A. On the top of 
this reservoir there was a force pump, BC, by which mercury could be 
forced into the apparatus. 

At the commencement of the experiment, the volume of the air in 
the manometer (164) was observed, and the initial pressure determined, 
by adding to the pressure of the atmosphere the height of the mercury 
in K above its level in H. If the level of the mercury in the manometer 
had been above the level in KL, it would have been necessary to subtract 
the difference. 

By means of the pump, water was injected into A. The mercury 
being then pressed by the water, rose in the tube GF, where it com¬ 
pressed the air, and in the tube KL, where it rose freely. It was only 
then necessary to measure the volume of the air in GF ; the height of 
the mercury in KL above the level in GF, together with the pressure of 
the atmosphere, was the total pressure to which the gas was exposed. 
These were all the elements necessary for comparing different volumes 
and the corresponding temperatures. The tube GF was kept cold during 
the experiment by a stream of cold water. 

The long tube was attached to a long mast by means of staples. The 
individual tubes were supported at the junction by cords, which passed 
round pulleys B and R/ and were kept stretched by small buckets, P, con¬ 
taining shot. In this manner, each of the thirteen tubes having been 
separately counterpoised, the whole column was perfectly free, notwith¬ 
standing its weight. 

Dulong and Arago investigated the pressure up to 27 atmospheres, and 
observed that the volume of air always diminished a little more than is 
required by Boyle and Mariotte’s law. But, as these differences were 
very small, they attributed them to errors of observation, and concluded 
that the law was perfectly exact, at any rate up to 27 atmospheres. 

M. Regnault investigated the same subject with an apparatus resem¬ 
bling that of Dulong and Arago, but in which all the sources of error 
were taken into account, and the observations made with remarkable 
precision. ITe experimented with air, nitrogen, carbonic acid, and hv- 
drogen. He found that air does not exactly follow Boyle and Mariotte’s 
law, but experiences a greater compressibility, which increases with the 
pressure; so that the difference between the calculated and the observed 
diminution of volume is greater in proportion as the pressure increases. 


- 164 ] APPLICATIONS OF BOYLE’S AND MARlOTTE’s LAW. 


129 


M. Regnault found that nitrogen was like air, but is less compressible. 
Carbonic acid exhibits considerable deviation from Boyle and Mariotte’s 
law even under small pressures. Hydrogen also deviates from Boyle and 
Mariotte’s law, but its compressibility diminishes with increased pressure. 

Carbonic acid deviates less from the law in proportion as the tempe¬ 
rature is higher. This is also the case with other gases. And experi¬ 
ment shows that the deviation from the law is greater, in proportion as 
the gas is nearer its liquefying point; and, on the contrary, the farther a 
gas is from this point, the more closely does it follow the law. For gases 
which have not been liquefied, the deviations from the law are inconsider¬ 
able, and may be quite neglected in ordinary physical and chemical ex¬ 
periments, where the pressures are not great. 

162. Applications of Boyle’s and Mariotte's law.— Obser¬ 
vations on the volumes of gases are only comparable when made at the 
same pressure. Usually, therefore, in gas analyses, all measurements are 
reduced to the standard pressure of 760 millimeters, or 29-92 inches. 
This is easily done by Mariotte’s law, for, since the volumes are inversely as 
the pressures, Y : V' = P' : P. Knowing the volume V at the pressure 
P we can easily calculate its volume V' at the given temperature P s , for 

y/p, _ Vp 

VP 

that is, V' = -p— 


Suppose a volume of gas to measure 340 cubic inches under a pressure 
of 535 mm. what will be its volume at the standard pressure, 760 mm. ? 

We have Y = 340 x 535 _ 333 cll ki c inches. 

760 

In like manner let it be asked, if I)' is the density of a gas when 
the barometer stands at H' mm., what will be its density D at the 
same temperature when the barometer stands at H mm. P Let M be the 
mass of the gas, V'its volume in the first case, V its volume in the second. 
Therefore, 

DV = M = D'V' 

1 ) _ V' P _ II 
0r ' I)' V P' H' 


Thus, if H' denote 760 mm., we have 

Density at II = (Density at standard pressure) 

163. Manometers.— Manometers are instruments for measuring the 
tension of gases or vapours. In all manometers the unit chosen is the 
pressure of one atmosphere or 30 inches of mercury at the standard 
temperature, which, as we have seen, is nearly 151bs. to the square inch. 

164. Manometer with compressed air. — The manometer with 

o 3 





130 


ON GASES. 


[ 165 - 


■ compressed air is founded on Mariotte’s law ; it consists of a glass tube 
closed at its upper extremity, and tilled with dry air. It is firinty 
cemented in a small iron box containing mercury. By a tubulure, A, in 
the side (tig. 109), this box is connected with the closed vessel containing 
the gas or vapour whose tension is to be measured. 

In the graduation of this manometer, the quantity of air contained in 
the tube is such, that when the aperture A communicates freely with 
the atmosphere, the level of the mercury is the same in the tube and 
in the tubulure. Consequently, at this level the number 1 is marked 
on the scale to which the tube i's affixed. As the pressure acting 
through the tubulure A increases, the mercury rises in the tube, until its 

weight added to the tension of the 
compressed air, is equal to the external 
pressure. It would consequently be 
incorrect to mark two atmospheres in 
the middle of the tube j for since the 
volume of the air is reduced to one-half, 
its tension is equal to two atmospheres, 
and, together with the weight of the 
mercury raised in the tube, is there¬ 
fore more than two atmospheres. The 
position of the number is a little below 
the middle, at such a height that the 
elastic force of the compressed air, 
together with the weight of the mercury 
iu the tube, is equal to two atmospheres. 
The exact.position of the numbers 2, 3, 
4, etc., on the manometer scale can only 
be determined by calculation. Some¬ 
times this manometer is made of one 
glass tube, as represented in fig. 110. 
The principle is obviously the same. 

165. Aneroid barometer.— This instrument derives its name from the 
circumstance that no liquid is used in its construction (a without, vrjpbg 
moist). Fig. Ill represents one of the forms of these instruments, con¬ 
structed by Mr. Casella; it consists of a cylindrical metal box, exhausted 
of air, the top of which is made of thin corrugated metal, so elastic 
that it readily yields to alterations in the pressure of the atmosphere. 

When the pressure increases, the top is pressed inwards ; when on the 
contrary it decreases, the elasticity of the lid, aided by a spring, tends to 
move it in the opposite direction. These motions are transmitted by 
delicate multiplying levers to an index which moves on a scale. The 
instrument is graduated empirically by comparing its indications under 
different pressures with those of an ordinary mercurial barometer. 






















LAWS OF THE MIXTURE OF GASES. 


131 


- 166 ] 

The aneroid has the advantage of being portable, and can be con¬ 
structed of such delicacy as to indicate the difference in pressure between 
the height of an ordinary 
table and the ground. It 
is hence much used in de¬ 
termining heights in moun¬ 
tain ascents. But it is 
liable to get out of repair, 
especially when it has been 
subjected to great varia¬ 
tions of pressure; and its in¬ 
dications must from time to 
time be compared by means 
of a standard barometer. 

106. Laws of the 
mixture of gases.— If a 
communication is opened 
between two closed vessels 
containing gases, they at 
once begin to mix, what¬ 
ever be their density, and 
in a longer or shorter time the mixture is complete and will continue so, 
unless chemical action or some other extraneous cause intervene. The 
laws which govern the mixture of gases may be thus stated :— 

(1) The mixture takes place rapidly and is homogeneous, that is, each 
portion of the mixture contains the two gases in the same proportion. 

(2) If the gases severally and the mixture have the same tempera¬ 
ture, and if the gases severally and the mixture occupy the same volume, 
then the pressure per unit of area exerted by the mixture will equal the 
sum of the pressures per unit of area exerted by the gases severally. 

From the second law a very convenient formula can be easily deduced. 
Let v v v 3 . . . . be the volumes of several gases under pressure of 
Pv Pv Pa • • • • respectively. Suppose these gases when mixed to have 
a volume V, under a pressure P, the temperatures being the same. By 
Boyle and Mariotte’s law we know that will occupy a volume P under 
a pressure p/ provided 

VPi = v iPi 

Similarly ^P<i = v <iP<i 

and so on. But we learn from the above law that 

P = Pi + Pz + • * • 

therefore VP = v iPi4- y 2P2+ y 3P3+ • • • 

It obviously follows that if the pressures are all the same, the volume 
of the mixture equals the sum of the separate volumes. 



Fig. ill. 










132 


ON GASES. 


[ 167 ” 


The first law was shown experimentally Berthollet, by means 
of an apparatus represented in fig. 112. It consists of two glass globes 
provided with stop-cocks, which can be screwed one on the other. The 
upper globe was filled with hydrogen, and the lower one with carbonic 
acid, which has 22 times the density of hydrogen. The globes having 
been fixed together were placed in the cellars of the Paris Observatory, 
and the stop-cocks then opened, the globe containing hydrogen being 

uppermost. Berthollet found after some 
time that the pressure had not changed, 
and that, in spite of the difference in den¬ 
sity, the two gases had become uniformly 
mixed in the two globes. Experiments 
made in the same manner with other gases 
gave the same results, and it was found 
that the diffusion was more rapid in pro¬ 
portion as the difference between the densi¬ 
ties was greater. 

The second law may be demonstrated by 
passing into a graduated tube over mercury, 
known volumes of gas at known pressures. 
The pressure and volume of the whole 
mixture are then measured, and found to 
be in accordance with the law. 

Gaseous mixtures follow Boyle and 
Mariotte’s law, like simple gases, as has been 
proved for air (161), which is a mixture of 
nitrogen and oxygen. 

liquids. Absorption. —Water and 



Pig. 112. 


167. 


Mixture of gases and 

many liquids possess the property of absorbing gases. Under the sanies® 
conditions of pressure and temperature a liquid does not absorb equai 
quantities of different gases. At the ordinary temperature and pressure 
water dissolves its volume of nitrogen, its volume of oxygen, its 
own volume of carbonic acid, and 430 times its volume of ammoniacal gas. 

The whole subject of gas absorption has been investigated by Bunsen, 
to whose work* the student is referred for further information. The 
general laws of gas-absorption are the following :— 

I. For the same gas, the same liquid, and the same temperature, the 
weight of gas absorbed is proportional to the pressure. This may also be 
expressed by saying that at all pressures the volume dissolved is the same ; 
or that the density of the gas absorbed is in a constant relation with that 
of the external gas which is not absorbed. 

Accordingly, when the pressure diminishes, the quantity of dissolved gas 

Walton and 


* Gasometric Methods, by R. Bunsen, translated by Dr. Roscoe. 
Maberlv. 




PRESSURE ON BODIES IN AIR. 


133 


- 168 ] 

decreases. If a solution of a g as be placed under the air pump and a vacuum 
created, the gas obeys its expansive force and escapes with effervescence. 

II. The quantity of gas absorbed is greater when the temperature is 
lower; that is to say, when the elastic force of the gas is less. 

III. The quantity o f gas which a liquid can dissolve is independent of the 
nature and of the quantity of other gases which it may already hold in solution. 

In every gaseous mixture each gas exercises the same pressure as it 
would if its volume occupied the whole space ; and the total pressure is 
equal to the sum of the individual pressures. When a liquid is in contact 
with a gaseous mixture, it absoibs a certain part of each gas, but less 
than it would if the whole space were occupied by each gas. The 
quantity of each gas dissolved is proportional to the pressure which the 
unabsorbed gas exercises alone. For instance, oxygen forms only about \ 
the quantity of air; and water, in ordinary conditions, absorbs exactly the 
same quantity of oxygen as it would if the atmosphere were entirely 
formed of this gas, under a pressure equal to | that of the atmosphere. 


CHAPTER III. 

PRESSURE ON BODIES IN AIR. BALLOONS. 



168. Archimedes’ principle applied to gases. —The pressure 
exerted by gases on bodies immersed in them is transmitted equally in 
all directions, as has been shown by 
the experiment with the Magdeburg 
hemispheres. It therefore follows 
that all which has been said about the 
equilibrium of bodies in liquids 
applies to bodies in air; they lose a 
part of their weight equal to that of 
the air which they displace. 

This loss of weight in air is demon¬ 
strated by means of the baroscope , 
which consists of a scalebeam, at one 
of whose extremities a small leaden 
weight is supported, and at the 
other there is a hollow copper sphere 
(fig. 113). In the air they exactly 
balance one another; but when they 
are placed under the receiver of the 
air pump and a vacuum is produced, 

the sphere sinks; thereby showing that in reality it is heavier than 
the small leaden weight. Before the air is exhausted each bodv is 























ON GASES. 


134 


[ 169 - 


buoyed up by the weight of the air which it displaces. Blit as the 
sphere is much the larger of the two, its weight undergoes most apparent 
diminution, and thus, though in reality the heavier body, it is ba¬ 
lanced by the small leaden weight. It may be proved by means of the 
same apparatus that this loss is equal to the weight of the displaced 
air. Suppose the volume of the sphere is 10 cubic inches. The 
weight of this volume of air is 3T grains. If now this weight be added 
to the leaden weight, it will overbalance the sphere in air, but will 
exactly balance it in vacuo. 

The principle of Archimedes is true for bodies in air ; all that has been 
said about bodies immersed in liquids applies to them, that is, that when 
a body is heavier than air it will sink, owing to the excess of its weight 
over the buoyancy. If it is as heavy as air, its weight will exactly 
counterbalance the buoyancy, and the body will float in the atmosphere. 
If the body is lighter than air, the buoyancy of the air will prevail, and 
the body will rise in the atmosphere until it reaches a layer of the same 
density as its own. The force of the ascent is equal to the excess of the 
buoyancy over the weight of the body. This is the reason why smoke, 
vapours, clouds, and air balloons rise in the air. 


AIR BALLOONS. 


169. Air balloons. —Air balloons are hollow spheres made of some 
light impermeable material, which, when filled with heated air, with 
hydrogen gas, or with coal gas, rise in the air in virtue of their relative 
lightness. 

They were invented by the brothers Montgolfier, of Annonay, and the 
first experiment was made at that place in June 1783. Their balloon 
was a sphere of 40 yards in circumference, and weighed 500 pounds. 
At the lower part there was an aperture, and a sort of boat was sus¬ 
pended, in which fire was lighted to heat the internal air. The balloon 
rose to a height of 2,200 yards, and then descended without any accident. 

Charles, a professor of physics in Paris, substituted hydrogen for hot 
air. He himself ascended in a balloon of this kind in December 1783. 
The use of hot air balloons was entirely given up in consequence of the 
serious accidents to which they were liable. 

Since then, the art of ballooning has been greatly extended, and manv 
ascents have been made. That which Gay-Lussac made in 1804 was the 
most remarkable for the facts with which it has enriched science, and for 
the height which he attained—23,000 feet above the sea level. At this 
height the barometer descended to 12-6 inches, and the thermometer, 
which was 31° C. on the ground, was 9 degrees below zero. 


AIK BALLOONS. 


135 


- 170 ] 

In these high regions, the dryness was such on the day of Gay-Lussac’s 
ascent, that hygrometric substances, such as paper, parchment, etc., 
became dried and crumpled as if they had been placed near the tire. 
The respiration and circulation of the blood were accelerated in conse¬ 
quence of the great rarefaction of the air. Gay-Lussac’s pulse made 
120 pulsations in a minute, instead of 66, the normal number. At this 
great height the sky had a very dark blue tint, and an absolute silence 
prevailed. 

One of the most remarkable recent ascents was made by Mr. Glaisher 
and Mr. -Coxwell, in a large balloon belonging to the latter. This was 
filled with 90,000 cubic feet of coal gas (sp. gr. 0’37 to 0*33) ; the weight 
of the load was 600 pounds. The ascent took place at 1 p.m. on 
September 5,1861; at 1° 28' they had reached a height of 15,750 feet, 
and in eleven minutes after a height of 21,000 feet, the temperature 
being — 10T ; at 1° 50' they were at 26,200 feet, with the thermometer at 
-15-2°. At 1° 52' the height attained was 39,000 feet, and the tempera¬ 
ture —160 C. At this height the rarefaction of the air was so great 
and the cold so intense that Mr. Glaisher fainted, and could no linger 
observe. According to an approximate estimation the lowest barometric 
height they attained was 7 inches, which would correspond to a height 
of 36,000 to 37,000 feet. 

170. Construction and management of balloons.— A balloon is 
made of long bands of silk sewed together and covered with caoutchouc 
varnish, which renders it air-tight. At the top there is a safety valve 
closed by a spring, which the aeronaut can open at pleasure, by means of 
a cord. A light wicker-work boat is suspended by means of cords to a 
net-work, which entirely covers the balloon. 

A balloon of the ordinary dimensions, which can carry three persons, 
is about 16 yards high, 12 yards in diameter, and its volume when it is 
quite full is about 680 cubic yards. The balloon itself weighs 200 
pounds; the accessories, such as the rope and boat, 100 pounds. 

The balloon is filled either with hydrogen or with coal gas. Although 
the latter is heavier than the former, it is generally preferred, because it 
is cheaper and more easily obtained. It is passed into the balloon from 
the gas reservoir by means of a flexible pipe. It is important not to 
fill the balloon quite full, for the atmospheric pressure diminishes as 
it rises (fig. 114), and the gas inside expanding in consequence of its 
elastic force, tends to burst it. It is sufficient for the ascent if the weight 
of the displaced air exceeds that of the balloon by 8 or 10 pounds. And 
this force remains constant so long as the balloon is not quite distended 
by the dilatation of the air in the interior. If the atmospheric pressure, 
for example, has diminished to one half, the gas in the balloon, according 
to Boyle and Mariotte’s law, has doubled its volume. . The volume of 



136 


ON GASES. 


[ 170 - 



the air displaced is therefore twice as great; hut, since its density has 
become only one half, the weight, and consequently the upward buoyancy, 
are the same. When once the balloon is completely dilated, if it con¬ 
tinue to rise the force of the ascent 
decreases, for the volume of the 
displaced air remains the same, but 
its density diminishes, and a time 
arrives at which the buoyancy is 
equal to the weight of the balloon. 
The balloon can now only take a 
horizontal direction, carried by the 
currents of air which prevail in the 
atmosphere. The aeronaut knows 
by the barometer whether he is 
ascending or descending; and by 
the same means he determines the 
height which he has reached. A 
long flag fixed to the boat would in¬ 
dicate, by the position it takes either 
above or below, whether the balloon 
is descending or ascending. 

When the aeronaut wishes to de¬ 
scend, he opens the valve at the top of 
the balloon by means of the cord, 
which allows gas to escape, and the 
balloon sinks. If he wants to descend 
more slowly, or to rise again, he 
empties out bags of sand, of which 
there is an ample supply in the car. 
The descent is facilitated by means 
of a grappling iron fixed to the 
boat. When once this is fixed to 
any obstacle, the balloon is lowered 
by pulling the cord. 

The only practical applications 
which air balloons have hitherto had 
Fig. 114 . have been in military reconnoitring. 

At the battle of Fleurus, in 1794, a 
captive balloon, that is, one held by a cord, was used, in which there was 
an observer who reported the movements of the enemy by means of 
signals. At the battle of Solferino the movements and dispositions of 
the Austrian troops were watched by a captive balloon, and in the war 
in America balloons were frequently used. The whole subject of military 























AIR BALLOONS. 


137 


- 171 ] 


ballooning has been treated in two papers by Lieut. Groves and by 
Captain Beaumont in a recent volume of the Professional Papers of the 
Royal Engineers. Many ascents have recently been made by Mr. 
Glaisher for the purpose of making meteorological observations in the 
higher regions of the atmosphere. Air balloons can only be truly useful 
when they can be guided, and as yet all attempts made with this view 
have completely failed. There is no other course at present than to rise 
in the air, until there is a 
current which has more or 
less the desired direction. 

171. Parachute. —The 
object of the parachute 
is to allow the aeronaut 
to leave the balloon, by 
giving him the means of 
lessening the rapidity of 
his descent. It consists 
of a large circular piece 
of cloth (fig. 115) about 
16 feet in diameter, and 
which by the resistance of 
the air spreads out like 
a gigantic umbrella. In 
the centre there is an 
aperture, through which 
the air compressed by 
the rapidity of the de¬ 
scent, makes its escape; 
for otherwise oscillations 
might be produced, which, 
when communicated to the 
boat, would be dangerous. 

In fig. 114 there is a parachute attached to the net-work of the balloon 
by means of a cord which passes round a pulley, and is fixed at the 
other end to the boat. When the cord is cut, the parachute sinks, at 
first very rapidly, but more slowly as it becomes distended, as represented 
in the figure. 















138 


ON GASES. 


[ 172 - 


CHAPTER IV. 

APPARATUS FOUNDED ON THE PROPERTIES OF AIR. 

172. Air pump. —The air pump is an instrument by which a vacuum 
can be produced in a given space, or rather by which air can be greatly 
rarefied, for an absolute vacuum cannot be produced by its means. It 
was invented by Otto von Guericke in 1650, a few years after the inven¬ 
tion of the barometer. 



Pig. 116 . 


The air pump, as now usually constructed, may be described as follows : 
in fig. 116, which shows the general arrangement, E is the receiver , in 
which the vacuum is to be produced. It is a bell glass, resting on a plate 
I) of thick glass ground perfectly smooth. In the centre of D, at C, there 
is an opening by which a communication is made between the interior of 

























172] APPARATUS POUNDED ON THE PROPERTIES OF AIR. 1 o9 

the receiver and of the cylinders P, Q. This communication is effected 
by a tube or pipe passing through the body of the plate A, and then 
branching off at right angles, as shown by Kco, Kcs, in fig. 117 , which 

represents a horizontal section of the machine. In the cylinders_which 

are commonly of glass, and which are firmly cemented to the plate A_ 



are two pistons P and Q, fitting air-tight. Each piston is moved by a 
rack, working with a pinion H, turned by a handle M. This is shown more 
plainly in fig. 118 , which represents a vertical section of the machine 
through the cylinders; here H is the pinion, and MN the handl.e. When 
M is forced down, one piston is raised, and the other depressed. When 
M’s action is reversed, the former piston is depressed, and the latter 
raised. 

The action of the machine is this : Each cylinder is fitted with a valve 
so contrived that when its piston is raised, communication is opened 
between the cylinder and the receiver; when it is depressed the com¬ 
munication is closed. Now if P were simply raised, a vacuum would be 
formed below P, but as a communication is opened with the receiver, 
E, the air in E expands so as to fill both the receiver and the cylinder. 
As soon as the piston begins to descend, the communication is closed, and 
none of the air in the cylinder returns to the receiver, but, by means of 
properly constructed valves, escapes into the atmosphere. Consequently, 
the rarefaction which the air in the receiver has undergone is permanent. 
Bv the next stroke a further rarefaction is produced ; and so on, at each 
succeeding stroke. 







































140 


ON GASES. 


[ 173 - 

It is plain that when the rarefaction has proceeded to a considerable 
extent the atmospheric pressure on the top of P will be very great, but 
it will be very nearly balanced by the atmospheric pressure on the top 
of the other piston. Consequently, the experimenter will have to over¬ 
come only the difference of the two pressures. It is for this reason that 
two cylinders are employed. 

To explain the action of the valves we must go into particulars. The 
general arrangement of the interior of the cylinders is shown in fig. 118. 

Fig. 121 shows the section of the piston in 
detail. The piston is formed of two brass 
discs (X and V), screwed to one another, and 
compressing between them a series of leathern 
discs (Z), whose diameters are slightly greater 
than those of the brass discs. The leather is 
thoroughly saturated with oil, so as to slide 
air-tight, though with but little friction, within 
the cylinder. To the centre of the upper disc 
is screwed a piece, B, to which the rack, IT, 
is riveted. The piece B is pierced so as to 
put the interior of the cylinder into commu¬ 
nication with the external air. This commu¬ 
nication is closed by a valve t , held down 
by a delicate spring r. When the piston is 
moved downward, the air below the piston 
is compressed until it forces up t and es¬ 
capes. The instant the action is reversed, 
the valve t falls, and is held down by the 
Fig. 121. spring, and the pressure of the external air, 

which is thereby kept from coming in. The communication be¬ 
tween the cylinder below the piston and the receiver is opened and 
closed by the valve marked o in fig. 118, and sg in fig. 121. The rod sg 
passing through the piston is held by friction, and is raised with it; but 
is kept from being lifted through more than a very small distance bv the 
top of the cylinder, while the piston, in continuing its upward motion, 
slides over sg. When the piston descends it brings the valve with it, 
which at once cuts off the communication between the cylinder and the 
receiver. 

173. Air pump gauge.— When the pump has been worked some time 
the pressure in the receiver is indicated by the difference of level of the 
mercury in the two legs of a glass tube bent like a syphon, one of which 
is open and the other closed like the barometer. This little apparatus, 
which is called the gauge , is fixed to an upright scale, and placed 
under a small bell jar, which communicates with the receiver E by 




































141 


- 173 ] APPARATUS FOUNDED ON THE PROPERTIES OF AIR. 


a stopcock, A, inserted in the tube leading from the orifice C to the 
cylinders, fig. 116. 

Before commencing to exhaust the air in the receiver, its elastic force 
exceeds the weight of the column of mercury, which is in the closed 
branch and which consequently remains full. But as the pump is 
worked, the elastic force soon diminishes, and is unable to support the 
weight of the mercury, which sinks and tends to stand at the same level 
in both legs. If an absolute vacuum could be produced, they would be 
exactly on the same level, for there would be no pressure either on the 
one side or the other. But with the very best machines the level is 
always about a thirtieth of an inch higher in the closed branch, which 
indicates that the vacuum is not absolute, for the elastic force of the 
residue is equal to the pressure of a column of mercury of that height. 

Practically the machine can never give an absolute vacuum, for, as we 
have seen, the air becomes ultimately so rarefied that, when the pistons 
are at the bottom of the cylinder, its elastic force cannot overcome the 
pressure on the valves in the inside of the piston, which, therefore,-do 
not open. 

Theoretically an absolute vacuum is also impossible; for, since the 
volume of each cylinder is, say, — ^ at °f the receiver, only A of the air 
in the receiver is extracted at each stroke of the piston, and consequently 
it is impossible to exhaust all the air which it contains, The theoretical 
degree of exhaustion after a given number of strokes is easily calculated as 
follows :—Let A denote the volume of the receiver, including in that term 
the pipe; B the volume of the cylinder between the highest and lowest 
positions of the piston, and assume for the sake of distinctness that there is 
only one cylinder, then the air which occupied A before the piston is 
lifted occupies A+B after it is lifted, and consequently if is the density 
at the end of the first stroke and D the original density, we must have 


D x = D 


A 

A -j- B 


If D 2 is the density at the end of the second stroke we have for just the 


ame reason 


1)2 ~ A + B D ( A + B/ 


Now this reasoning will apply to n strokes . \ 

consequently D„ = D (Ag )“ 

If there are two equal cylinders, the same formula is true, but in this 
case in counting n , upstrokes and downstrokes equally reckon as one. 

It is obvious that the exhaustion is never complete since D n can be zero 
only when n is infinite. However, a number of strokes not excessively 







142 


ON GASES. 


[ 174 - 

great would render the exhaustion sensibly complete even if A is several 
times greater than B. Thus if A = 10 B, a hundred strokes will reduce 
the density from D to 0-0004 D, that is if the initial pressure is 30 in. the 
pressure at the end of 100 strokes is 0-012 of an inch. 

Practically, however, a limit is placed on the rarefaction that can be 
produced by any given machine; for, as we have seen, the air becomes 
ultimately so rarefied that, when the pistons are at the bottom of the 
cylinder its elastic force cannot overcome the pressure on the valves in 
the inside of the piston, they therefore do not open, and there is no 
further action of the machine. 

174. Doubly exhausting- stopcock.— M. Babinet has invented an 
improved stopcock, by which the exhaustion of the air can be carried to 
a very high degree. This stopcock is placed in the fork of the pipe 
leading from the receiver to the two cylinders: it is perforated by 
several channels, which are successively used by turning it into two 
different positions. Fig. 117 represents a horizontal section of the stop¬ 
cock B, in such a position that, by its central opening and two lateral 
openings, it forms a communication between the orifice K of the plate, 
and the two valves o and s. The machine then works as has been 
described. In fig. 120 the stopcock has been turned a quarter, and 
the transversal channel dl, which was horizontal in fig. 117, is now 
vertical, and its extremities are closed by the side of the hole in which 
the stopcock works. But a second channel, which was closed before, 
and which has taken the place of the first, now places the right cylinder 
alone in communication with the receiver by the channel, cbs (fig. 120) 
and it further connects the right with the left cylinder by a channel aeo 
(fig. 120) or aico (fig. 119). This channel passes from a central opening, 
a, placed at the base of the right cylinder e, across the stopcock to the 
valve o of the other cylinder, as represented in figs. 119 and 120: but 
this channel is closed by the stopcock when it is in its first position, as 
is seen in figs. 117 and 118. 

The right piston in rising exhausts the air of the receiver, but when it 
descends the exhausted air is driven into the left cylinder through the 
orifice a, the channel io, and the valve o (fig. 119), which is open. When 
the same piston ascends, that of the left sinks; but the air which is 
above it does not return into the left cylinder because the stopcock o is 
now closed. As the right cylinder continues to exhaust the air in the 
receiver, and to force it into the left cylinder, the air accumulates here, 
and ultimately acquires sufficient tension to raise the valve of the piston 
Q, which was impossible before the stopcock was turned, for it is only 
when the valves in the piston no longer open, that a quarter of a turn is 
given to the stopcock. 

175. Bianchi's air pump.— M. Bianchi lias invented an air pump which 


-175] 


APPARATUS FOUNDED ON THE PROPERTIES OF AIR. 


14;> 


has several advantages. It is made entire!} 7 of iron, and it has only one 
cylinder, which oscillates in a horizontal axis fixed at its base, as seen in 
fig. 122. A horizontal shaft, with a heavy fly-wheel, V, works in a frame, 
and is turned by a handle, M. A crank, in , which is joined to the top of 



the piston-rod, is fixed to the same shaft, and consequently at every 
revolution of the wheel the cylinder makes two oscillations. 

In some cases, as in that shown in the figure, the crank and the fly-wheel 
are on parallel axes connected by a pair of cog-wheels. The modification 
in the action produced by this arrangement is as follows. If the cog- 





















144 


ON GASES. 


[176- 


wheel on the former axis has twice as many teeth as that on the latter 
axis the pressure which raises the piston is doubled: an advantage which 
is counterbalanced by the inconvenience that now the piston will make 
one oscillation for one revolution of the fiy-wheel. 

The machine is double acting; that is, the piston P P (fig. 123) pro¬ 
duces a vacuum both in ascending and descending. This is effected by 
the following arrangements: In the piston there is a valve b opening 
upwards as in the ordinary machine. The piston rod, A A, is hollow, 
and in the inside there is a copper tube, X, by which the air makes its 
escape through the valve b. At the top of the cylinder there is a 
second valve, a, opening upwards. An iron rod, D, works with gentle 
friction in the piston, and terminates at its ends in two conical valves, 
s and s', which fit into the openings of the tube, BC, leading to the 
receiver. 

Let us suppose the piston descends. The valve s' is then closed, and 
the valve s being open, the air of the receiver passes into the space above 
the piston, while the air in the space below the piston undergoes 
compression, and raising the valve, escapes by the tube X, which com¬ 
municates with the atmosphere. When the piston ascends, the ex¬ 
haustion takes place through s', and the valve s being closed, the com¬ 
pressed air escapes by the valve a. 

The machine has a stop-cock for double exhaustion, similar to that 
already described (174). It is also oiled in an ingenious manner. A 
cup, E, round the rod is filled wfith oil, which passes into the annular 
space between the rod AA and the tube X; it passes then into a tube 
o o, in the piston, and forced by the atmospheric pressure, is uniformly 
distributed on the surface of the piston. 

The apparatus is of iron, and can consequently be made of much 
greater dimensions than the ordinary machine. A vacuum can also be 
produced with it in far less time and in larger apparatus. 

176. Sprengel's air pump.— Sprengel has devised a form of air-pump, 
which depends on the principle of converting the space to be exhausted 
into a Torricellian vacuum. Theidea and construction of the apparatus 
are thus described by the inventor. 

If an aperture be made in the top of a barometer tube the mercurv 
sinks and draws in air; if the experiment be so arranged as to allow 
air to enter along wfith mercury, and that the supply of air is limited 
while that of mercury is unlimited, the air will be carried away, and a 
vacuum produced. The following is the simplest form of the apparatus 
in which this action is realised. In fig. 123 c d is a glass tube longer than 
a barometer, open at both ends, and connected by means of india-rubber 
tubing with a funnel A filled with mercury and supported by a stand. 
Mercury is allowed to fall in this tube at a rate regulated by a clamp 


-177] 


APPARATUS FOUNDED ON THE PROPERTIES OF AIR. 


145 



at c; the lower end of the tube cd fits in the flask B, which has a spout 
at the side a little higher than the lower end of cd ; the upper part 
has a branch at x to which a receiver It can he tightly fixed. When the 
clamp at c is opened, the first portion of mercury which runs out closes the 
tube and prevents air from entering 
below. As the mercury is allowed 
to run down, the exhaustion begins, 
and the whole length of the tube 
from x to d is filled with cylinders 
of air and mercury having a down¬ 
ward motion. Air and mercury 
escape through the spout of the 
bulb B which is above the basin 
A, where the mercury is collected. 

It is poured back from time to time 
into the funnel A to be repassed 
through the tube until the ex¬ 
haustion is complete. As this 
point is approached the enclosed 
air between the mercury cylinders 
is seen to diminish, until the lower 
part of cd forms a continuous 
column of mercury about 30 inches 
high. Towards this stage of the 
process a noise is heard like 
that of a water hammer when 
shaken ; the operation is completed 
when the column of mercury en¬ 
closes no air, and a drop of mercury 
falls on the top of the column 
without enclosing the slightest air 
bubble. The height of the column 
then represents the height of the 
column of mercury in the baro¬ 
meter in other words, it is a baro- 
meter whose Torricellian vacuum 

is the receiver R. This apparatus has been used with great success in 
experiments in which a very complete exhaustion is required as in the 
preparation of Geissler’s tubes. (See Book X. Chapter VI.) It may 
be advantageously combined with an exhausting syringe which removes 
the greater part of the air, the exhaustion being completed as above. 

177. Condensing pump. —The condensing pump is an apparatus for 
compressing air or any other gas. The form usually adopted is the 

H 








14G 


ON GASES. 


[ 177 - 

following : In a cylinder, A, of small diameter (fig. 120), there is a solid 
piston, the rod of which is moved by the hand. The cylinder is provided 
with a screw which fits into the receiver, K. Fig. 125 show T s the 
arrangement of the valves, which are so constructed that the lateral 
valve, o, opens from the outside, and the lower valve, s, from the 
inside. 



When the piston descends, the valve o closes, and the elastic force of 
the compressed air opens the valve s, which thus allows the compressed 
air to pass into the receiver. When the piston ascends, s closes and o 
opens, and permits the entrance of fresh air, which in turn becomes com¬ 
pressed by the descent of the piston, and so on. 

This apparatus is chiefly used for charging liquids with gases. For 


































































- 178 ] APPARATUS FOUNDED ON THE PROPERTIES OF AIR. 147 

this purpose the stopcock, B, is connected with a reservoir of the gas, by 
means of the tube, D. The pump exhausts this gas, and forces it into 
the vessel K, in which the liquid is contained. The artificial gaseous 
waters are made hv means of analogous apparatus. 

178. Uses of tlie air pump.— A great many experiments with the 
air pump have been already described. Such are the mercurial rain 
(13), the fall of bodies in vacuo (68), the bladder (138), the bursting 



Fig. 127. Fi S- 128 - 


of a bladder (144), the Magdeburg hemispheres (145), and the baro¬ 
scope (168). 

The fountain in vacuo (fig. 127) is an experiment made with the air 
pump, and shows the elastic force of the air. It is a flask containing 
water and air; the neck is closed by a cork through which passes a tube 
dipping in the liquid. The flask being placed under the receiver, a jet 
of water issues from the top of the tube as soon as the air is sufficiently 
rarefied. This is due to the elastic force of the air enclosed in the flask. 

h 2 





















148 


ON GASES. 


[178- 

Fig. 128 represents an experiment illustrating the effect of atmospheric 
pressure on the human body. A glass vessel, open at both ends, being 
placed on the plate of the machine, the upper end of the cylinder is closed 
by the hands, and a vacuum is made. The hand then becomes pressed by 
the weight of the atmosphere, and can only be taken away by a great 
effort. And as the elasticity of the fluids contained in the organs is not 
counterbalanced by the weight of the atmosphere, the palm of the hand 
swells, and blood tends to escape from the pores. 



A 


B 


Fig. 129. 




Fig. 130. 


By means of the air pump it may be shown that air, by reason of the 
oxygen it contains, is necessary for the support of combustion and of life. 
For if we place a lighted taper under the receiver, and begin to exhaust 
the air, the flame becomes weaker as rarefaction proceeds, and is finally 
extinguished. Similarly an animal faints and dies, if a vacuum is formed 
in a receiver under which it is placed. Mammalia and birds soon die in 



















- 180 ] APPARATUS FOUNDED ON THE PROPERTIES OF AIR. 149 

vacuo. Fishes and reptiles support the loss of air for a much longer 
time. Insects can live several days in vacuo. 

Substances liable to ferment may be kept in vacuo for a long time 
without alteration, as they are not in contact with oxygen, which is 
necessary for fermentation. Food kept in hermetically closed cases, 
from which the air had been expelled, has been found as fresh after 
several years as on the first day. 

179. Hero’s fountain —Hero’s fountain, Which derives its name from 
its inventor, Hero, who lived at Alexandria, 120 b.c., depends on the 
elasticity of the air. It consists of a brass dish, D (fig. 129), and of two 
glass globes, M and N. The dish communicates with the lower part of 
the globe, N, by a long copper tube, B; and another tube, A, connects the 
two globes. A third tube passes through the dish to the lower part of the 
globe, M. This tube having been taken out, the globe, M, is partially 
filled with water, the tube is then replaced, and water is poured into the 
dish. The water flows through the tube, B, into the lower globe, and 
expels the air, which is forced into the upper globe; the air thus com¬ 
pressed, acts upon the water, and makes it jet out as represented in the 
figure. If it were not for the resistance of the atmosphere, and friction, 
the liquid would rise to a height above the water in the dish equal to 
the difference of the level in the two globes. 

180. Intermittent fountain.— The intermittent fountain depends 
partly on the elastic force of the air and partly on the atmospheric pres¬ 
sure. It consists of a stoppered glass globe, C (fig. 130), provided with 

4 two or three capillary tubulures, D. A glass tube open at both ends 
reaches at one end to the upper part of the globe, C ; the other end ter¬ 
minates just above a little aperture in the dish, B, which supports the 
whole apparatus. 

The water with which the globe, C, is nearly two-thirds filled, runs 
out by the tubes, D, as shown in the figure; the internal pressure at D 
being equal to the atmospheric pressure, together with the weight of the 
column of water, CD, while the external pressure at that point is only 
that of the atmosphere. These conditions prevail so long as the lower 
end of the glass tube is open, that is, so long as air can enter C and keep 
the air in C at the same density as the external air ; but the apparatus is 
arranged so that the orifice in the dish B does not allow so much water 
to flow out as it receives from the tubes, D, in consequence of which 
the level gradually rises in the dish, and closes the lower end of the 
glass tube. As the external air cannot now enter the globe, C, the air 
becomes rarefied in proportion as the flow continues, until the pressure 
of the column of water, CD, together with the tension of the air 
contained in the globe, is equal to this external pressure at D ; the flow 
consequently stops. But as water continues to flow out of the dish, the 




ON GASES. 


150 


[ 181 - 


tube A becomes open again, air enters, and the flow recommences, and so 
on, as long as there is water in the globe, C. 

181. The syphon.— The syphon is a bent tube open at both ends and 
with unequal legs (fig. 131). It is used in transferring liquids in the 
following manner: The syphon is filled with some liquid, and the two 
ends being closed, the shorter leg is dipped in the liquid, as represented 
in fig. 131; or the shorter leg having been dipped jin the liquid, the air 
is exhausted by applying- the mouth at B. A vacuum is thus pro¬ 
duced, the liquid in C rises and fills the tube in consequence of the 
atmospheric pressure. It will then run out through the syphon as long 
as the shorter end dips in the liquid. 

A syphon of the form represented in fig." 132 is used where the. 
presence of the liquid in the mouth would be objectionable. A tube 
M, is attached to the longer branch, and it is filled by closing the end P, 
and sucking at O. An enlargement, M, renders the passage of any liquid 
into the mouth more difficult. 



Fig. 131. 


Fig. 132. 


To explain this flow of water from the syphon, let us suppose it filled 
and the short leg immersed in the liquid. The pressure then acting on 
C, and tending to raise the liquid in the tube, is the atmospheric pressure 
minus the height of the column of liquid DC. In like manner, the pres¬ 
sure on the end of the tube B, is the weight of the atmosphere less the 
pressure of the column of liquid AB. But as this latter column is 
longer than CD, the force acting at B is less than the force acting at C 
and consequently a flow takes place proportional to the difference 
between these two forces. The flow will therefore be more rapid in 
proportion as the difference of level between the aperture B, and the 
surface of the liquid in C, is greater. 

182. The intermittent syphon —In the intermittent syphon the 






















PUMPS. 


151 


- 184 ] 


flow is not continuous. It is arranged in a vessel, so that the shorter leg 
is near the bottom of the vessel, while the longer leg passes through it 
(fig. 133). Being fed by a constant supply of 
water, the level gradually rises both in the 
vessel and in the tube to the top of the syphon, 
which it fills, and water begins to flow out. 

But the apparatus is arranged so that the flow 
of the syphon is more rapid than that of the 
tube which supplies the vessel, and consequently 
the level sinks in the vessel until the shorter 
branch no longer dips in the liquid; the sy¬ 
phon is then empty, and the flow ceases. But 
as the vessel is continually fed from the same 
source, the level again rises, and the same Fig. 133. 

series of phenomena is reproduced. 

The theory of the intermittent syphon explains the natural inter¬ 
mittent springs which are found in many countries, and of which there is 
an excellent example near Giggleswick in Yorkshire. Many of these 
springs furnish water for several days or months, and then, after stopping 
for a certain interval, again recommence. In others the flow stops and 
recommences several times in an hour. 

These phenomena are explained by assuming that there are subter¬ 
ranean fountains, which are more or less slowly filled by springs, and 
which are then emptied by fissures so occurring in the ground as to form 
an intermittent syphon. 

183. Different kinds of pumps. — Pumps are machines which serve 
to raise water either by suction, by pressure, or by both effects combined; 
they are consequently divided into suction or lift pumps , force pumps, and 
suction and forcing pumps. 

184. Suction pump. —Fig. 134 represents a model of a suction pump 
such as is used in lectures, but which has the same arrangement as the 
pumps in common use. It consists, 1st, of a glass cylinder, B, at the 
bottom of which there is a valve, S, opening upwards ; 2nd, of a suction 
tube, A, which dips into the reservoir from which water is to be raised ; 
3rd, of a piston , which is moved up and down by a rod worked by a 
handle, P. The piston is perforated by a hole, the upper aperture is 
closed by a valve, 0, opening upwards. 

When the piston rises from the bottom of the cylinder, a vacuum is 
produced below, and the valve O is kept closed by the atmospheric 
pressure, while the air in the pipe A, in consequence of its elasticity, raises 
the valve S, and partially passes into the cylinder. The air being thus 
rarefied, water rises in the pipe until the pressure of the liquid column, 
together with the tension of the rarefied air which remains in the tube, 







ON GASES. 


152 


[ 185 - 


counterbalances the pressure of the atmosphere on the water of the 
reservoir. 

When the piston descends, the valve S closes by its own weight, 

and prevents the return of the 
air from the cylinder into the 
tube A. The air compressed by 
the piston opens the valve 0, and 
escape s into the atmosphere by 
the pipe C. With a second stroke 
of the piston the same series of 
phenomena is produced, and after 
a few strokes the water reaches 
the cylinder. The effect is now 
somewhat modified; during the 
descent of the piston, the valve 
S closes, and the water raises the 
valve O, and passes above the 
piston, by which it is rais d into 
the upper reservoir D. There is 
now no more air in the pump, 
and the water, forced by the at¬ 
mospheric pressure, rises with the 
piston, provided that when it is at 
the summit of its course it ig 
not more than 34 feet above the 
level of the water in which the 
tube A dips, for we have seen 
(147) that a column of water of 
this height is equal to the pres¬ 
sure of the atmosphere. 



Fig. 134. 


In practice the height of the tube A does not often exceed 26 to 28 
feet, for, although the atmospheric pressure can support a higher column, 
the vacuum produced in the barrel is not perfect, owing to the fact that 
the piston does not fit exactly on the bottom of the barrel. But when 
the water has passed the piston, it is the ascending force of the latter 
which raises it, and the height to which it can be brought depends on the 
force which moves the piston. 

185. Suction and force pump.— The action of this pump, a model of 
which is represented in fig. 135, depends both on exhaustion and on 
pressure. At the base of the barrel, where it is connected with the tube 
A, there is a valve, S, which opens upwards. Another valve, 0, opening 
in the same direction, closes the aperture of a conduit, which passes from 
a hole, o, near the valve S into a vessel, M, which is called the air 














PUMPS. 


153 


-158] 

chamber. From this chamber there is another tube, D, up which the 
water is forced. 

At each ascent of the piston B, which is solid, the water rises through 
the tube A into the barrel. When the piston sinks, the valve S closes, 
and the water is forced through the valve 0 into the reservoir M, end 
from thence into the tube D. The height to which it can be raised in 
this tube depends solely on the motive force which works the pump. 



If the tube D were a prolongation of the tube J ao, the flow would be 
intermittent; it would take place when the piston descended, and would 
cease as soon as it ascended. But between these tubes there is an interval, 
which, by means of the air in the reservoir M, ensures a continuous flow. 
The water forced into the reservoir M divides into two parts, one of 
which, rising in D, presses on the water in the reservoir by its weight, 
while the other, in virtue of this pressure, rises in the reservoir above the 
lower orifice of the tube D, compressing the air above; Consequently, 
when the piston ascends, and no longer forces the water into M, the airof the 

h 3 




























154 


ON GASES. 


[ 186 - 

reservoir, by the pressure it has received, reacts on the liquid, and raises it 
in the tube D, until the piston again descends, so that the jet is continuous. 

186. Fire engine. —The principle of the suction and forcing pump is 
applied in the case of the hydraulic press, and also of the tire engine. 

The fire engine differs from the 
model described, in the fact that 
the barrels dip into the water 
which is to be raised. Fig. 136 
represents a section of this ma¬ 
chine. There are two solid pis¬ 
tons, P and P', the rods of which 
are worked by a lever not shown 
in the figure. When the piston 
P' is raised the valve d' opens, 
and water enters the barrel. 
When it is forced down, the 
valve d' closes, and water is forced 
through the valve c' into the 
larger air chamber A. One end of 
the tube at is near the bottom 
of the air chamber, while the other fits into the roof, and on the out¬ 
side of the roof there is a tube, bb', to which the hose is attached. By 
means of the pressure which the compressed air in the chamber exerts 
on the water a strong j et is forced through the delivery tube, and can be 
sent in any direction. Both pistons are so fastened to the lever that when 
one is forced down the other rises, consequently water is being forced 
into the air chamber without cessation. 

187. Velocity of efflux. Torricelli’s theorem.— Let us imagine 
an aperture made in the bottom of any vessel, and consider the case of a 
particle of liquid on the surface, without reference to those which are 
beneath. If this particle fell freely, it would have a velocity on reaching 
the orifice equal to that of any other body falling through the distance 
between the level of the liquid and the orifice. This, from the laws of 
falling bodies, is V2gh, in which g is the accelerating force of gravity, and 
h the height. If the liquid be maintained at the same level, for instance 
by a stream of water running into the vessel sufficient to replace what 
has escaped, the particles will follow one another with the same velocity, 
and will issue in the form of a stream. Since pressure is transmitted 
equally in all directions, a liquid would issue from an orifice in the side 
with the same velocity, provided the depth were the same. 

The law of the velocity of efflux was discovered by Torricelli. It mav 
be enunciated as follows. The velocity of efflux is the velocity which a 
freely falling body would have on reaching the orifice after having started 











DIRECTION OF JET. 


155 


- 189 ] 

from a state of rest at the surface. It is algebraically expressed by the 
formula 

It follows directly from this law, that the velocity of efflux depends 
on the depth of the orifice below the surface, and not on the nature of 
the liquid. Through orifices of equal size and of the same depth, water 
and mercury would issue with the same velocity, for although the 
density of the latter liquid is greater, the weight of the column, and 
consequently the pressure, is greater too. It follows further that the 
velocities of efflux are directly proportional to the square roots of the 
depths of the orifices. Water would issue from an orifice 100 inches 
below the surface with ten times the velocity with which it would 
issue from one an inch below the surface. 

The quantities of water which issue from orifices of different areas, 
are very nearly proportional to the size of the orifice, provided the level 
remains constant. 

188. Direction of the jet from lateral orifices. —From the principle 
of the equal transmission of pressure, water issues from an orifice in the 
side of a vessel with the same velocity as from an aperture in the bottom 
of a vessel at the same depth. Each particle of a jet issuing from the 
side of a vessel begins to move horizontally with the velocity above 
mentioned, but is at once drawn downward by the force of gravity, in 
the same manner as a bullet fired from a gun, with its axis horizontal. 
It is well known that the bullet describes a parabola with a vertical axis, 
the vertex being the muzzle of the gun. Now since each particle of the 
jet moves in the same curve, the jet itself take the parabolic form, as 
shown in fig. 137. 

It may be remarked, that in every parabola there is a certain point 
called the focus, and that the 
distance from the vertex to the 
focus fixes the magnitude of a 
parabola in much the same 
manner as the distance from 
the centre to the circumference 
fixes the magnitude of a circle. 

Now it is easily capable of proof 
that the focus is as much below 
as the surface of the water is 
above the orifice. Accordingly 
the jets formed by water com¬ 
ing from orifices at different depths below the surface, take different 
orms, as shown in fig. 137. 

189. Height of the jet.— If a jet issuing from an orifice in a vertical 
direction has the same velocity as a body would have which fell from 







156 


ON GASES. 


[ 190 - 

tlie surface of the liquid to that orifice, the jet ought to rise to the level 
of the liquid. It does not, however, reach this; for the particles 
which fall hinder it. But by inclining the jet at a small angle with the 
vertical, it reaches about ~ of the theoretical height, the difference being 
due to friction and to the resistance of the air. By experiments of this 
nature the truth of Torricelli’s law has been demonstrated. 

190. Quantity of efflux. Vena contracta,— If we suppose the 
sides of a vessel containing water to be thin, and the orifice to be a 
small circle whose area is A, we might think that the quantity of water 
E discharged per second would be given by the formula A \Z2gh, 
since each particle has, on the average, a velocity equal to */2gh, and 
particles issue from each point of the orifice. But this is by no means 
the case. This may be explained by reference to fig. 138, in which AB 
represents an orifice in the bottom of a vessel—what is true in this case 
being equally true of an orifice in the side of the vessel. Every particle 
above AB endeavours to pass out of the vessel, and in so doing exerts a 
pressure on those near it. Those that issue near A and B exert pressures 
in the directions MM and NN; those near the centre of the orifice in 
the direction RQ, those in the intermediate parts in the directions PQ, 
PQ. In consequence, the water within the space PQP is unable to 
escape, and that which does escape, instead of assuming a cylindrical 
form, at first contracts, and takes the form of a truncated cone. It is 
found that the escaping jet continues to contract, until at a distance 
from the orifice about equal to the diameter of the orifice. This part of 
the jet is called the vena contracta. It is found that the area of its 
smallest section is about f or 062 of that of the orifice. 
Accordingly the true value of the efflux per second is 
given approximated by the formula 
E = 062A ^ 2 ~gh 

or the actual value of E is about 0-62 of its theoretical 
amount. 

191. Influence of tubes on the quantity of efflux. 

—The result given in the last article has reference to an 
aperture in a thin wall. If a cylindrical or conical efflux- 
tube or ajutage is fitted to the aperture, the amount of the 
efflux is considerably increased, and in some cases falls but little short of 
its theoretical amount. 

A short cylindrical ajutage, whose length is from two to three times 
its diameter, has been found to increase the efflux per second to about 
0-82A */Xgli. In this case, the water on entering the ajutage forms a 
contracted vein (fig. 139), just as it would do on issuing freely into the 
air; but afterwards it expands, and, in consequence of the adhesion of 
the water to the interior surface of the tube, has, on leaving the ajutage, 


par 

^ \ ? 




M| i N 


Pig. 138. 



QUANTITY OF EFFLUX. 


157 


- 192 ] 

a section greater than that of the contracted vein. The contraction of 
the jet within the ajutage causes a partial vacuum. If an aperture is 
made in the ajutage, near the point of greatest 
contraction, and fitted with a vertical tube, 
the other end of which dips into water (fig. 

139), it is found that water rises in the vertical 
tube, thereby proving the formation of a partial 
vacuum. 

If the ajutage has the form of a conic frustum 
whose larger end is at the aperture, if the 
dimensions are properly chosen, the efflux per 
second may be raised to 0-92A\/2^7i. If the 
smaller end of a frustum of a cone of suitable 
dimensions be fitted to the orifice, the efflux 
may be still further increased, and fall very 
little short of the theoretical amount. 

When the ajutage has more than a certain 
length, a considerable diminution takes place in 
the amount of the efflux, for example if its 
length is 48 times its diameter, the efflux is 
reduced to 0'63A^/2gh. This arises from the 
fact, that when water passes along cylindrical 
tubes, the resistance increases with the length. This effect will be best 
understood by the following statement. If in fig. 139, we suppose the 
ajutage to be replaced by a tube exceeding its diameter in length by a 
hundred times, at least, the efflux per second E x will be related to that 
from the ajutage E as given above in a manner approximately given by 

the formula Ej=Ex 7*376where D denotes the diameter of the 

tube, and L its length, thus if the diameter were 1 inch, and the length 
300 feet, the efflux per second E r would be about one-eighth part of E. 
This result is true of water at ordinary temperatures. The resistance 
which gives rise to this result is called hydraulic friction ; it is indepen¬ 
dent of the material of the tube, provided it be not roughened; but 
depends in a considerable degree on the viscosity of the liquid; for 
instance, ice-cold water experiences a greater resistance than lukewarm 
water. 

192. Form of the jet.— After the contracted vein, the jet has the 
form of a solid rod for a short distance, but then begins to separate into 
drops which present a peculiar appearance. They seem to form a series of 
ventral and nodal segments (fig. 141). The ventral segments consist of 
drops extended in a horizontal direction, and the nodal segments in a 
longitudinal direction. And as the ventral and nodal segments have 


Eig. 139. 



Fig. 140. 









158 


ON GASES. 


[193- 

respectively a fixed position, eacli drop must alternately become elongated 
and flattened while it is falling (fig. 142). Between any two drops 
there are smaller ones, so that the whole jet has a tube-like appear¬ 
ance. 

If the aperture is not circular the form of the jet undergoes curious 
changes. 

j 193. Hydraulic tourniquet. —If water be contained in a vessel, 
and an aperture made in one of the sides, the pressure at this point is 



Fig. 141. Fig. 142. Fig. 143. 


removed, for it is expended in forcing out the water; but it remains on 
the other side; and if the vessel were moveable in a horizontal direction 
it would move in a direction opposite that of the issuing jet. This is il¬ 
lustrated by the apparatus known as the hydraulic tourniquet , or Barker's 
mill (fig. 143). It consists of a glass vessel, M, containing water, and 
capable of moving about its vertical axis. At the lower part there is 
a tube, C, bent horizontally in opposite directions at the two ends. If 
the vessel were full of water and the tubes closed, the pressures on the 
sides of C would balance each other, being equal and acting in contrary 
directions; but, being open, the water runs out, the pressure is not 
exerted on the open part, but only on the opposite side, as shown in the 
figure, A. And this pressure, not being neutralised by an opposite 












WATER-WHEELS. 


159 


- 195 ] 

pressure, imparts a rotatory motion in the direction of the arrow, the 
velocity of which increases with the height of the liquid, and the size 
of the aperture. 

Segner’s water wheel and the reaction machine depend on this prin¬ 
ciple. Kotating fireworks also act on the same principle : that is, an 
unbalanced reaction from the heated gases which issue from openings in 
them gives them motion in the opposite direction. 

194. Water wheels. Turbines. —When water is continuously flow¬ 
ing from a higher to a lower level, it may be used as a motive power. 
This is effected by means of water wheels ; that is, wheels provided with 
buckets or float-boards at the circumference, and on which the water 
acts either by pressure or by impact. 

Water wheels turn in a vertical plane round a horizontal axis, and are 
of two principal kinds, undershot and overshot. 

In undershot wheels the float-boards are at right angles to the circum¬ 
ference of the wheel. The lowest float-boards are immersed in the- 
water, which flows with a velocity depending on the height of the fall. 
Such wheels are applicable where the quantity of water is great, but the 
fall inconsiderable. 

Overshot wheels are used with a small quantity of water which has a 
high fall, as with small mountain streams. On the circumference of the 
wheel there are buckets of a peculiar shape. The water falls into the 
buckets on the upper part of the wheel, which is thus moved by the 
weight of the water, and as each bucket arrives at the lowest point of 
revolution it discharges all the water, and ascends empty. 

The turbine is a horizontal water-wheel, and is similar in principle to 
the hydraulic tourniquet. But instead of the horizontal tubes there is a 
horizontal drum, containing curved vertical walls; the water, in issuing 
from the turbine, pressing against these walls, exerts a reaction, and 
turns the whole wheel about a vertical axis. 

Turbines have the advantage of being of small bulk for their power, 
and equally efficient for the highest and the lowest falls. 

In all prime movers worked by a fall of water, it is of the utmost im¬ 
portance to prevent the water from acting on the machine by impact, 
and thereby to prevent the great loss of power which is always occasioned 
by the impact of imperfectly elastic bodies. 

195. Mariotte’s bottle, its use. —Mariotte’s bottle presents many 
curious effects of the atmospheric pressure, and furnishes a means of 
obtaining a constant flow of water. It consists of a large narrow- 
mouth bottle, in the neck of which there is a tightly-fitting cork (fig. 
144). Through this a tube passes, open at both ends. In the sides of 
the bottle there are three tubulures, each with a narrow orifice, and 
which can be closed at will. 


160 


ON GASES. 


[195- 

The bottle and tlie tube being quite filled with water, let us consider 
what will be the effect of opening successively one of the tubulures, a, b, 
and c, supposing, as represented in the figure, 
that the lower extremity of g is between the 
tubulures b and c. 

i. If the tubulure b is open the water flows 
out, and the surface sinks in the tube g until 
it is on the same level as b, when the flow 
stops. This flow arises from the excess of 
pressure at the point e over that at b. The 
pressure at e is the same as the pressure of the 
atmosphere. But when once the level is the 
same at b and at e, the efflux ceases, for the 
atmospheric pressure on all points of the same 
horizontal layer, be, is the same (90). 

ii. If now the tubulure b is closed, and a 
opened, no efflux takes place ; on the contrary, 
air enters by the orifice a, and water ascends in 

the tube g, as high as the layer ad, and then equilibrium is established. 

iii. If the orifices a and b are closed, and c opened, an efflux having 
constant velocity takes place, as long as the level of the water is not 
below the open end, l, of the tube. Air enters bubble by bubble at l, 
and takes the place of the water which has flowed out. 

In order to show that the efflux at the orifice c is constant, it is neces¬ 
sary to demonstrate that the pressure on the horizontal layer ch is always 
equal to that of the atmosphere in addition to the pressure of the column 
hi. Now suppose that the level of the water has sunk to the layer ad. 
The air which has penetrated into the flask supports a pressure equal to 
that of the atmosphere diminished by that of the column of liquid, pn, 
or II— pn. In virtue of its elasticity this pressure is transmitted to the 
layer ch. But this layer further supports the weight of a column of 
water, pm, so that the pressure at m is really ^?m+H— pn, or 11 +wm, 
that is to say, 11+ hi. 

In the same manner it may be shown that this pressure is the same 
when the level sinks to b, and so on as long as the level is higher than 
the aperture l. The pressure on the layer ch is therefore constant, and 
consequently the velocity of the efflux. But when once the level is below 
the point l, the pressure decreases, and with it the velocity. 

To obtain a constant flow by means of Mariotte’s flask it is filled with 
water, and the orifice which is below the tube l is opened. The rapidity 
of the flow is proportional to the square root of the height, hi. 














- 198 ] 


PROPAGATION OF SOUND. 


161 


BOOK V. 

ACOUSTICS. 


CHAPTER I. 

PRODUCTION, PROPAGATION, AND REFLECTION OF SOUND. 

196. Object of acoustics.— The study of sounds, and that of the 
vibrations of elastic bodies, form the object of acoustics. 

Music considers sounds with reference to the pleasurable feelings they 
are calculated to excite. Acoustics is concerned with the questions of 
the production, transmission and comparison of sounds. To which may 
be added the physiological question of the perception of sounds. 

197. Sound and noise. —Sound is a peculiar sensation excited in the 
organ of hearing by the vibratory motion of bodies, when this motion is 
transmitted to the ear through an elastic medium. 

All sounds are not identical; they present differences by which they 
may be distinguished, compared, and their relations determined. 

Sounds are distinguished from noises. Sound properly so called, or 
musical sound , is that which produces a continuous sensation, and the 
musical value of which can be determined: while noise is either a 
sound of too short a duration to be determined, like the report of a 
cannon, or else it is a confused mixture of many discordant sounds, 
like the rolling of thunder or the noise of the waves. Nevertheless, the 
difference between sound and noise is by no means precise; Savart 
has shown that there are relations of height in the case of noise, as 
well as in that of sound, and there are said to be certain ears suffi¬ 
ciently well organised to determine the musical value of the sound pro¬ 
duced by a carriage rolling on the pavement. 

198. Cause of sound. —Sound is always the result of rapid oscil¬ 
lations imparted to the molecules of elastic bodies, when the state of 
equilibrium of these bodies has been disturbed either by a shock or 
friction. Such bodies tend to regain their first -position of equilibrium, 
but only reach it after performing, on each side of that position, very 
rapid vibratory movements, the amplitude of which quickly decreases. 

A body which produces a sound is called a sonorous body j as under¬ 
stood in England and Germany. In France, on the contrary, a vibration 







162 


ACOUSTICS. 


[ 199 - 

means a movement to or fro. The French vibrations are with us semi¬ 
vibrations, an oscillation or vibration is the movement of the vibrating 
molecule in only one direction; a double or complete vibration comprises 
the oscillation both backwards and forwards. Vibrations are very readily 
observed. If a light powder is sprinkled on a body which is in the act 
of yielding a musical sound, a bell jar held horizontally in the hand, for 
example, a rapid motion is imparted to the powder which renders visible 
the vibrations of the body: and in the same manner, if a stretched cord 
be smartly pulled and let go, its vibrations are apparent to the eye. 

199. Sound is not propagated in vacuo. —The vibrations of 
elastic bodies can only produce the sensation of sound in us, by the 
intervention of a medium interposed between the ear and the sonorous 
body, and vibrating with it. This medium is usually the air, but all 
gases, vapours, liquids, and solids also transmit sounds. 

The following experiment shows that the presence of a ponderable 
medium is necessary for the propagation of sound. A small metallic 
bell, which is continually struck by a small hammer by means of clock¬ 
work, or an ordinary musical box, is placed under the receiver of the air 

pump (fig. 145). As long as the receiver 
is full of air at the ordinary pressure, 
the sound is transmitted, but in propor¬ 
tion as the air is exhausted the sound 
becomes feebler, and is imperceptible in 
a vacuum. 

To ensure the success of the experi¬ 
ment, the bellwork or musical box must 
be placed on wadding; for otherwise the 
vibrations would be transmitted to the 
air through the plate of the machine. 

200. Sound is propagated in all 
elastic bodies.— If, in the above ex¬ 
periment, after the vacuum has been 
made, any vapcfer or gas be admitted, 
the sound of the bell will be heard, 
showing that sound is propagated in 
this medium as in air. 

Sound is also propagated in liquids. 

Fig. i 45 . When two bodies strike against each 

other under water, the shock is dis¬ 
tinctly heard. And a diver at the bottom of the water can hear the 
sound of voices on the bank. 

The conductibility of solids is such, that the scratching of a pen at the 
end of a piece* o# wood is heard at the other end. The earth conducts 


















PROPAGATION OF SOUND. 


- 201 ] 


163 


sound so well, that at night, when the ear is applied to the ground, the 
steps of horses or any other noise at great distances is heard. 

201. Propagation of sound in the air.— In order to simplify 
the theory of the propagation of sound in the air, we shall first con¬ 
sider the case in which it is propagated in a cylindrical tube of indefinite 
length. Let MN, fig. 146, be a tube filled with air at a constant pres¬ 
sure and temperature, and let P be a piston oscillating rapidly from A to 


R"' 

H" 

H' 

H 

a 

A 


1 1 
) M : 

( i 




\ |l 




p 


Pig. 146. 

a. When the piston passes from A to a it compresses the air in the tube. 
But in consequence of the great compressibility, the condensation of the 
air does not take place at once throughout the whole length of the tube, 
but solely within a certain length all, which is called the condensed wave. 

If the tube MN be supposed to be divided into lengths equal to «H, 
and each of these lengths divided into layers parallel to the piston, it 
may be shown by calculation, that when the first layer of the wave aH 
comes to rest the motion is communicated to the first layer of the second 
wave, HIP, and so on from layer to layer in all parts of H'H", 

The condensed wave advances in the tube, each of its parts having suc¬ 
cessively the same degrees of velocity and condensation. 

When the piston returns in the direction aA, a vacuum is produced 
behind it which causes an expansion of the air in contact with its pos¬ 
terior face. The next layer expanding in turn brings the first to its 
original state of condensation, and so on from layer to layer. Thus, when 
the piston has returned to A, an expanded wave is produced of the same 
length as the condensed wave, and directly following it in the tube 
where they are propagated together, the corresponding layers of the two 
waves possessing equal and contrary velocities. 

The whole of a condensed and expanded wave forms an undulation ; 
that is, an undulation comprehends that part of the column of air 
affected during the backwards and forwards motion of the piston. 
The length of an undulation is the space which sound traverses during 
a complete vibration of the body which produces it. This length is 
less in proportion as the vibrations are more rapid. 

It is important to remark that if we consider a single row of particles, 
which when at rest occupy a line parallel to the axis of the cylinder, for in¬ 
stance, those along AH'' (fig. 146), we shall find they will have respectively 
at the same instant all the various velocities which the piston has had 
successively while oscillating from A to a and back Jo A. So that if 
in fig. 26 AH' represents the length of one undulation, the curved line 
















164 


ACOUSTICS. 


[ 202 - 

H'PQA will represent the various velocities which all the points in 
the line AH" have simultaneously : for instance, at the instant the piston has 
returned to A, the particle at M will he moving to the right with 
a velocity represented by QM, the particle at N will be moving to the 
left with a velocity represented by PN, and so on of the other particles. 

When an undulatory motion is transmitted through a medium the 
motions of any two particles are said to be in the same phase when those 
particles move with equal velocities in the same direction ; the motions 
are said to be in opposite phases when the particles move with the same 
velocities in opposite directions. It is plain from an inspection of fig. 26 
that when any two particles are separated by a distance equal to half an 
undulation, their motions are always in opposite phases, but if their dis¬ 
tance equals the length of an undulation their motions are in the same phase. 

A little consideration will show that in the condensed wave the con¬ 
densation will be greatest at the middle of the wave, and likewise that 
the expanded wave will be most rarefied at its middle. 

It is an easy transition from the theory of the motion of sonorous 
waves in a cylinder to that of their motions in an uninclosed medium. 
It is simply necessary to apply in all directions, to each molecule of the 
vibrating body, what has been said about a piston moveable in a tube. 
A series of spherical waves alternately condensed and rarefied is pro¬ 
duced around each centre of disturbance. As these waves are contained 
within two concentrical spherical surfaces, whose radii gradually increase 
while the length of the undulation remains the same, their mass increases 
with the distance from the centre of disturbance, so that the amplitude 
of the vibration of the molecules gradually lessens, and the intensity 
of the sound diminishes. 

It is these spherical waves, alternately condensed and expanded, 
which in being propagated transmit sound. If many points are dis¬ 
turbed at the same time, a system of waves is produced around each 
point. But all these waves are transmitted one through the other 
without modifying either their lengths or their velocities. Sometimes 
condensed or expanded waves coincide with others of the same nature 
to produce an effect equal to their sum; sometimes they meet and 
produce an effect equal to their difference. If the surface of still water 
be disturbed at two or more points the coexistence of waves becomes 
sensible to the eye. 

202. Causes which influence the intensity of sound.— Manv 

causes modify the force or the intensity of the sound. These are, the dis¬ 
tance of the sonorous body, the amplitude of the vibrations, the density 
of the air at the place where the sound is produced, the direction of 
the currents of air, and lastly, the proximity of other sonorous bodies. 

i. The intensity of sound is inversely as the square of the distance 


PROPAGATION OF SOUND. 


165 


- 203 ] 

of the sonorous body from the ear. This law has been deduced by 
calculation, but it may be also demonstrated experimentally. Let us 
suppose several sounds of equal intensity, for instance, bells of the same 
kind, struck by hammers of the same weight, falling from equal heights. 
If four of these bells are placed at a distance of 20 yards from the ear, 
and one at a distance of 10 yards, it is found that the single bell pro¬ 
duces a sound of the same intensity as the four bells struck simultane¬ 
ously. Consequently, for double the distance the intensity of the sound 
is only one fourth. 

The distance at which sounds can be heard depends on their intensity. 
The report of a volcano at St. Vincent was heard at Demerara, 300 miles 
off', and the firing at Waterloo was heard at Dover. 

ii. The intensity of the sound increases with the amplitude of the 
vibrations of the sonorous body. The connection between the intensity of 
the sound and the amplitude of the vibrations, is readily observed by 
means of vibrating cords. For if the cords are somewhat long the 
oscillations are perceptible to the eye, and it is seen that the sound is 
feebler in proportion as the amplitude of the oscillations decreases. 

iii. The intensity of sound depends on the density of the air in the place 
in which it is produced. As we have already seen (199), when an alarum 
moved by clockwork is placed under the bell-jar of the air pump, the 
sound becomes weaker in proportion as the air is rarefied. 

In hydrogen, which is about ~ the density of air, sounds are much 
feebler, although the pressure is the same. In carbonic acid, on the con¬ 
trary, whose density is 1*529, sounds are more intense. On high mountains, 
where the air is much rarefied, it is necessary to speak with some effort in 
order to be heard, and the discharge of a gun produces only a feeble soimd. 

iv. The intensity of sound is modified by the motion of the atmosphere 
and the direction of the wind. In calm weather sound is always better 
propagated than when there is wind j in the latter case, for an equal 
distance, sound is more intense in the direction of the wind than in the 
contrary direction. 

v. Lastly, sound is strengthened by the proximity of a sonorous body. 
A string made to vibrate in free air and not near a sounding body has 
but a very feeble sound; but when it vibrates above a sounding box, 
as in the case of the violin, guitar, or violoncello, its sound is much more 
intense. This arises from the fact that the box and the air which it 
contains vibrate in unison with the string. Hence the use of sounding 
boxes in stringed instruments. 

203. Apparatus to strengthen sound. —The apparatus represented 
in fig. 147 was used by Savart to show the influence of boxes in 
strengthening sound. It consists of a hemispherical brass vessel A, 
which is set in vibration by means of a strong bow. Near it there is a 




ACOUSTICS. 


166 



hollow cardboard cylinder B, closed at the further end. By means of a 
handle this cylinder can he turned on its support, so as to be inclined at 
any given degree towards the vessel. The cylinder is fixed on a slide C, 
by which means it can be placed at any distance from A. When the 
vessel is made to vibrate the strengthening of the sound is very remark¬ 
able. But the sound loses almost all its intensity if the cylinder is 
turned away, and it becomes gradually weaker when the cylinder is re¬ 
moved to a greater distance, showing that the strengthening is due to the 
vibration of the air in the cylinder. 

The cylinder B is made to vibrate in unison with the brass vessel by 
adjusting it to a certain depth, which is effected by making one part 
slide into the other. 

Vitruvius states that in the theatres of the ancients resonant brass 
vessels were placed to strengthen the voices of the actors. 



Fig. 147. 


204. Influence of tubes on the transmission of sound.— The law 

that the intensity of sound decreases in inverse proportion to the square of 
the distance does not apply to the case of tubes, especially if they are 
straight and cylindrical. The sonorous waves in that case are not propa 
gated in the form of increasing concentrical spheres, and sound can be 
transmitted to a great distance without any perceptible alteration. M. Biot 
found that in one of the Paris water pipes, 1040 yards long, the voice lost 
so little of its intensity, that a conversation could be kept up at the ends 
of the tube in a very low tone. The weakening of sound becomes, how¬ 
ever, perceptible in tubes of large diameter, or where the sides are rough. 



VELOCITY OF SOUND IN GASES. 


167 


— 2 °5j 

I This property of transmitting sounds was first used in England for 
speaking tubes. They consist of caoutchouc tubes of small diameter 
passing from one room to another. If a person speaks at one end of the 
i tube, he is distinctly heard by a person at the other end. 

From M. Biot’s experiments it is evident that a communication may 
be made between two towns by means of speaking tubes. The velocity 
of sound is 1125 feet in a second at 16-6 C., so that a distance of 50 miles 
would be traversed in four minutes. 

One of the most important applications of acoustical principles is the 
Stethoscope. It consists of a cylinder of hard wood about a foot long and 
I I 5 inch broad at one end, and in which a longitudinal passage is bored. 
One end of the stethoscope is held against the diseased part of the body, 
and the ear is held against the other. The practised physician can 
detect the existence of internal cavities by the peculiar sound emitted, 
and which is strengthened by resonance. 

205. Velocity of sound in gases. —Since the propagation of sonorous 
waves is gradual, sound requires a certain time for its transmission from 
one place to another, as is seen in numerous phenomena. For example, 
the sound of thunder is only heard some time after the flash of lightning 
i has been seen, although both the sound and the light are produced simul¬ 
taneously ; and in like manner we see a mason in the act of striking a 
j stone before hearing the sound. 

The velocity of sound in air has often been the subject of experimental 
: determination. 

The most accurate of the direct measurements was made by Moll and 
Van Beck in 1823. Two hills, near Amsterdam, Ivooltjesberg and 
Zevenboomen, were chosen as stations; their distance from each other as 
determined trigonometrically was 57,971 feet, or nearly eleven miles. 

I Cannon were fired at stated intervals simultaneously at each station, and 
; the time which elapsed between seeing the flash and hearing the sound 
was noted by chronometers. This time could be taken as that which 
! the sound required to travel between the two stations; for it will be subse¬ 
quently seen that light takes an inappreciable time to travel between the 
( above distance. Introducing corrections for the barometric pressure, 
temperature and hygTometric state, and eliminating the influence of the 
wind, Moll and Van Beck’s results as recalculated by Schroder van der 
Kolk gives 1092-78 feet as the velocity of sound in one second in dry air 
and under a pressure of 760 mm. 

The velocity of sound increases with the increase of temperature ; it 
may be calculated for any temperature t° from the formula 


v= 1093^/1+0-003665* 

where 1093 is the velocity at 0° C., and 0-003665 the coefficient of expan- 





168 


ACOUSTICS. 


[ 205 - 

sion for 1° C. This amounts to an increase of nearly two feet for every 
degree Centigrade. For the same temperature it is independent of the den¬ 
sity of the air, and consequently of the pressure. It is the same for the 
same temperature with all sounds, whether they be strong or weak, deep or 
acute. M. Biot found, in his experiments on the conductivity of sound 
in tubes, that when a well-known air was played on a flute at one end of 
a tube 1040 yards long, it was heard without alteration at the other end, 
from which he concluded that the velocity of different sounds is the same. 
For the same reason the tune played by a band is heard at a great dis¬ 
tance without alteration, except in intensity, which could not be the case 
if some sounds travelled more rapidly than others. 

This cannot, however, be admitted as universally true. Eamshaw, by 
a profound mathematical investigation of the laws of the propagation of 
sound, has found that the velocity of a sound depends on its strength, 
and accordingly that a violent sound ought to be propagated with greater 
velocity than a gentler one. This conclusion is confirmed by an observa¬ 
tion made by Captain Parry on his Arctic expedition. During artillery 
practice it was found by persons stationed at a considerable distance from 
the guns, that the report of the cannon was heard before the command to 
fire given by the officer. And more recently, Mallet made a series of 
experiments on the velocity with which sound is propagated in rocks, by 
observing the times which elapsed before blastings made at Holyhead 
were heard at a distance. He found that the larger the charge of gun¬ 
powder, and therefore the louder the report, the more rapid was the 
transmission. With a charge of 2000 pounds of gunpowder the velocity 
was 967 feet in a second, while with a charge of 12,000 it was 1210 feet 
in the same time. 

MM. Bravais and Martins found, in 1844, that sound travelled with 
the same velocity from the base to the summit of the Faulhorn, as from 
the summit to the base. 

Mallet has investigated the velocity of the transmission of sound in 
various rocks, and finds that it is as follows: 

Wet sand. 825 ft. in a second. 

Contorted, stratified quartz and slate rock . 1088 „ 

Discontinuous granite. 1306 „ 

Solid granite. 1664 „ 

The velocity of sound varies in different gases. Dulong caused organ 
pipes to sound by means of different gases, and found that the velocity of 
sound at zero was as follows : 

Carbonic acid. 856 ft. in a second. 

Oxygen.1040 

Air.1093 


v 






VELOCITY OF SOUND. 


- 206 ] 


169 


Carbonic oxide.1106 ft. in a second. 

Hydrogen.4163 „ 

206. Formulae for calculating the velocity of sound in gases. 

—For calculating the velocity of sound in gases Newton gave a rule 
equivalent to the formula 



in which v represents the velocity of the sound or the distance it travels 
in a second, e the elasticity of the gas, and d its density. 

This formula expresses that the velocity of the propagation of sound 
in gases is directly as the square root of the elasticity of the gas, and inversely 
as the square root of its density. It follows that the velocity of sound is 
the same under any pressure, for although the elasticity increases with 
greater pressure, the density increases in the same ratio. At Quito, 
where the mean pressure is only 21’8 inches, the velocity is the same as 
at the sea level, provided the temperature is the same. 

If g be the force of gravity, h the barometric height reduced to the 
temperature zero, and 8 the density of mercury, also at zero, it is clear 
that for a gas under the atmospheric pressure, e = ghl ; and for zero 
Newton’s formula becomes 



Now if we suppose the temperature of a gas to increase from 0° to t° 
its volume will increase from unity at zero to l + a£ at t, a being the 
coefficient of expansion of the gas. But the density varies inversely as 
the volume, therefore d becomes c?-*-(l + a). Hence 



The values of v, obtained by this formula, are less than the experi¬ 
mental results. Laplace assigned as a reason for this discrepancy the 
heat produced by pressure in the condensed waves ; and, by considerations 
based on this idea, Poisson and Biot have found that Newton’s formula 



of the gas for a constant pressure, and c' its specific heat for a constant 
volume, see Book VI. When thus modified the results calculated by 
the formula agree with the experimental results. 

c 

The physical reason for introducing the constant - into the equation 

for the velocity of sound may be understood from the following con¬ 
siderations. We have already seen that sound is propagated in air by a 
series of alternate condensations and rarefactions of the layers. At each 


i 







170 


ACOUSTICS. 


[ 207 - 

condensation, heat is evolved, and this heat increases the elasticity and 
thus the rapidity with which each condensed layer acts on the next; but 
in the rarefaction of each layer, the same amount of heat disappears as 
was developed by the condensation, and its elasticity is diminished by the 
cooling. The effect of this diminished elasticity of the cooled layer is 
the same as if the elasticity of an adjacent wave had been increased, and 
the rapidity with which this latter would expand upon the dilated wave 
would be greater. Thus while the average temperature of the air is 
unaltered, both the heating which increases the elasticity and the chilling 
which diminishes it concur in increasing velocity. 

Knowing the velocity of sound, we can calculate approximately the 
distance at which it is produced. Light travels with such velocity that 
the flash or the smoke accompanying the report of a gun may be con¬ 
sidered to be seen simultaneously with the explosion. Counting then 
the number of seconds which elapse between seeing the flash and hear¬ 
ing the sound, and multiplying this number by 1125, we get the distance 
in feet at which the gun is discharged. In the same way the distance 
of thunder may be estimated. 

207. Velocity of sound in liquids and in solids.— The velocity of 
sound in water was investigated in 1827 by Colladon and Sturm. They 
moored two boats at a known distance in the Lake of Geneva. The first 
supported a bell immersed in water, and a bent lever provided at one end 
with a hammer which struck the bell, and at the other with a lighted wick, 
so arranged that it ignited some powder the moment the hammer struck 
the bell. To the second boat was affixed an ear-trumpet, the bell of 
which was in water, while the mouth was applied to the ear of the 
observer, so that he could measure the time between the flash of light, 
and the arrival of sound by the water. By this method the velocity was 
found to be 4708 feet in a second at the temperature ST°, or four times 
as great as in air. 

The velocity of sound, which is different in different liquids, can be 
calculated by a formula analogous to that given above (206) as appli¬ 
cable to gases. In this way are obtained the number given in the 
following table. As in the case of gases, the velocity varies with the 
temperature, which is therefore appended in each case: 


River water (Seine) 

. 13°C.= 

4714 ft. 

in a second. 

» n v • 

. 30 = 

5013 


Artificial sea-water 

. 20 = 

4768 


Solution of common salt 

. 18 = 

5132 

y y 

„ „ chloride of calcium 

. 23 = 

6493 

i % 

Absolute alcohol 

. 23 = 

3804 

/ f 

yy 

Turpentine .... 

. 24 = 

3976 

yy 

Ether. 

. 

3801 

)> 



REFLECTION OF SOUND. 


171 


- 208 ] 

Asa general rule, this elasticity of solids, as compared with the density, 
is greater than that of liquids, and consequently the propagation of sound 
is more rapid. 

The difference is well seen in an experiment by M. Biot, who found 
that when a bell was struck by a hammer, at one end of an iron tube 
3120 feet long, two sounds were distinctly heard at the other end. The 
first of these was transmitted by the tube itself with a velocity x ; and 
the second by the enclosed air with a known velocity a. The interval 
between the sounds was 2*5 seconds. The value of x obtained from the 
equation 

3120 3120 
-= 2o 

a X 

shows that the velocity of sound in the tube is between 9 and 10 times 
as great as that in air. 

To this class of phenomena belongs the fact that if the ear is held 
against a rock in which a blasting is being made at a distance, two 
distinct reports are heard, one transmitted through the rock to the ear, 
and the other transmitted through the air. 

The velocity of sound in other solids has also been determined theore¬ 
tically by Wertheim, by means of their coefficient of elasticity. 

The following table gives the velocity, expressed in feet per second:— 


Lead . 


4030 

Pine 

. 

10900 

Gold . 


5717 

Oak 


12622 

Silver 


8553 

Ash 


13314 

Copper 


. 11666 

Elm 


13516 

Steel wire . 


. 15470 

Fir 


15218 

Iron 


. 16822 

Aspen 


16677 

The velocity in 

the direction of the 

fibres was greater than 

across them. 


208. Reflection of sound. —So long as sonorous waves are not 
obstructed in their motion they are propagated in the form of concentric 
spheres; but when they meet with an obstacle, they follow the general 
law of elastic bodies; that is, they return upon themselves, forming new 
concentric waves, which seem to emanate from a second centre on the 
other side of the obstacle. This phenomenon constitutes the reflection 
of sound. 

Fig. 148 represents a series of incident waves reflected from an 
obstacle PQ. Taking, for example, the incident wave MCDN, emitted 
from the centre A, the corresponding reflected wave is represented by 
the arc, CKD, of a circle, whose centre a is as far beyond the obstacle 
PQ as A is before it. 

If any point C of the reflecting surface be joined to the sonorous centre, 
and if the perpendicular CH be let fall on the surface of this body, the 

i 2 










ACOUSTICS. 


172 


[209- 


angle ACH is called the angle of incidence , and the angle BCH, formed 
by the prolongation of aC, is the angle of reflection. 



Fig. 148. 


The reflection of sound is subject to the two following laws: 

J. The angle of reflection is equal to the angle of incidence. 

II. The incident sonorous ray , and the reflected ray, are in the same 
plane perpendicular to the reflecting surface. 

From these laws it follows that the wave which in the figure is pro¬ 
pagated in the direction AC, takes the direction CB after reflection, so 
that an observer placed at B hears, besides the sound proceeding from 
the point A, a second sound, which appears to come from C. 

The laws of the reflection of sound are the same as those for light 
and radiant heat, and may be demonstrated by similar experiments. One 
of the simplest of these is made with conjugate mirrors (see chapter 
on Kadiant Heat) : if in the focus of one of these mirrors a watch is 
placed, the ear placed in the focus of the second mirror hears the ticking 
very distinctly, even when the mirrors are at a distance of 12 or 13 yards. 

209. Echoes and resonances. —An echo is the repetition of a sound 
in the air, caused by its reflection from some obstacle. 

A very sharp quick sound can produce an echo when the reflecting 
surface is 55 feet distant, but for articulate sounds at least double that 
distance is necessary, for it may be easily shown that no one can pronounce 
or hear distinctly more than five syllables in a second. Now, as the 
velocity of sound at ordinary temperatures may be taken at 1,125 feet in 
a second, in a fifth of that time sound would travel 225 feet. If the 
reflecting surface is 112-5 feet distant sound would travel through 225 
feet in going and returning. The time which elapses between the articu¬ 
lated and the reflected sound would, therefore, be a fifth of a second, the- 







REFLECTION OF SOUND. 


173 


-209] 

two sounds would not interfere, and the reflected sound would be distinctly- 
heard. A person speaking with a loud voice in front of a reflector at 
a distance of 112-5 feet can only distinguish the last reflected syllable: 
such an echo is said to be monosyllabic. If the reflector were at a dis¬ 
tance of two or three times 112-5 feet the echo would be disyllabic, 
trisyllabic , and so on. 

When the distance of the reflecting surface is less than 112-5 feet, the 
direct and the reflected sound are confounded. They cannot be hekrd 
separately, but the sound is strengthened. This is what is calledX. 
resonance, and is often observed in large rooms. Bare walls are very 
resonant ; but tapestry and hangings, which are bad reflectors, deaden 
the sound. 

Multiple echoes are those which repeat the same sound several times ; 
this is the case when two opposite surfaces (for example, two parallel 
walls) successively reflect sound. There are echoes which repeat the 
same sound 20 or 30 times. An echo in the chateau of Simonetta, in 
Italy, repeats a sound 30 times. At Woodstock there is one which 
repeats from 17 to 20 syllables. 

As the laws of the reflection of soimd are the same as those of light 
and heat, curved surfaces produce acoustic foci like the luminous and 
calorific foci produced by concave reflectors. If a person standing under 
the arch of a bridge speaks with his face turned towards one of the piers, 
the sound is reproduced near the other pier with such distinctness that 
a conversation can be kept up in a low tone, which is not heard by any 
one standing in the intermediate spaces. 

There is a square room with an elliptical ceiling, on the ground floor 
of the Conservatoiie des Arts et Metiers, in Paris, which presents this 
phenomenon in a remarkable degree when persons stand in the two foci 
of the ellipse. 

It is not merely by solid surfaces, such as walls, rocks, etc., that sound 
is reflected. It is also reflected by clouds, and on passing into a layer of 
air of greater density than its own; it is also further reflected by the 
vesicles of mist. When the weather is foggy, sounds undergo in¬ 
numerable partial reflections, and are rapidly destroyed. 

Whispering galleries are formed of smooth walls having a continuous 
curved form. The mouth of the speaker is presented at one point, and 
the ear of the hearer at another and distant point. In this case, the 
sound is successively reflected from one point to the other until it reaches 
the ear. 

Different parts of the earth’s surface are unequally heated by the sun, 
owing to the shadows of trees, evaporation of water, and other causes, so 
that in the atmosphere there are numerous ascending and descending 
currents of air of different density. Whenever a sonorous wave passes 




174 


'acoustics. 


[ 210 - 

from a medium of one density into another it undergoes partial reflection, 
which, though not strong enough to form an echo, distinctly weakens 
the direct sound. This is doubtless the reason, as Humboldt remarks, 
why sound travels further at night than at day time; even in the South 
American forests, where the animals, which are silent by day, fill the 
atmosphere in the night with thousands of confused sounds. 

210. Refraction of sound _It will be shown in the sequel that 

refraction is the change of direction which light and heat experience on 
passing from one medium to another. Sondhauss has found that 
sonorous waves are refracted like light and heat. He constructed gaseous 
lenses, by filling spherical or lenticular collodion envelopes with carbonic 
acid. With envelopes of paper or of goldbeater’s skin the refraction of 
sound is not perceptible. 

Sondhauss cut equal segments out of a large collodion balloon, and 
fastened them on the two sides of a sheet iron ring a foot in diameter, so 
as to form a hollow biconvex lens about 4 inches thick in the centre. 
This was filled with carbonic acid, and a watch was placed in the direction 
of the axis: the point was then sought, on the other side of the lens, at 
which the sound was most distinctly heard. It was found that when the 
ear was removed from the axis, the sound was scarcely perceptible ; but 
that at a certain point on the axial line it was very distinctly heard. 
Consequently the sonorous waves in passing from the lens had converged 
towards the axis, their direction had been changed; in other words, they 
had been refracted. 

The refraction of sound may be easily demonstrated by means of one 
of the very thin india-rubber balloons, used as children’s toys, inflated by 
carbonic acid. If the balloon be filled with hydrogen no focus is 
detected, it acts like a convex lens, and the divergence of the rays is 
increased, instead of their being converged to the ear. 



Fig. 149. 


211.— Speaking- trumpet.—Ear trumpet.— These instruments are 
based both on the reflection of sound, and on its conductibility in 
tubes. 

The speaking trumpet , as its name implies, is used to render the voice 
audible at great distances. It consists of a slightly conical tin or brass 
tube (fig. 149), very much wider at one end (which is called the bell), and 




175 


- 212 ] MEASUREMENT OF THE NUMBER OF VIBRATIONS. 

provided with a mouthpiece at the other. The larger the dimensions of 
this instrument the greater is the distance at which the voice is heard. 
Its action is usually ascribed to the successive reflections of sonorous 
waves from the sides of the tube, by which the waves tend more and 
more to pass in a direction parallel to the axis of the instrument. It has, 
however, been objected to this explanation, that the sounds emitted by 
the speaking trumpet are not stronger solely in the direction of the axis, 
but in all directions, that the bell would not tend to produce parallelism 
in the sonorous wave, whereas it certainly exerts considerable influence 
in strengthening the sound. No satisfactory explanation has been given 
of the effect of the bell. 

The ear trumpet is used by persons who are hard of hearing. It is 
essentially an inverted speaking trumpet, and consists of a conical metallic 
tube, one of whose extremities, terminating in a bell , receives the sound, 
while the other end is introduced into the ear. This instrument is the 
reverse of the speaking trumpet. The bell serves as mouthpiece; that 
is, it receives the sounds coming from the mouth of the person who 
speaks. These sounds are transmitted by a series of reflections to the 
interior of the trumpet, so that the waves, which would become greatly 
developed, are concentrated on the auditory apparatus, and produce a far 
greater effect than divergent waves would have done. 


CHAPTER II. 

MEASUREMENT OF THE NUMBER OF VIBRATIONS. 

Several means have been devised for measuring the number of vibrations 
corresponding to a given sound,—for example, Savart’s wheel, the syren, 
Duhamel’s method, and the phonautograph of M. Scott. We will here 
describe the first three, reserving the description of the phonautograph 
for a later chapter. 

212. Savart’s apparatus. — Savart's toothed wheel , so called from the 
name of its inventor, is an apparatus by which the absolute number of 
vibrations corresponding to a given note can be determined. It consists 
of a solid oak frame in which there are two wheels, A and B (fig. 150) j 
the larger wheel, A, is connected with the toothed wheel by means of a 
strap, and a multiplying wheel, thereby causing the toothed wheel to 
revolve with great velocity; a card, E, is fixed on the frame, and, in 
revolving, the toothed wheel strikes against it, and causes it to vibrate. 
The card being struck by each tooth, makes as many vibrations as there 
are teeth. At the side of the apparatus there is an indicator, H, which 






176 acoustics. [ 213 - 

gives the number of revolutions of the wheel, and consequently the 
number of vibrations in a given time. 

When the wheel is moved slowly the separate shocks against the 
card are distinctly heard, but if the velocity is gradually increased, the 
sound becomes higher and higher. Having obtained the sound whose 
number of vibrations is to be determined, the revolution of the wheel is 
.continued with the same velocity for a certain number of seconds. The 
number of turns of the toothed wheel B is then read off on the indicator, 
and this multiplied by the number of teeth in the wheel gives the total 
number of vibrations. Dividing this by the corresponding number of 
seconds, the quotient gives the number of vibrations per second for the 
given sound. 



Fig. 150. 


213. Syren.—The syren is an apparatus which, like Savart’s wheel, 
is used to measure the number of vibrations of a body in a given time. 
The name i syren ’ was given to it by its inventor, Cagniard Latour, 
because it yields sounds under water. 

It is made entirely of brass. Fig. 151 represents it ffxed on the 
table of a bellows, by which a continuous current of air can be sent 
through it. Figs. 152 and 153 show the internal details. The lower 
part consists of a cylindrical box, 0, closed by a ffxed plate, B. On this 
plate a vertical rod, T, rests, to which is fixed a disc, A, moving with 
the rod. In the plate B there are equidistant circular holes, and in the 
disc, A, are an equal number of holes of the same size, and the same 
distance from the centre as those of the plate. These holes are not 
perpendicular to the disc ; they are all inclined to the same extent in the 
same direction in the plate, and are inclined to the same extent in the 
opposite direction in the disc, so that when they are opposite each other 
















177 


- 213 ] MEASUREMENT OF THE NUMRfcR OF VIBRATIONS. 

they have the appearance represented in mn, fig. 153. Consequently, 
when a current of air from the bellows reaches the hole m, it strikes 
obliquely against the sides of the hole n, and imparts to the disc A a 
rotatory motion in the direction wA. 

For the sake of simplicity, let us first suppose that in the moveable 
disc A there are eighteen holes, and in the fixed plate B only one, which 
faces one of the upper holes. The wind from the bellows striking 
against the sides of the latter, the moveable disc begins to rotate, and 
the space between two of its consecutive holes closes the hole in the 
lower plate. But as the disc continues to turn from its acquired velocity 
two holes are again opposite each other, a new impulse is produced, and 



Fig. 151. Fig. 152. 


so on. During a complete revolution of the disc the lower hole is 
eighteen times open and eighteen times closed. A series of effluxes and 
stoppages is thus produced, which makes the air vibrate, and ultimately 
produces a sound when the successive impulses are sufficiently rapid. If 
the fixed plate, like the moving disc, has eighteen holes, each hole would 
separately produce the same effect as a separate one, the sound would be 
eighteen times as intense, but the number of vibrations would not be 
increased. 

In order to know the number of vibrations corresponding to the sound 
produced, it is necessary to know the number of revolutions of the disc 
A in a second. For this purpose an endless screw on the rod T transmits 
the motion to a wheel, «, with 100 teeth. On this wheel, which moves 
by one tooth for every turn of the disc, there is a catch, P, which at each 

i 3 

























178 


ACOUSTICS. 


[ 214 - 

complete revolution, moves one tootli of a second wheel, b (fig. 152). 
On the axis of these wheels there are two needles which move round 
dials represented in fig. 151. One of these indices gives the number 
of turns of the disc A, the other the number of hundreds of turns. 
By means of two screws, D and C, the wheel a can be uncoupled from 
the endless screw. 

Since the sound rises in proportion to the velocity of the disc A, the 
wind is forced until the desired sound is produced. The same current 
is kept up for a certain time, two minutes for example, and the number 
of turns read off. This number multiplied by 18, and divided by 120, 
indicates the number of vibrations in a second. 

With the same velocity the syren gives the same sound in air as in 
water: the same is the case with all gases, and it appears, therefore, that 
any given sound depends on the number of vibrations, and not on the 
nature of the sounding body. 

The buzzing and humming noise of certain insects is not vocal, but is 
produced by very rapid flapping of the wings against the air or the body. 
The syren has been ingeniously applied to count the velocity of the 
undulations thus produced, which is effected by bringing it into unison 
with the sound. It has thus been found that the wings of a gnat flap at 
the rate of 15,000 times in a second. 

214. Bellows. — In acoustics a belloivs is an apparatus by which 
wind instruments, such as the syren and organ pipes, are worked. 
Between the four legs of a table there is a pair of bellows, S (fig. 154), 
which is worked by means of a pedal, P. D is a reservoir of flexible 
leather, in which is stored the air forced in by the bellows. If this 
reservoir is pressed by means of weights on a rod, T, moved by the 
hand, the air is driven through a pipe, E, into a chest, C, fixed on the 
table. In this chest there are small holes closed by leather valves, which 
can be opened by pressing on keys in front of the box. The syren or 
sounding pipe is placed in one of these holes. 

215. Iiimit of perceptible sounds. —Before Savart’s researches, 
physicists assumed that the ear could not perceive a sound when the 
number of single vibrations was below 32 for deep sounds, or above 
18,000 for acute sounds. But he showed that these limits were much 
too close, and that the faculty of perceiving sounds depends rather on 
their intensity than on their height; so that when extreme sounds are 
not heard it arises from the fact that they have not been produced with 
sufficient intensity to affect the organ of hearing. 

By increasing the diameter of the toothed wheel, and consequently 
the amplitude and intensity of the vibrations, Savart pushed the limit of 
acute sounds to 48,000 single vibrations in a second. 

For deep sounds, he substituted for the toothed wheel an iron bar 


179 


- 216 ] MEASUREMENT OF THE NUMBER OF VIBRATIONS. 

about two feet long, which revolved on a horizontal axis between two 
thin wooden plates, about 0-08 of an inch from the bar. As often as the 
bar passed, a grave sound was produced, due to the displacement of the 
air. As the motion became accelerated, the sound became continuous, 
very grave and deafening. By this means Savart found, that with 14 to 
16 single vibrations in a second, the ear perceived a distinct but very deep 
sound. 



Fig. 154. 


M. Despretz, however, who has investigated the same subject, disputes 
Savart’s results as to the limits of deep sounds, and holds that no sound 
is audible that is made by less than 32 single vibrations per second. On 
the other hand, he holds that acute sounds are audible up to those 
corresponding to 73,700 single vibrations per second. 

216. Duhamel's graphic method.— When the syren or Savart’s 
wheel is used to determine the exact number of vibrations corresponding 
to a given sound, it is necessary to bring the sound which they produce 
into unison with the given sound, and this cannot be done exactly unless 
the experimenter have a practised ear. M. Pub am el's graphic method is 













180 


ACOUSTICS. 


[ 216 - 

very simple and exact, and free from this difficulty. It consists in fixing 
a fine point to the body emitting the sound, and causing it to trace the 
vibrations on a properly prepared surface. 

The apparatus consists of a wood or metal cylinder A, fig. 155, fixed to 
a vertical axis 0, and turned by a handle. The lower part of the axis is 
a screw working in a fixed nut, so that according as the handle is turned 
from left to right or from right to left, the cylinder is raised or depressed. 
Round the cylinder is rolled a sheet of paper covered with an inadhesive 


film of lampblack. On this film the vibrations register themselves. 
This is effected as follows : Suppose the body emitting the note to be a 
steel rod. It is held firmly at one end, and carries at the other a fine 
point which grazes the surface of the cylinder. If the rod is made to 
vibrate and the cylinder is at rest, the point would describe a short line; 
but if the cylinder is turned the point produces an undulating trace , 
containing as many undulations as the point has made vibrations. Con¬ 
sequently the number of vibrations can be counted. It remains only to 
determine the time in which the vibrations were made. 

There are several ways of doing this. The simplest is to compare the 
curve traced by the vibrating rod with that traced by a tuning fork 
(222), which gives a known number of vibrations per second, for example, 



Fig. 155. 



PHYSICAL THEORY OF MUSIC. 


181 


-217] 


500. One prong of the fork is furnished with a point, which is placed 
in contact with the lampblack. The fork and the rod are then set 
vibrating together, and each produces its own undulating trace. When 
the paper is unrolled it is easy by counting the number of vibrations 
each has made in the same distance to determine the number of 
vibrations made per second by the elastic rod. Suppose, for instance, 
that the tuning fork made 150 vibrations, while the rod made 165 
vibrations. Now we already know that the tuning fork makes one 
vibration in the part of a second, and therefore 150 vibrations in 
of a second. But in the same time the rod makes 165 vibrations, 

therefore it makes one vibration in the of a second > and there¬ 


fore it makes per second 

^ 150 


or 550 vibrations. 


CHAPTER III. 

THE PHYSICAL THEORY OF MUSIC. 

217. Properties of musical tones,— A simple musical tone results 
from a continuous rapid isochronous vibration, provided the number of 
the vibrations falls within the very wide limits mentioned in the last 
chapter (215). Musical tones are in most cases compound. The dis¬ 
tinction between a simple and a compound musical tone will be explained 
later in the chapter. The tone yielded by a tuning fork furnished 
with a proper resonance box is simple', that yielded by a wide stopped 
organ pipe, or by a flute, is nearly simple ; that yielded by a musical 
string is compound. 

Musical tones have three leading qualities, namely pitch, intensity, and 
timbre or colour. 

i. The pitch of a musical tone is determined by the number of 
vibrations per second yielded by the body producing the tone. 

ii. The intensity of the tone depends on the extent of the vibrations. 
It is greater when the extent is greater, and less when it is less. It is, 
in fact, nearly or exactly proportional to the square of the extent or 
amplitude of the vibrations which produce the tone. 

iii. The timbre, or what may be conveniently called the colour , is that 
peculiar quality of tone which distinguishes a note when sounded on 
one instrument, from the same note when sounded on another. Thus 
when the C of the treble stave is sounded on a violin, and on a flute, 
the two notes will have the same pitch, that is, are produced by the same 










182 


ACOUSTICS. 


[ 218 - 

number of vibrations per second, and they-may have the same intensity, 
and yet the two tones will have very distinct qualities, that is, their 
timbre or colour is different. The cause of the peculiar colour of tones 
will be considered later in the chapter. 

218. ziXusical intervals, —Let us suppose that a musical tone, which 
for the sake of future reference we will denote by the letter C, is pro¬ 
duced by m vibrations per second, and let us further suppose that any 
other musical tone, X, is produced by n vibrations per second, n being 
greater than m; then the interval from the note C to the note X is the 
ratio n : m, the interval between two notes being obtained by division 
not by subtraction. Although two or more tones may be separately 
musical, it by no means follows that when sounded together they pro¬ 
duce a pleasurable sensation. On the contrary, unless they are concordant 
the result is harsh, and ordinarily the reverse of pleasurable. We have 
therefore to enquire what notes are fit to be sounded together. Now 
when musical tones are compared it is found that if they are separated 
by an interval of 2 : 1, 4 : 1, etc., they so closely resemble one another 
that they may for most purposes of music be considered as the same tone. 
Thus, suppose c to stand for a musical note produced by 2m vibrations 
per second, and then C and c so closely resemble one another as to be 
called in music by the same name. The interval from C to c is called an 
octave, and c is said to be an octave above C, and conversely C an octave 
below c. If we now consider musical sounds that do not differ by an 
octave it is found that if we take three notes X, Y, and Z, resulting re¬ 
spectively from d, q, and r vibrations per second, these three notes when 
sounded together will be concordant if the ratio of p: q : r equals 4:5:0. 
Three such notes form a harmonic triad, and if sounded with a fourth 
note, which is the octave of X, constitute what is called in music a major 
chord. Any of the notes of a chord may be altered by one or more octaves 
without changing its distinctive character; for instance, C, E, G, and c. 
are a chord, and C, c, e , g, form the same chord. 

If, however, the ratio p: q: r equals 10 : 12 : 15, the three sounds are 
slightly dissonant, but not so much so as to disqualify them from pro¬ 
ducing a pleasurable sensation, at least under certain circumstances. 
When these three notes and the octave to the lower are sounded together 
they constitute what in music is called a minor chord. 

219. The musical scale. —The series of sounds which connects a 
given note C with its octave c is called the diatonic scale or gamut. 
The notes composing it are denoted by the letters C, D, E, F, G, A, B. 
The scale is then continued by taking the octaves of these notes, namely 
c, d, e, f, g, a, b, and again the octaves of these last, and so on. 

The notes are also denoted by names, viz. do, re, mi, fa, sol, la, si, do. 
The relations existing between the notes are these:—C, E, G, form a 


PHYSICAL THEORY OF MUSIC. 


183 


- 219 ] 

major triad, G, B, d, form a major triad, and F, A, c, form a major 
triad. C, G, and F have, for this reason, special names, being called 
respectively, the tonic , dominant, and sub-dominant, and the three triads 
the tome , dominant, and sub-dominant triads or chords respectively. 
Consequently, the numerical relations between the notes of the scale will 
be given by the three proportions— 

C : E : G :: 4 : 5 : 6 

G : B : 2D :: 4 : 5 : t> 

F : A : 2C :: 4 : 5 : 6 

Hence if m denotes the number of double vibrations corresponding to 
the note C, the number of vibrations corresponding to the remaining 
notes will be given by the following table— 

CDEFGABc 
m | m fm f m § m § m ~ 5 m 2m 

The intervals between the successive notes being respectively— 

C to D D to E E to F F to G G to A A to B B to c 

9 10 16 9 1J> 9 16 

8 9 15 8 9 8 15 

It will be observed that there are here three kinds of intervals, f, ^, 

and y§ : of these the two former are called a tone, the last a semitone. 
The two tones however are not identical, but differ by an interval of ~, 
which is called a comma. Two notes which differ by a comma can be 
readily distinguished by an educated ear. The interval between the 
tonic and any note is denominated by the position of the latter note in the 
scale ; thus the interval from C to G is a fifth. The scale we have now 
considered is called the major scale, as being formed of major triads. 
If the minor triad were substituted for the major, a scale would be 
formed that could be strictly called a minor scale. As scales are usually 
written, however, the ascending scale is so formed that the tonic bears a 
minor triad, the dominant and sub-dominant bear major triads, while in 
the descending scale they all bear minor triads. Practically, in musical 
composition, the dominant triad is always major. If the ratios given 
above are examined it will be found that in the major scale the interval 
from C to E equals f, while in the minor scale it equals f. The former 
interval is called a major third, the latter a minor third. Hence the 
major third exceeds the minor third by an interval of §f. This interval 
is called a semitone, though very different from the interval above called 
by that name. 

A complete discussion of the number of notes, and the intervals between 
them, will be found in an article by Mr. Ellis, in vol. xiii. of the Pro¬ 
ceedings of the Royal Society (p. 93), ‘On a Perfect Musical Scale.’ 




184 


ACOUSTICS. 


[ 221 - 


220. On semitones and on scales with different keynotes. —It 

will be seen from the last article that the term ‘semi tone ’does not denote 
a constant interval, being in one case equivalent to — and in another to 
ff. It is found convenient for the purposes of music to introduce notes 
intermediate to the seven notes of the gamut; this is done by increasing 
or diminishing those notes by an interval of §f. When a note (say C) is 
increased by this interval it is said to be sharpened, and is denoted by the 
symbol C#, called ‘ C sharp; ’ that is Ctf -*-C=§f. When it is decreased 
by the same interval it is said to be flattened, and is represented thus, 
Bb, called ‘ B flat; ’ that is B -^Bb =§f. If the effect of this be examined 
it will be found that the number of notes in the scale from C up to c 
has been increased from seven to twenty-one notes, all of which can be 
easily distinguished by the ear. Thus, reckoning C to equal 1, we have— 


C Cl Dt> D D # 

125279 75 

X 24 25 8 64 


Eb E etc. 

6 I pfp 

5 4 e,C - 


Hitherto we have made the note C the tonic or key note. Any other 
of the twenty-one distinct notes above-mentioned, e.g. G, or F, or Cl, etc. 
may be made the key note, and a scale of notes constructed with refer¬ 
ence to it. This will be found to give rise in each case to a series of notes, 
some of which are identical with those contained in the series of which 
C is the key note, but most of them different. And of course the same 
would be true for the minor scale as well as for the major scale, and 
indeed for other scales which may be constructed by means of the funda¬ 
mental triads. 

221. On musical temperament. —The number of notes that arise 
from the construction of the scales described in the last article is enor¬ 
mous ; so much so as to prove quite unmanageable in the practice of music; 
and particularly for music designed for instruments with fixed notes, 
such as the pianoforte. Accordingly it becomes practically important to 
reduce the number of notes, which is done by slightly altering their just 
proportions. This process is called temperament. By tempering the 
notes, however, more or less dissonance is introduced, and accordingly 
several different systems of temperament have been devised for rendering 
this dissonance as slight as possible. The system usually adopted—at 
least in intention—is called the system of equal temperament. It 
consists in the substitution between C and c of eleven notes at 
equal intervals, each interval being, of course, the twelfth root of 2, 
or 1*05946. By this means the distinction between the semitones is 
abolished, so that, for example, C# and D& become the same note. The 
scale of twelve notes thus formed is called the chromatic scale. It of 
course follows that major triads become slightly dissonant. Thus in the 
diatonic scale, if we reckon C to be 1, E is denoted by 1*25000, and G 



-222] PHYSICAL THEORY OF MUSIC. 185 

by 1-50000. On the system of equal temperament if C is denoted by 1, 
E is denoted by 1-25992 and G- by 1-49831. 

222. The number of vibrations producing- each note. The 
tuning- fork. —Hitherto we have denoted the number of vibrations corre¬ 
sponding to the note C by m, and have not assigned any numerical value 
to that symbol. In the theory of music it is usual to assign 256 double 
vibrations to the middle C. This, however, is arbitrary. An instrument 
is in tune provided the intervals between the notes are correct, when 
C is yielded by any number of vibrations per second not differing much 
from 256. Moreover, two instruments are in tune with one another if, 
being separately in tune, they have any one note, for instance, C, yielded 
by the same number of vibrations. Consequently, if two instruments have 
one note (say C) in common, they can then be brought into tune jointly, 
by having their remaining notes separately adjusted with reference to that 
fundamental note. A tuning fork is an instrument yielding a constant 
sound, and is used as a standard for tuning musical instruments. It 
consists of an elastic steel rod, bent as represented in fig. 156. It 
is made to vibrate either by drawing a bow across the ends, or by 
striking one of the legs against a hard 
body, or by rapidly separating the two legs 
by means of a steel rod, as shown in the 
figure. The vibration produces a note 
which is always the same for the same 
tuning fork. The note is strengthened by 
fixing the tuning fork on a box open at one 
end, called a resonance box. 

It has been remarked for some years 
that not only has the pitch of the tuning 
fork, that is, concert pitch, been getting 
higher in the large theatres of Europe, 
but also that it is not the same in London, 

Paris, Vienna, Milan, etc. This is a source 
of great inconvenience both to composers 
and singers, and a commission was ap¬ 
pointed to establish in France a tuning 
fork of uniform pitch, and to prepare a 
standard which would serve as an invari¬ 
able type. In accordance with the recom¬ 
mendations of that body, a normal tuning 
fork has been established, which is compulsory on all musical estab¬ 
lishments in France, and a standard has been deposited in the Conser¬ 
vatory of Music in Paris. 

It performs 870 single vibrations per second, and gives the standard 



Fig. 156. 



186 


ACOUSTICS. 


[223- 

note a , or the a in the treble stave. Consequently, with reference to this 
standard, the middle C would result from 261 double vibrations per second. 

223. On compound musical tones and harmonics. —When any 
given note (say C) is sounded on most musical instruments, not that 
tone alone is produced, but a series of tones, each being of less intensity 
than the one preceding it. If C, which may be called the primary 
tone, is denoted by unity, the whole series is given by the numbers 
1, 2, 3, 4, 5, 6, 7, etc., in other words, first the primary C is sounded, 
then its octave becomes audible, then the fifth to that octave, then the 
second octave, then the third, fifth, and a note between the sixth and 
seventh to the second octave, and so on. These secondary tones are 
called the harmonics of the primary tone. Though feeble in comparison 
with the primary tone, they may, with a little practice, be heard, when 
the primary tone is produced on most musical instruments; when, for 
instance, one of the lower notes is sounded on the pianoforte. For the 
purpose of experimentally proving the presence of the harmonics as 
distinct tones, Professor Helmholtz constructed an instrument called a 
resonance globe. The principle involved in its construction is this: A volume 
of air contained in an open vessel, for example a bottle, when caused to 
vibrate, tends to yield a certain note, and consequently when that note 
is sounded in its neighbourhood, to strengthen it. A resonance globe is a 
glass globe furnished with two openings, one of which is turned towards 
the origin of the sound, and the other, by means of an india-rubber tube, 
is applied to the ear. If the tone proper to the resonance g^obe exists 
among the harmonics of the compound tone that is sounded, it is 
strengthened by the globe, and thereby rendered distinctly audible. 
Further, other things being the same, the note proper to a given globe 
depends on the diameter of the globe and that of the uncovered 
opening. Consequently, by means of a series of such globes the 
whole series of harmonics in a given compound tone can be rendered 
distinctly audible, and their existence put beyond a doubt. Professor 
Helmholtz’s researches show that the different colour or quality of the 
sounds yielded by different musical instruments is due to the different 
intensities of the harmonics which accompany the primary tones of those 
sounds. The leading results of these researches into the colour of sounds 
may be thus stated: 

i. Simple tones, as those produced by a tuning fork with a resonance 
box, and by wide covered pipes, are soft and agreeable without any rough¬ 
ness, but weak, and in the deeper notes dull. 

ii. Musical sounds accompanied by a series of harmonics, say up to the 
sixth, in moderate strength are full and musical. In comparison with 
simple tones they are grander, richer, and more sonorous. Such are the 
sounds of open organ pipes, of the pianoforte, etc. 


PHYSICAL THEORY OF MUSIC. 


187 


-224] 

iii. If only the uneven harmonics are present, as in the case of narrow 
covered pipes, of pianoforte strings struck in the middle, clarionets, etc., 
the sound becomes indistinct; and when a greater number of harmonics 
are audible the sound acquires a nasal character. 

iv. If the harmonics beyond the sixth and seventh are very distinct, 
the sound becomes sharp and rough. If less strong the harmonics are 
not prejudicial to the musical usefulness of the notes. On the contrary, 
they are useful as imparting character and expression to the music. Of 
this kind are most stringed instruments, and most pipes furnished with 
tongues, etc. Sounds in which the harmonics are particularly strong 
acquire thereby a peculiarly penetrating character, such are those yielded 
by brass instruments. 

224. Seats. —When two simple tones are sounded together it is in 
many cases found that they alternately strengthen and weaken one an¬ 
other. When this is so, they are said to beat with one another. This may 
be explained as follows: Suppose AB, in fig. 157, to be a row of particles 
transmitting the sound; suppose the vibrations producing the one tone to 


Fig. 157. 



Fig. 158. 


be indicated by the continuous curved line; then on the one hand the 
ordinates of the different points of AB give the velocities with which 
those points are simultaneously moving, and, on the other hand, each point 
will have successively the different velocities represented by the successive 
ordinates. In like manner let the dotted line show the vibrations which 
produce the second tone. - And, for the sake of distinctness, suppose the 
number of vibrations per second producing the former tone to be to that 
producing the latter in the ratio of 3 : 2. Now let us consider any point 
which when at rest occupies the position N; draw the ordinate cutting 
the former curve in P and the latter in Q. If the tones were sounded 
separately the velocity of N at a given instance produced by the former 
tone would be PN, and that of N at the same instant produced by the 
latter tone would be QN. Consequently, as they are sounded together, 
N’s actual velocity at the given instant is the sum of these, or PN-f-QN. 
If at the same instant we consider the point n, its velocity will consist 







188 


ACOUSTICS. 


[ 224 - 

of pn and nq j ointly, but as these are in opposite directions, its actual 
amount will be pn — nq. Hence the actual velocity resulting from the 
coexistence of the two tones will be indicated by the curve in fig. 158, 
whose ordinates equal the (algebraical) sum of the corresponding ordi¬ 
nates of the two curves in fig. («), that is, if AN, An, . . . represent equal 
distances in both figures, the curve is described by taking RN equal to 
PN-fQN, rn equal to pn — qn, and so on. This curve shows by its suc¬ 
cessive ordinates the simultaneous velocities of the different particles of 
AB, and the successive velocities of each particle. Consequently it also 
represents the successive velocities communicated to the drum of the 
ear. An inspection of the figure will show that the velocities are first 
great, then small, then great, and so on, the drum being first moved 
rapidly for a short time, then for a short time nearly brought to rest, and 
so on. In short, the effect of the beating of tones on the ear as compared 
with that of a continuous tone is strictly analogous to the effect produced 
on the eye by a flickering as compared with a steady light. 

It may be proved that when two simple tones are produced by m and 
n double vibrations per second, they produce m—n beats per second: 
thus, if C is produced by 128, and D by 144 double vibrations per second, 
they will on being soimded together produce 16 beats per second. It 
has been ascertained that the beats produced by two tones are not audible 
unless the ratio m : n is less than the ratio 6 : 5. Hence, in the case 
represented by fig. 158, though the alternations of intensity exist, they 
would not be audible. Also, if the tones have very different intensities, 
the intensity of the beat is very much disguised. 

It is found that when beats are fewer than 10 per second or more than 
70 per second they are disagreeable, but not to the extent of producing 
discord. Beats from 10 to 70 per second may be regarded as the source 
of all discord in music, the maximum of dissonance being attained when 
about 30 beats are produced per second. For example, if c and B are 
sounded together the effect is very discordant, the interval between those 
notes being 16 : 15, so that the beats are audible, and the number of 
beats per second being 16. On the other hand, if C, E, and G are sounded 
together there is no dissonance, but if O, E, G, B are sounded together 
the discord is very marked, since C produces c, which is discordant with 
B. It will be remarked that C, E, G is a major triad, while E, G, B is 
a minor triad. 

A compound musical tone being composed of simple tones represented 
by 1, 2, 3, 4, 5, 6, 7, etc., does not give rise to any simple tones capable 
of producing an audible beat up to the seventh, the sixth and seventh 
are the first that produce an audible beat. It is for this reason that there 
is no trace of roughness in a compound tone, unless the seventh harmonic 
be audible. 


PHYSICAL THEORY OF MUSIC. 


189 


- 226 ] 

If we were to represent graphically a compound tone we should proceed 
to construct a curve out of simple tones of different intensities in the same’ 
manner as fig. 158 is constructed from two simple tones of equal intensity 
represented by fig. 15. It is evident that the resulting curve will take dif¬ 
ferent forms according to the presence or absence of different harmonics 
and their different intensities ; in other words, the colour of the notes 
produced by different instruments will depend upon the form of the 
vibrations producing the sound. 

225. Combinational tones. —Besides the beats produced when two 
musical notes are sounded together, there is another and distinct pheno¬ 
menon, which may be thus described: Suppose two simple tones to be 
simultaneously produced by vibrations of finite extent, and of n and m 
vibrations per second. It has been shown by Helmholtz that they 
generate a series of other tones. The principal one of these, which may 

1 be called the differential tone , is produced by n—m vibrations per 
second. Its intensity is generally very small, but it is distinctly audible 
in beats. It has been called the grave harmonic , as generally its 
pitch is much lower than that of the notes by which it is generated. It 
has been supposed to be caused by the beats becoming too numerous to 
be distinguished, and coalescing into a continuous sound, and this sup¬ 
position was countenanced by the fact that its pitch is the same as the 
beat number. The supposition is shown to be erroneous, first, by the 
existence of the differential tones for intervals that do not beat, and 
secondly, by the fact that, under certain circumstances, both the beats 
I and the differential tones may be heard together. 

226. The physical constitution of musical chords. —Let us sup¬ 
pose two compound tones to be sounded together, say C and G, then we 
obtain two series of tones each consisting of a primary and its harmonics, 

| namely, denoting C by 4, the two series, 4, 8, 12, 16, . . . and 6, 12, 18, 
| 24, etc. Now, if instead of producing the two notes C and G, we had 
| sounded the octave below C, we should have produced the series 2, 4, 
6, 8, 10, 12, 14, 16, 18, etc It is plain that the two former series 
when joined differ from the last in the following respects: (a) The 
; primary tone 2 is omitted, (b) In the case of the last series, the con¬ 
secutive tones continually decrease in intensity, whereas in the two former 
! series, 4 and 6 are of the same intensity, 8 is of lower intensity, but the 
j two 12’s will strengthen each other, and so on. (c) Certain of the har- 
I monies of the primary 2 are omitted, for example 10, 14, etc., do not occur 
in either of the two former series. In spite of these differences, however, 
the two compound notes affect the ear in a manner very closely 
resembling a single compound tone ; in short, they coalesce into a single 
tone with an artificial colour. It may be added that in the case above 
taken C and G produce as a combination tone 2 (that is 6—4), so that, 






190 


ACOUSTICS. 


[ 227 - 

strictly speaking, the 2 is not wanted in the series produced by C and 
G, only it exists in very diminished intensity. The same explanation 
will apply to all possible chords, for example in the case of the major chord, 
C, E, G, we have a tone of artificial colour expressed by the series of 
simple tones, 4, 5, 6, 8, 10, 12, 15, 16, 18, etc., together with the 
combination tones, 1, 1, 2. It will be remarked that in the whole of 
this series there are no dissonant tones introduced, except 15, 16, and 
16, 18, and this dissonance will be inappreciably slight, since 15 is the 
third harmonic of 5, and the 16 the fourth harmonic of 4, so that 
their intensities will be different, as also will be the intensities of 16 
and 18. On the other hand, nearly all the tones which form a natural 
compound tone are present, namely there are 1,2,4, 5, 6, 8, 10, 12, etc., in 
place of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, etc. In short, the major 
triad differs only from a natural compound tone, in that it consists of 
a series of simple tones of different intensities, and omits those which by 
beating with its neighbouring tone would produce dissonance, for example 
7, which would beat with 6 and 8; 9, which would beat with 8 and 
10; and 11, which would beat with 10 and 12. It is this circum¬ 
stance which renders the major chord of such great importance in 
harmony. If the constituents of the minor chord are similarly dis¬ 
cussed, namely three compound tones whose primaries are proportional to 
10, 12, 15, it will be found to differ from the major chord in the follow¬ 
ing principal respects : (a) The primary of the natural tone to which it 
approximates is very much deeper than that of the corresponding 
major chord. ( b ) It introduces the differential tones, 2, 3, 5, which 
form a major chord. Now it has already been remarked that when a 
major and minor chord are sounded together they are distinctly dissonant, 
for example when C, E, G, A, are sounded together. Accordingly, the fact 
of the differential tones forming a major chord shows that an elementary 
dissonance exists in every minor chord. 


CHAPTER IV. 

VIBRATIONS OF STRETCHED STRINGS, AND OF COLUMNS OF AIR. 

227. Vibrations of strings. —By a string is meant the string of a 
musical instrument, such as a violin, which is stretched by a certain force, 
and is commonly of catgut or is a metallic wire. The vibrations which 
strings experience may be either transversal or longitudinal , but prac¬ 
tically the former are alone important. Transversal vibrations may 






VIBRATIONS OF STRINGS. 


191 


- 229 "; 

be produced by drawing a bow across tbe string, as in the case of the 
violin; or by striking the string, as in the case of the pianoforte ; or by 
pulling them transversely and then letting them go suddenly, as in the 
case of the guitar and the harp. 

228. Sonometer.— The sonometer is an apparatus by which the 
transverse vibrations of strings may be studied. It is also called 
monochord , because it has generally only one string. In addition to the 
string, it consists of a thin wooden box to strengthen the sound ; on this 
there are two fixed bridges A and D (fig. 159), over which passes the 
string, which is commonly a metallic wire. This is fastened at one end, 
and stretched at the other by a weight P, which can be increased at will. 
By means of a third moveable bridge B, the length of that portion of 
the wire which is to be put in vibration can be altered at pleasure. 

229. laws of the transverse vibrations of strings,— If l be the 
length of a string, that is, the vibrating part between two bridges A 
and B (fig. 159), r the radius of the string, d its density, P the stretching- 
weight, and n the number of vibrations per second, it is found by calcu¬ 
lation that n ~2ri\/ ^ 5 77 being the ratio of the circumference to 

./ Si 

the diameter. This formula is frequently written n =—j- x 9*8257 

where c is such a length of the string or wire used that its weight would 
be the same as the stretching weight. 



Fig. 159. 

From this formula the following laws have been deduced: 

I. The tension being constant, the number of vibrations per second is 
inversely as the length. 

II. The number of vibrations per second is inversely as the radius of 
the string. 

III. The number of vibrations per second is directly as the square root of 

the stretching weight or tension. 

m 
















192 ACOUSTICS. [ 230 - 

IV. Jhe number of vibrations per second of a string is inversely as the 
square root of i*s density. 

These laws are applied in the construction of stringed instruments, in 
which the length, diameter, tension, and substance of the strings are so 
chosen, that such and such notes may he elicited from them. 

230. Nodes and loops.— Let us suppose the string AD (fig. 160) 
to begin vibrating, the ends A and D being fixed, and while it is doing 
so let a point B be brought to rest by a stop, and let us suppose DB to 
be one third part of AD. The part DB must now vibrate about B and 
D as fixed points in the manner indicated by the continuous and dotted 
lines $ now all parts of the same string tend to make a vibration in the 
same time; accordingly, the part between A and B will not perform a 
single vibration, but will divide into two at the point C, and vibrate in 
the manner shown in the figure. If BD were one fourth part of AD, 
the part AB would be subdivided at C and C into three vibrating 

o 


Fig. 160 . 




Fig. 161 . 

portions each equal to BD. The points B, C, C , are called nodes or nodal 
points; the middle point of the part of the string between any two 
consecutive nodes is called a loop, or a ventral segment. It will be 
remarked that the ratio of BD : BA must be that 'of some two whole 
numbers, for example 1 : 2, 1 : 3, 2:3, etc., otherwise the nodescannot be 
formed,. since the two portions of the string cannot then be made to 
vibrate in the same time, and the vibrations will interfere with and soon 
destroy one another. 

If now we refer back to fig. 160, the existence of the node at C can 
be easily proved by bending some light pieces of paper, and placing 
them on the string. Say three pieces, one at C and the others respec¬ 
tively midway between B and G, and between C and A. The one at C 
experiences only a very slight motion, and remains in its place, thereby 





























- 232 ] MOUTH AND HEED INSTRUMENTS. 193 

proving the existence of a node at C ; the other two are violently- 
shaken, and in most cases thrown off the string. 

When a musical string vibrates between fixed points A and B, its 
motion is not quite so simple as might be inferred from the above 
description. In point of fact, partial vibrations are soon produced, and 
superimposed upon the primary vibrations. The partial vibrations 
correspond to the half, third, fourth, etc. parts of the string. It is by 
these partial vibrations that the harmonics are produced which accom¬ 
pany the primary note due to the primary vibrations. 

231. Wind instruments. —In the cases hitherto considered the sound 
results from the vibrations of solid bodies, and the air only serves as a 
vehicle for transmitting them. In wind instruments, on the contrary, 
when the sides of the tube are of adequate thickness, the enclosed 
column of air is the sonorous body. In fact, the substance of the tubes 
is without influence on the primary tone; with equal dimensions it is 
the same whether the tubes are of glass, of wood, or of metal. These 
different materials simply do no more than give rise to different har¬ 
monics, and impart a different colour to the compound tone produced. 

In reference to the manner in which the air in tubes is made to vibrate, 
wind instruments are divided into mouth instruments and reed instruments. 

232. Mouth instruments.— In mouth instruments all parts of the 
mouthpiece are fixed. Fig. 162 represents the mouthpiece of an organ 
pipe, and fig. 163 that of a whistle, or of a flageolet. In both figures, 
the aperture ib is called the mouth ; it is here 
that air enters the pipe; b and o are the lips, 
the upper one of which is bevelled. The 
mouthpiece is fixed at one end of a tube, the 
other end of which may be either opened or 
closed. In fig. 162 the tube can be fitted 
on a wind-chest by means of the foot P. 

When a rapid current of air enters by the 
mouth, it strikes against the upper lip, and 
a shock is produced which causes the air to 
issue from bo in an intermittent manner. In 
this way, pulsations are produced which, trans¬ 
mitted to the air in the pipe, make it vibrate, 
and a sound is the result. In order that a pure 
note may be produced, there must be a certain 
relation between the form of the lips and the 
magnitude of the mouth; the tube also 
ought to have a great length in comparison 
with its diameter. The number of vibrations depends in general on the 
dimensions of the pipe, and the velocity of the current of air. 

K 



Fig. 163. Fig. 162. 

















194 


ACOUSTICS. 


[ 233 - 


233. Reed instruments.— In reed instruments a simple elastic 
tongue sets the air in vibration. The tongue, which is either of metal 
or of wood, is moved by a current of air. The mouthpieces of the oboe, 
the bassoon, the clarionet, the child’s trumpet, are different applications 
of the reed, which, it may be remarked, is seen in its simplest form in the 
Jew’s harp. Some organ pipes are reed pipes, others are mouth pipes. 

Fig. 164 represents a model of a reed pipe as commonly shown in 
lectures. It is fixed on the wind-chest Q of a bellows, and the vibra¬ 
tions of the reed can be seen through a piece of glass, E, fitting into the 
sides. A wooden bom, H, strengthens the sound. 

Fig. 165 shows the reed out of the pipe. It consists of four pieces: 
1st, a rectangular wooden tube closed below and open above at o ; 2nd, a 


copper plate cc forming one side of the 
tube, and in which there is a longitu¬ 
dinal aperture, through which air passes 
from the tube MN to the orifice o ; 3rd, 
a thin elastic plate i called the tongue, 
which is fixed at its upper end, and 
which grazes the edge of the longitu¬ 
dinal aperture, nearly closing it; 4th, a 
curved wire r, which presses against the 
tongue, and can be moved up and down. 
It thus regulates the length of the 
tongue, and determines the 
pitch of the note. It is by 
this wire that reed pipes are 
tuned. The reed being re¬ 
placed in the pipe MN, when 
a current of air enters by the 
foot P, the tongue is com¬ 
pressed, it bends inwards, and 
affords a passage to air, which 
escapes by the orifice o. But 
being elastic the tongue re¬ 
gains its original position, and 
performing a series of oscilla¬ 
tions, successively opens and 
closes the orifice. In this way sonorous waves result and produce a note, 
whose pitch increases with the velocity of the current. 

In this reed, the tongue vibrates alternately before and behind the 
aperture, merely grazing the edges, as is seen in the harmonium, con¬ 
certina, etc .; such a reed is called a free reed. But there are other reeds 
called beating reeds, in which the tongue, which is larger than the orifice, 




Fig. 164. 


Fig. 165. Fig. 166. 





























- 235 ] NODES AND LOOPS OF AN ORGAN PIPE. 195 

strikes against the edges at each oscillation. The reed of the clarionet, 
represented in fig. 166, is an example of this; it is kept in its place by 
the pressure of the lips. The reeds of the hautboy and bassoon are also 
of this kind. 

234. Of the tones produced by the same pipe. —Daniel Bernouilli 
discovered that the same organ pipe can be made to yield a succession of 
tones by properly varying the force of the current of air. The results he 
arrived at may be thus stated :— 

i. If the pipe is open at the end opposite to the mouthpiece, then, 
denoting the primary tone by 1, we can, by gradually increasing the force 
of the current of air, obtain successively the tones 2, 3, 4, 5, etc., that is 
to say, the harmonics of the primary tone. 

ii. If the pipe is closed at the end opposite to the mouthpiece, then, 
denoting the primary tone by 1, we can, by gradually increasing the force 
of the current of air, obtain successively the tones 3, 5, 7, etc., that is to 
say, the uneven harmonics of the primary tone. 

It must be added that if a closed and an open pipe yield the same 
primary tone, the closed pipe must be half the length of the open pipe, 
if in other respects they are the same. 

In any case it is impossible to produce from the given pipe a tone not 
included in the above series respectively. 

Although the above laws are enunciated with reference to an organ 
pipe, they are of course true of any other pipe of uniform section. 

235. On the nodes and loops of an organ pipe.— The vibrations 
of the air producing a musical tone take place in a direction parallel to 
the axis of the pipe—not transversely, as in the case of the portions of 
a vibrating string. In the former case, however, as well as in the latter, 
the phenomena of nodes and loops may be produced. But now by a node 
must be understood a section of the column of air contained in the pipe 
where the particles remain at rest, but where there are rapid alternations 
of condensation and rarefaction. By a loop or ventral segment must be 
understood a section of the column of air contained in the pipe, where 
the vibrations of the particles of air have the greatest amplitudes, and 
where there is no change of density. The sections of the column of air 
are, of course, made at right angles to its axis. When the column of air 
is divided into several vibrating portions it is found that the distance 
between any two consecutive loops is constant, and that it is bisected by 
a node. We can now consider separately the cases of the open and 
closed pipes. 

i. In the case of the open pipe, whatever tone it produces, there must 
be a loop at each end, since the inclosed column of air is in contact with 
the external air at those points. When the primary tone is produced 

k 2 


190 


ACOUSTICS. 


[235- 

there will be a loop at each end, and a node at the middle section of the 
pipe, the nodes and loops dividing the column into tivo equal parts. 
When the first harmonic (2) is produced, there will be a loop at each 
end, and a loop in the middle, the column being divided into four equal 
parts by the alternate loops and nodes. When the second harmonic (3) 
is produced, the column of air will be divided into six equal parts by the 
alternate nodes and loops, and so on. It will be remarked that the 
successive modes of division of the vibrating column are the only ones 
compatible with the alternate recurrence at equal intervals of nodes and 
loops, and with the occurrence of a loop at each end of the pipe. 

ii. In the case of the closed pipe, there will still be a loop at the end 
next to the mouthpiece, but there will be a node at the closed end, since 
the air in contact with a fixed stop must be at rest. Accordingly the 
successive modes of division of the column of air must be compatible 
with this arrangement, and it will be found that when the primary tone 
is produced, there will be merely a loop at one end, and a node at the 
other. When the first harmonic (3) is produced, the column is divided 
into three equal parts by alternate loops and nodes. When the second 
harmonic (5) is produced, the column is divided into five equal parts, and 
so on. 

There are several experiments by which the existence of nodes and 
loops can be shown. 

(a) If a fine membrane is stretched over a pasteboard ring, and has 
sprinkled on it some fine sand, it can be gradually let down a tube as 
shown in fig. 169. Now suppose the tube to be producing a musical 
note. As the membrane descends it will be set in vibration by the 
vibrating air. But when it reaches a node it will cease to vibrate, for 
there the air is at rest. Consequently the grains of sand, too, will be at 
rest, and their quiescence will indicate the position of the node. On the 
other hand, when the membrane reaches a loop, that is, a point where 
the amplitude of the vibrations of the air attains a maximum, it will be 
violently agitated, as will be shown by the agitation of the grains of sand. 
And thus the positions of the loops can be rendered manifest. 

( b ) Again, suppose a pipe to be constructed with holes bored in one 
of its sides, and these covered by little doors which can be opened and 
shut, as shown in fig. 167. Let us suppose the little doors to be shut 
and the pipe to be caused to produce such a tone that the nodes are at 
N and N' and the loops at V, V', V". At the latter points the density 
is that of the external air, and consequently if the door at V' is opened 
no change is produced in the note. At the former points N and N' there 
are alternately condensation and rarefaction taking place. If now the 
door at N' is opened this alternation of density is no longer possible, for 
the density at this open point must be the same as that of the external air, 


NODES AND LOOPS OF AN ORGAN PIPE. 


197 


-235] 

and consequently N' becomes a loop and the note yielded by the tube is 
changed. The change of notes produced by changing the fingering of 
the flute is, of course, one form of this experiment. 

(c) Suppose A, in fig. 168, to be a pipe emitting a certain note, and 
suppose P to be a plug, fitting the tube, fastened to the end of a long rod 
by which it can be forced down the tube. Now when the plug is in¬ 



serted, whatever be its position, there will be a node in contact with it. 
Consequently as it is gradually forced down, the note yielded by the pipe 
will keep on changing. But every time it reaches a position which was 
occupied by a node before its insertion, the note becomes the same as the 
note originally yielded. For now the column of air vibrates in exactly 
the same manner as it did before the plug was put in. 































198 


ACOUSTICS. 


[236- 

(cT) Fig. 170 shows the manner in which the following beautiful ex¬ 
periment is performed. The figure represents an organ pipe, on one side 
of which is a chest P filled with coal gas, by 
means of the tube S. The gas from the chest 
comes out in three jets at A, B, C, and is then 
ignited. The manner in which the gas passes 
from the chest to the point of ignition is shown 
in the smallest figure, which is an enlarged 
section of A. A circular hole is bored in the 
side of the pipe and covered with a membrane 
r. A piece of wood is fitted into the hole so 
as to leave a small space between it and the 
membrane. The gas passes from the chest, in 
the direction indicated by the arrow, into the 
space between the membrane and the piece of 
wood and so out by the tube m , at the mouth 
of which it is ignited. Now suppose the pipe 
to be caused to yield its primary note, then 
as it is an uncovered pipe there ought to 
be a node at B, its middle point. Conse¬ 
quently there ought to be rapid changes of 
density at B; these would cause the mem¬ 
brane r to vibrate, and thereby blow out the 
flame m, and this is what actually happens. 
If by increasing the force of the wind the 
octave to the primary note is produced, B will 
be a loop, and A and C nodes. Consequently 



Fig. 170. 


the flames at A and C will now be extinguished, as is, in point of fact, 
the case. But at B, there being no change of density, the membrane is 
unmoved, and the flame continues to burn steadily. 

By each and all of these experiments it is shown that in a given pipe, 
whether open or closed, there are always a certain number of nodes, and 
midway between any two consecutive nodes there is always a loop or 
ventral point. 

286. Explanation of the existence of nodes and loops in a 
musical pipe. —The existence of nodes and loops is to be explained by 
the co-existence in the same pipe of two equal waves travelling in con¬ 
trary directions. 

Let A be a point from which a series of waves sets out towards B, and 
let the lengths of these waves, whether of condensation or rarefaction, be 
AC, CD, orDB. And letB be the point from which the series of exactly 
equal waves sets out towards A. It must be borne in mind that in the 
case of a wave of condensation originating at A the particles move in the 













NODES AND LOOPS OF AN ORGAN PIPE. 


199 


- 236 ] 


direction A to B, but in a wave of condensation originating at B they 
move in the direction B to A. Now let us suppose that condensation at 
C, caused by the wave from A, begins at the same instant that condensa¬ 
tion caused by the wave from B begins at D. Consequently, restricting 
our attention to the particles in the line CD, at any instant the velocities 
of the particles in CD due to the former wave will be represented by the 
ordinates of the curve SPRT, while those due to the wave from B will 
be represented by the co-ordinates of the curve TQrS. Then, since the 
waves travel with the same velocity and are at C and D respectively 



at the same instant, we must have, for any subsequent instant, CR 
equal to Dr. If, therefore, N is the middle point between C and D, 
we must have rN equal to RN, and consequently PN equal to QN, 
that is to say, if the particle at N transmitted only one vibration, its 
motion at each instant would be in the opposite phase to that of its 
motion if it transmitted only the other vibration. In other words the 
particle N will at every instant tend to be moved with equal velocity in 
opposite directions by the two waves, and therefore will be permanently 
at rest. That point is therefore a node. In like manner there is a node at 
N' midway between A and C, and also at N" midway between B and D. 
In regard to the motion of the remaining particles it is plain that their 
respective velocities will be the (algebraical) sum of the velocities they 
would at each instant receive from the waves separately. Hence at the 
instant indicated by the diagram they are given by the ordinates of the 
curve HNK. This curve will change from instant to instant, and at 
the end of the time occupied by the passage of a wave of condensation 
(or of rarefaction) from C to D will occupy the position shown by the 
dotted line hNk. Hence it is evident that particles near N have but 
small changes of velocity, while those near 0 and D experience large 
changes of velocity. 

If the curve HK were produced both ways it would always pass 
through N' and N"; the part, however, between N and N' would 
sometimes be on one side and sometimes on the other side of AB. 
Hence all the particles between N' and N have, simultaneously, first a 
motion in the direction A to B, and then a motion in the direction B to 
A, those particles near C having the greatest amplitude of vibration. 
Hence near N and N' there will be alternately the greatest condensation 
and rarefaction. 





200 


ACOUSTICS. 


[237- 


This explanation applies to the case in which AB is the axis of an open 
organ pipe, A being the end where the mouthpiece is situated. The 
waves from B have their origin in the reflection of the series of waves 
from A. In the particular case considered, the note yielded by the pipe is 
that indicated by 3, that is, the fifth above the octave to the primary note. 
A similar explanation can obviously be applied to all other cases, and 
whether the end be opened or closed. But in the latter case the series of 
waves from the closed end must commence at a point distant from the 
mouthpiece by a space equal to one half, or three halves, or five halves, 
etc. of the length of a wave of condensation or expansion. 

237. Chemical harmonicon.— The air in an open tube may be made 
to give a sound by means of a luminous jet of hydrogen, coal gas, etc. 
When a glass tube about 12 inches long is held over a lighted jet of 
hydrogen (Sg. 172), a note is produced, which, if the tube is in a certain 
position, is the fundamental note of the tube. The sounds, doubtless, arise 
from the successive explosions produced by the periodic combinations of 
the atmospheric oxygen with the issuing jet of hydrogen. The apparatus 
is called the chemical harmmicon. 

The phenomena of the chemical harmonicon 
and of surging flames have been investigated 
by Prof. Tyndall, whose Lectures on Sound 
contain a number of very beautiful experiments 
on this subject. 

The note depends on the size of the flame 
and the length of the tube: with a long tube, 
by varying the position of the jet in the tube, 
the series of notes in the ratio 1 : 2 : 3 : 4 : 5 
is obtained. 

If, while the tube emits a certain sound, the 
voice or the syren (213) be gradually raised 
to the same height, as soon as the note is 
nearly in unison with the harmonicon, the 
flame becomes agitated, jumps up and down, 
and is finally steady when the two sounds 
are in unison. If the tone of the syren is 
gradually heightened, the pulsations again 
commence; they are the optical expressions 
of the beats (224) which occur near perfect 
unison. 

If, while the jet burns in the tube and pro¬ 
duces a note, the position of the tube is slightly 
altered, a point is reached at which no sound is heard. If now the voice, 
or the syren, or the tuning fork, be pitched at the note produced by the 



Fig. 172. 













STRINGED AND WIND INSTRUMENTS. 


201 


- 239 ] 

jet, it begins to sing, and continues to sing even after the syren is silent. 
A mere noise, or shouting at an incorrect pitch, affects the flame, but 
does not cause it to sing. 

238. Stringed instruments. —Stringed musical instruments depend 
on the production of transverse vibrations. In some, such as the piano, 
the sounds are constant , and each note requires a separate string: hi 
others, such as the violin and guitar, the sounds are varied by the 
fingering, and can be produced by fewer strings. 

In the piano the vibrations of the strings are produced by the stroke of 
the hammer , which is moved by a series of bent levers communicating 
with the keys. The sound is strengthened by the vibrations of the air in 
the sounding board on which the strings are stretched. Whenever a key 
is struck, a damper is raised which falls when the finger is removed from 
the key and stops the vibrations of the corresponding string. By means 
of a pedal all the dampers can be simultaneously raised, and the vibrations 
then last for some time. 

The harp is a sort of transition from the instruments with constant to 
those with variable sounds. Its strings correspond to the natural notes 
of the scale: by means of the pedals the lengths of the vibrating parts 
can be changed, so as to producesharps and flats. The sound is strengthened 
by the sounding box, and by the vibrations of all the strings harmonic 
with those played. 

In the violin and guitar each string can give a great number of sounds, 
according to the length of the vibrating part, which is determined by the 
pressure of the fingers of the left hand while the right hand plays the 
bow, or the strings themselves. In both these instruments the vibrations 
are communicated to the upper face of the sounding box, by means of the 
bridge over which the strings pass. These vibrations are communicated 
from the upper to the lower face of the box, either by the sides or by an 
intermediate piece called the sound post. The air in the interior is set in 
vibration by both faces, and the strengthening of the sound is produced 
by all these simultaneous vibrations. The value of the instrument con¬ 
sists in the perfection with which all possible sounds are intensified, 
which depends essentially on the quality of the wood, and the relative 
arrangement of the parts. 

239. Wind instruments. —All wind instruments may be referred 
to the different types of sonorous tubes which have been described. In 
some, such as the organ, the notes are Jixed , and require a separate pipe 
for each note; in others the notes are variable , and are produced by only 
one tube: the flute, horn, etc., are of this class. 

In the organ the pipes are of various kinds, namely, mouth pipes, open 
and stopped, and reed pipes with apertures of various shapes. By means 
of stops the organist can produce any note by both kinds of pipe. 

x 3 


202 


ACOUSTICS. 


[ 240 - 

In the Jiute, the mouthpiece consists of a simple lateral circular aper¬ 
ture ; tne current of air is directed by means of the lips, so that it grazes 
the edge of the aperture. The holes at different distances are closed 
either by the fingers or by keys; when one of the holes is opened, a loop 
is produced in the corresponding layer of air, which modifies the distri¬ 
bution of nodes and loops in the interior, and thus alters the note. The 
whistling of a key is similarly produced. 

The pandcean pipe consists of tubes of different sizes corresponding to 
the different notes of the gamut. 

In the trumpet, the horn, the trombone, cornet-a-piston, and ophicleide, 
the lips form the reed, and vibrate in the mouthpiece. In the horn, 
different notes are produced by altering the distance of the lips. In the 
trombone , one part of the tube slides within the other, and the performer 
can alter at will the length of the tube, and thus produce higher or lower 
notes. In the cornet-h-piston, the tube forms several convolutions; pistons 
placed at different distances can, when played, cut off communication 
with other parts of the tube, and thus alter the length of the vibrating 
column of air. 


CHAPTER V. 

VIBRATIONS OF RODS, PLATES, AND MEMBRANES. 

240. Vibrations of rods.— Rods and narrow plates of wood, of glass, 
and especially of tempered steel, vibrate in virtue of their elasticity; like 
strings they have two. kinds of vibrations, longitudinal and transverse. 
The latter are produced by fixing the rods at one end, and passing a bow 
over the free part. Longitudinal vibrations are produced by fixing the 
rod at any part, and rubbing it in the direction of its length with a piece 
of cloth sprinkled with resin. But in the latter case the sound is only 
produced when the point of the rod at which it has been fixed is some 
aliquot part of its length, as a half, a third, or a quarter. 

It is shown by calculation that the number of transverse vibrations made 
in a given time by rods and thin plates of the same kind is directly as their 
thickness, and inversely as the square of their length. The width of the plate 
does not affect the number of vibrations. A wide plate, however, 
requires a greater force to set it in motion than a narrow one. It is, 
of course, understood that one end of the vibrating plate is held firmly. 

In elastic rods of the same kind the number of Imgitudinal vibrations is 
inversely as their length, whatever be the diameter and form of their trans- 
verse section. 






VIBRATIONS OF RODS AND PLATES. 


203 


~24l] 

Fig. 173 represents an instrument invented by Marloye, based 
on the longitudinal vibration of rods. It consists of a solid wooden 
pedestal in which are fixed 
twenty thin deal rods, some col¬ 
oured and others white. They 
are of such a length that the 
white rods give the diatonic scale, 
while the coloured ones give the 
half notes, and complete the 
chromatic scale. The instrument 
is played by rubbing the rods 
in the direction of their length 
between the finger and thumb, 
which have been previously 
covered with powdered resin. 

The notes produced resemble 
those of a pandsean pipe. 

The tuning-fork , the triangle , 
and musical boxes, are examples 
of the transverse vibrations of 
rods. In musical boxes small 
plates of steel of different dimen¬ 
sions are fixed on a rod, like the 
teeth of a comb. A cylinder, 
whose axis is parallel to this rod, 
and whose surface is studded with 
steel teeth, arranged in a certain Fig. 173. 

order, is placed near the plates. 

By means of a clockwork motion the cylinder rotates, and the teeth 
striking the steel plates set them in vibration, producing a tune, which 
depends on the arrangement of the teeth on the cylinder. 

241. Vibrations of plates.— In order to make a plate vibrate it is 
fixed in the centre (fig. 174), and a bow rapidly drawn across one of the 
edges; or else it is fixed at any point of its surface, and caused to vibrate 
by rapidly drawing a string covered with resin against the edges of a 
central hole (fig. 175). 

Vibrating plates contain nodal lines (230), which vary in number and 
position according to the form of the plates, their elasticity, the mode of 
excitation, and the number of vibrations. These nodal lines may be 
made visible by covering the plate with fine sand before it is made to 
vibrate. As soon as the vibrations commence, the sand leaves the 
vibrating parts, and accumulates on the nodal lines, as seen in figs. 174 
and 175. 













































204 


ACOUSTICS. 


[ 242 - 

The position of the nodal lines may he determined by touching the 
points at which it is desired to produce them. Their number increases 
with the number of vibrations, that is, as the note given by the plates is 
higher. The nodal lines always possess great symmetry of form, and the* 
same form is always produced on the same plate under the same conditions. 
They were discovered by Chladni. 

The vibrations of plates are governed by the following law : In plates 
of the same kind and shape, and giving the same system of nodal lines, the 
number of vibrations per second is directly as the thickness of the plates, and 
inversely as their area. 

Gongs and cymbals are examples of instruments in which sounds are 
produced by the vibration of metallic plates. The glass harmonicon 
depends on the vibrations of glass plates. 



Fig. 174. 


Fig. 175. 


242. Vibrations of membranes.— In consequence of their flexibility, 
membranes cannot vibrate unless they are stretched, like the skin of a drum. 
The sound they give is more acute in proportion as they are smaller and 
more tightly stretched. To obtain vibrating membranes, Savart fastened 
goldbeater’s-skin on wooden frames. 

In the drum, the skins are stretched on the ends of a cylindrical box. 
When one end is struck, it communicates its vibrations to the internal 
column of air, and the sound is thus considerably strengthened. The 
cords stretched against the lower skin strike against it when it vibrates, 
and produce the sound characteristic of the drum. 

Membranes either vibrate by direct percussion, as in the drum, or they 
may be set in vibration by the vibrations of the air, as Savart has observed, 




VIBRATIONS OF MEMBRANES. 


205 


-242] 

provided these vibrations are sufficiently intense. Fig. 156 shows a 
membrane vibrating under the influence of the vibrations in the air caused 
by a sounding bell. Fine sand strewed on the membrane shows the for¬ 
mation of nodal lines just as upon plates. 

There are numerous instances in which solid bodies are set in vibration 
by the vibrations of the air. The condition most favourable for the pro¬ 
duction of this phenomenon is, that the body to be set in vibration is 
under such conditions that it can readily produce vibrations of the same 
duration as those transmitted to it by the air. The following are some 
of these phenomena: 

If two violoncello strings tuned in unison are stretched on the same 
sound-box, as soon as one of them is sounded, the other is set in vibra¬ 
tion. This is also the case if the interval of the strings is an octave, or 
a perfect fifth. A violin string may also be made to vibrate, by sounding 
a tuning fork. 


Fig. 176. 

Two large glasses are taken of the same shape, and as nearly as 
possible of the same dimensions and weight, and are brought in unison 
by pouring into them proper quantities of water. If now one of them 
is sounded, the other begins to vibrate, even if it is at some distance, but 
if water be added to the latter, it ceases to vibrate. 

Breguet found that if two clocks, whose time was not very different, 
were fixed on the same metallic support, they soon attained exactly the 
same time. 

Membranes are eminently fitted for taking up the vibrations of the 
air on account of their small mass, their large surface, and the readiness 
with which they subdivide. With a pretty strong whistle, nodal lines 
may be produced in a membrane stretched on a frame, even at the end 
of a large room. 

The phenomenon so easily produced in easily moved bodies is also 
found in large and less elastic masses; all the pillars and walls of a 
church vibrateTnore or less while the bells are being rung. 





206 


ACOUSTICS. 


[ 243 - 


CHAPTER VI. 

GRAPHICAL METHODS OF STUDYING VIBRATORY MOVEMENTS. 

243. 3VI. Xiissajous’ method of making: vibrations apparent. 

—The method of M. Lissajous exhibits the vibratory motion of bodies 
either directly or by projection on a screen. It has also the great 
advantage that the vibratory motions of two sounding bodies may be 
compared without the aid of the ear , so as to obtain the exact relation 
between them. 

This method, which depends on the persistence of visual sensations 
on the retina, consists in fixing a small mirror on the vibrating body, 
so as to vibrate with it, and impart to a luminous ray a vibratory motion 
similar to its own. 



Fig. 177. 


M. Lissajous uses tuning forks, and fixes to one of the prongs a small 
metallic mirror, m (fig. 177), and to the other a counterpoise, n, which 
is necessary to make the tuning fork vibrate regularly for a long 
time. At a few yards’ distance from the mirror there is a lamp 
surrounded by a dark chimney, in which there is a small hole, giving 









244 ] GRAPHICAL METHODS OF STUDYING VIBRATORY MOVEMENTS. 207 

a simple luminous point. The tuning 1 fork being at rest, the . eye is 
placed so that the luminous point is seen at o. The tuning fork is 
then made to vibrate, and the image elongates so as to form a persistent 
image oi, which diminishes in proportion as the amplitude of the oscilla¬ 
tion decreases. If, during the oscillation of the mirror, it is made to 
rotate by rotating the tuning fork on its axis, a sinuous line, oix , is 
produced instead of the straight line oi. These different effects are 
explained by the successive displacements of the luminous pencil, and 
by the duration of these luminous impressions on the eye after the 
cause has ceased, a phenomenon to which we shall revert in treating of 
vision. 



Fig. 178. 


If, instead of viewing these effects directly they are projected on the 
screen, the experiment is arranged as shown in fig. 178, the pencil 
reflected from the vibrating mirror is reflected a second time from a 
fixed mirror, m, which sends it towards an achromatic lens, l, placed so 
as to project the images on the screen. 

244. Combination of two vibratory motions in the same 
direction. —M. Lissajous has resolved the problem of the optical com¬ 
bination of two vibratory motions — vibrating at first in the same 
direction, and then at right angles to each other. 






















208 


ACOUSTICS. 


[ 245 - 

Fig. 179 represents the experiment as arranged for combining two 
parallel motions. Two tuning forks provided with mirrors are so 
arranged that the light reflected from one of them reaches the other, which 
is almost parallel to it, and is then sent towards a screen after having 
passed through a lens. 

If now the first tuning fork alone vibrates, the image on the screen is 
the same as in experiment 179 ; but if they both vibrate, supposing they 
are in unison, the elongation increases or diminishes according as the 
simultaneous motions imparted to the image by the vibrations of the 
mirrors do or do not coincide. 



Fig. 179. 


If the tuning forks pass their position of equilibrium in the same time, 
and in the same direction, the image attains its maximum; and the 
image is at its minimum when they pass at the same time but in opposite 
directions. Between these two extreme cases the amplitude of the 
image varies according to the time which elapses between the exact 
instant at which the tuning forks pass through their position of rest 
respectively. The ratio of this time to the time of a double vibration is 
called a difference of phase of the vibration. 

If the tuning forks are exactly in unison, the luminous appearance on 
the screen experiences a gradual diminution of length in proportion as 
the amplitude of the vibration diminishes ; but if the pitch of one is very 
little altered, the magnitude of the image varies periodically, and, while 
the beats resulting from the imperfect harmony are distinctly heard, the 
eye sees the concomitant pulsations of the image. 

245. Optical combination of two vibratory motions at right 
angles to each other.— The optical combination of two rectangular 
vibratory motions is effected as shown in the figure 180, that is, by 
means of two tuning forks, one of which is horizontal and the other 
vertical, and both provided with mirrors. If the horizontal fork first 






- 245 ] GRAPHICAL METHODS OF STUDYING VIBRATORY MOVEMENTS. 209 

vibrates alone, a horizontal luminous outline is seen on the screen, while 
the vibration of the other produces a vertical image. If both tuning 
forks vibrate simultaneously the two motions combine, and the reflected 
pencil describes a more or less complex curve, the form of which depends 



Fig. 180 . 



on the number of vibrations of the two tuning forks in a given time. 
This curve, gives a valuable means of comparing the number of vibrations 
of two sounding bodies. 



Fig. 181 shows the luminous image on the screen when the tuning 
forks are in unison, that is, when the number of vibrations is equal. 

The fractions below each curve indicate the differences of phase; 
between them. The initial form of the curve is determined by the 









210 


ACOUSTICS. 


[ 245 - 


difference of phase. The curve retains exactly the same form when t e 
tuning forks are in unison, provided that the amplitudes of the two 
rectangular vibrations decrease in the same ratio. 

If the tuning forks are not quite in unison, the initial difference o 
phase is not preserved, and the curve passes through all its variations. 






1 

8 


Z i 

8 




Fig. 182. 


Fig. 182 represents the different appearances of the luminous image 
when the difference between the tuning forks is an octave ; that is, when 
the numbers of their vibrations are as 1 : 2 ; and fig. 183 gives the 
series of curves when the numbers of the vibrations are as 3 : 4. 



It will be seen that the curves are more complex when the ratios or 
the numbers of vibrations are less simple. M. Lissajous has examined 
these curves theoretically (Annales de Physique et de Chimie, 1857), and 
has calculated their general equations. 

When these experiments are made with a Dubescq’s photo-electrical 
















-246] THE PHONAUTOGRAPII. 211 

| apparatus instead of an ordinary lamp, the phenomena are remarkably 
i brilliant. 

246. Iieon Scott’s Phonautogrraph.— This beautiful apparatus pas¬ 
s' sesses the great advantage of being able to register not only the vibra- 
• tions produced by solid bodies, but also those produced by wind in¬ 
struments, by the voice in singing, and even by any noise whatsoever, 
1 for instance, that of thunder, or the report of a cannon. It consists of an 
ellipsoidal cask, AB, about a foot and a half long and a foot in its 
f greatest diameter. It is made of plaster of Paris, a substance which can 
» be made to vibrate only with difficulty, and therefore has but little ten- 



Fig. 184. 


dency to deaden the vibrations of the air within it. The end A is open, 
but the end B is closed by a solid bottom, to the middle of which is 
1 fitted a brass tube a, bent at an elbow and terminated by a ring on 
which is fixed a flexible membrane, either bladder, or very thin indian 
' rubber. A second ring, which is forced more or less on the first by 
means of a screw, serves to stretch the membrane to the required amount. 
The tube a can be turned so as to be inclined at different angles to the 
membrane. Near the centre of the membrane, fixed by sealing wax, is a 
very light style, which, of course, shares the movements of the membrane. 

I In order that the style might not be at a node, M. Scott fitted the 















212 


ACOUSTICS. 


[ 246 - 

stretching ring with a moveable piece i, which he calls a subdivider, and 
which, being made to touch the membrane first at one point and then at 
another, enables the experimenter to alter the arrangements of the nodal 
lines at will. By means of the subdivider the point is made to coincide 
with a loop, that is, a point where the vibrations of the membrane are a 
maximum. In construction the phonautograph is very analogous to the 
organ of hearing, the ellipsoid corresponding to the auditory canal, the 
membrane to the tympanum, and the subdivider to the chain of little 
bones which touch the tympanum. 

This being the construction, it follows that when a sound is produced 
near the apparatus, the air in the ellipsoid, the membrane, and the style 
will vibrate in unison with it, and it only remains to trace on a sensitive 
surface the vibrations of the style, and to fix them. For this purpose 
there is placed in front of the membrane a copper cylinder C, turning 
round a horizontal axis by means of a handle m. On the prolonged 
axis of the cylinder a screw is cut which works in a nut; consequently, 
when the handle is turned, the cylinder gradually advances in the 
direction of its axis. Round the cylinder is wrapped a sheet of paper, 
covered with a thin layer of lampblack. The lampblack is deposited 
by setting the cylinder in motion, and moving beneath it a smoky 
flame. 

The apparatus is used by bringing the prepared paper into contact 
with the point of the style, and then setting the cylinder in motion 
round its axis. So long as no sound is heard the style remains at rest, 
and merely removes the lampblack along a line which is a helix on the 
cylinder, but which becomes straight when the paper is unwrapped. 
But when a sound is heard, the membrane and the style vibrate in 
unison, and the line traced out is no longer straight but undulates ; each 
undulation corresponding to a double vibration of the style. Conse¬ 
quently the figures thus obtained faithfully denote the number, ampli¬ 
tude, and isochronism of the vibrations. The figures are large if the 
sound is loud, very small if the sound is very weak ; they are stretched 
out when the sound is low, squeezed together when it is high. When 
the sound is clear they are free and regular, feeble and irregular when it 
is confused. It would seem, however, that the figures do not represent 
the whole vibration of the membrane, but only the part of it which 
takes place in a direction parallel to the axis of the cylinder. 

Fig. 185 shows the trace produced when a simple note is sung, and 
strengthened by means of its upper octave. The latter note is repre¬ 
sented by the curve of lesser amplitude. Fig. 186 represents the sound 
produced jointly by two pipes whose notes differ by an octave. Fig. 187 
in its lower line represents the rolling sound of the letter R when 


THE PHONAUTOGRAPH. 


- 246 ] 


213 


pronounced with a ring; and fig. 188 on its lower line represents the 
sound produced by a tin plate when struck with the finger. 

The upper lines of figs. 187 and 188 are the same, and represent the 
perfectly isochronous vibrations of a tuning fork placed near the ellipsoid. 
These lines were traced by a fine point on one branch of the fork, which 
was thus found to make exactly 500 vibrations per second. In conse¬ 
quence, each undulation of the upper line corresponds to the -~o P ar f °f 
a second. And thus these lines become very exact means of measuring 



Fig. 185. 



Fig. 186. 



Fig. 187. 



Fig. 188 . 


short intervals of time. For example, in fig. 187, each of the separate 
shocks producing the rolling sound of the letter It corresponds to about 
18 double vibrations of the tuning fork, and consequently lasts about 
~~ or about ~ a second. 

The curves once traced, it remains to fix them on the blackened paper. 
For this purpose, M. Scott dipped them first into a bath of pure alcohol; 
and when they were dry, he then dipped them into a solution of resin— 
for instance, sandarack—in alcohol. By this means the lampblack is 
perfectly fixed. 






214 


ON HEAT. 


[ 247 - 


BOOK VI. 

ON HEAT 


CHAPTER I. 

PRELIMINARY IDEAS. THERMOMETERS. 

247. Heat. Hypothesis as to its nature. —In ordinary language the 
term heat is not only used to express a particular sensation, but also to 
describe that particular state or condition of matter which produces 
this sensation. Besides producing this sensation, heat acts variously upon 
bodies; it melts ice, boils water, makes metals red-hot, and so forth. 

Two theories as to the cause of heat are current at the present time ; 
these are the theory of emission , and the theory of undulation. 

On the first theory, heat is caused by a subtle imponderable fluid, which 
surrounds the molecules of bodies, and which can pass from one body to 
another. These heat atmospheres , which thus surround the molecules, exert 
a repelling influence on each other, in consequence of which heat acts in 
opposition to the force of cohesion. The entrance of this substance into our 
bodies produces the sensation of warmth, its egress the sensation of cold. 

On the second hypothesis the heat of a body is caused by an oscillating 
or vibratory motion of its material particles, and the hottest bodies are 
those in which the vibrations have the greatest vel^cit^ and the greatest 
amplitude. Hence on this view, heat is not a substance, but a condition 
of matter , and a condition which can be transferred from one body to 
another. It is also assumed that there is an imponderable elastic ether, 
which pervades all bodies and infinite space, and is capable of trans¬ 
mitting a vibratory motion with great velocity. A rapid vibratory 
motion of this ether produces heat, just as sound is produced by a 
vibratory motion of atmospheric air, and the transference of heat from 
one body to another is effected by the intervention of this ether. 

This hypothesis is now admitted by the most distinguished physicists; 
it affords a better explanation of the phenomena of heat than any other 
theory, and it reveals an intimate connection between heat and light. 
In accordance with it, heat is a form of motion; and it will hereafter be 




GENERAL EFFECTS OF HEAT. 


215 


- 248 ] 

( shown that heat may he converted into motion, and reciprocally motion 
may he converted into heat. 

Jn what follows, however, the phenomena of heat will be considered, 
as far as possible, independently of either hypothesis; but we shall sub- 
I sequently return to the reasons for the adoption of the latter hypothesis. 

248. General effects of heat. —The general action of heat upon 
! bodies is to develope a repulsive force between their molecules which is 
continually struggling with molecular attraction. Under its influence 
therefore, bodies tend to expand —that is, to assume a greater volume j 
and then to change their state of aggregation —that is, to pass from the 
solid to the liquid, or from the liquid to the gaseous state. 

All bodies expand by the action of heat. As a general rule gases are 
the most expansible, then liquids, and lastly, solids. 

In solids which have definite figures, we can either consider the ex¬ 
pansion in one dimension, or the linear expansion ; in two dimensions, the 
superficial expansion, or in three dimensions, the cubical expansion or the 
expansion of volume, although one of these never takes place without 
the other. As liquids and gases have no definite figures, the expansions 
of volume have in them alone to be considered. 

To show the linear expansion of solids, the apparatus represented in 
fig. 189 may be used. A metallic rod, A, is fixed at one end by a screw 



Fig. 189. 

B, while the other end presses against the short arm of an index, K, 
which moves on a scale. Below the rod there is a sort of cylindrical 
lamp in which alcohol is burned. The needle, K, is at first at the zero 
point, but as the rod becomes heated it expands, and moves the needle 
along the scale. 

The cubical expansion of solids is shown by a Gravesande's ring. It 
consists of a brass ball, a (fig. 190), which at the ordinary temperature 
passes freely through a ring, m, almost of the same diameter. But 
when the ball has been heated, it expands and no longer passes through 
the ring. 





















216 


ON HEAT. 


[ 249 - 

In order to show the expansion of liquids, a large glass bulb provided 
with a capillary stem is used. When the 
bulb and a part of the stem contain some 
coloured liquid, as soon as heat is applied, 
the liquid rapidly rises in the stem, and the 
expansion thus observed is far greater than 
in the case of solids. 

The same apparatus may be used for 
showing the expansion of gases. Being 
filled with air, a small thread of mercury 
is introduced into the capillary tube to 
serve as index. When the globe is heated 
Fig. 190. in the slightest degree, even by approaching 

the hand, the expansion is so great that the index is driven to the end 
of the tube, and is finally expelled. Hence even for a very small degree 
of heat, gases are highly expansible. 

In these different experiments the bodies contract on cooling, and 
when they have attained their former temperature they resume their 
original volume. Certain metals, however, especially zinc, form an 
exception to this rule, and it appears to be also the case with some hinds 
of glass. 



MEASUREMENT OF TEMPERATURES. THERMOMETRY. 

249. Temperature. —The temperature or hotness of a body may be 
defined as being the greater or less extent to which it tends to impart 
sensible heat to other bodies. The temperature of any particular body is 
varied, by adding to it or withdrawing from it a certain amount of sensi¬ 
ble heat. The temperature of a body must not be confounded with the 
quantity of heat it possesses; a body may have a high temperature and 
yet have a very small quantity of heat, and conversely a low temperature 
and yet possess a large amount of heat. If a cup of water be taken from 
a bucketful, both will indicate the same temperature, yet the quantities 
they possess will be different. This subject of the quantity of heat will 
be afterwards more fully explained in the chapter on Specific Heat. 

250. Thermometers. — Thermometers are instruments for measuring- 
temperatures. Owing to the imperfections of our senses we are unable 
to measure temperatures by the sensations of heat or cold which they 
produce in us, and for this purpose recourse must be had to the physical 
action of heat on bodies. These actions are of various kipds, but the 
expansion of bodies has been selected as the easiest to observe. But heat 
also produces electrical phenomena in bodies; and on these the most 








-252] THERMOMETERS. 217 

delicate methods of observing temperatures have been based, as we shall 
see in a subsequent chapter. 

Liquids are best suited for the construction of thermometers—the ex¬ 
pansion of solids being too small, and that of gases too great. Mercury 
and alcohol are the only liquids used—the former because it only boils at 
a very high temperature, and the latter because it does not solidify at the 
greatest known cold. 

The mercurial thermometer is the most extensively used. It consists 
of a capilhiry glass tube, at the end of which is blown the bulb, a cylin¬ 
drical or spherical reservoir. Both the bulb and a part of the stem are 
filled with mercury, and the expansion is measured by a scale graduated 
either on the stem itself, or on a frame to which it is attached. 

Besides the manufacture of the bulb, the construction of the ther¬ 
mometer comprises three operations; the calibration of the tube or its 
division into parts of equal capacity, the introduction of the mercury 
into the reservoir, and the graduation. 

251. Division of the tube into parts of equal capacity.— As the 
indications of the thermometer are only correct 
when the divisions of the scale correspond to 
equal expansions of the mercury in the reservoir, 
the scale must be graduated so as to indicate 
parts of equal capacity in the tube. If the tube 
were quite cylindrical, and of the same diameter 
throughout, it would only be necessary to divide 
the tube into equal lengths. But as the diameter 
of glass tubes is usually greater at one end than 
another, parts of equal capacity in the tube are 
represented by unequal lengths of the scale. 

In order, therefore, to select a tube of 
uniform calibre, a thread of mercury about 
an inch long is introduced into the capillary 
tube, and moved in different positions in the 
tube, care being taken to keep it at the same 
temperature. If the thread is of the same 
length in every part of the tube, it shows that 
the capacity is everywhere the same; but if 
the thread occupies different lengths the tube 
is rejected, and another one sought. 

252. Filling; the thermometer. —In order 
to fill the thermometer with mercury, a small 
funnel, C (fig. 191), is blown on it at the top, 
and is filled with mercury; the tube is then 
slightly inclined, and the air in the bulb expanded by heating it with 

L 





218 


ON HEAT. 


[253- 


a spirit lamp. The expanded air partially escapes by the funnel, and 
on cooling, the air which remains contracts, and a portion of 'the 
mercury passes into the bulb, D. The bulb is then again warmed, 
and allowed to cool, a fresh quantity of mercury enters, and so on, until 
the bulb and part of the tube are full of mercury. The mercury is then 
heated to boiling; the mercurial vapours in escaping carry with them 
the air and moisture which remain in the tube. The tube, being full of 
the expanded mercury and of mercurial vapour, is hermetically sealed at 
one end. When the thermometer is cold the mercury ought to fill the 
bulb and a portion of the stem. 

258. Graduation of the thermometer. —The thermometer being 
filled, it requires to be graduated, that is, to be provided with a scale to 
which variations of temperature can be referred. And first of all, two 
points must be fixed which represent identical temperatures and can 
always be easily produced. 

Experiment has shown that ice always melts at the same point 
whatever be the degree of heat, and that distilled water under the same 
pressure, and in a vessel of the same kind, always boils at the same tem¬ 
perature. Consequently, for the first fixed point, or zero, the tempera¬ 
ture of melting ice has been taken; and for a second fixed point, the 
temperature of boiling water in a metallic vessel under the normal 
atmospheric pressure of 760 millimeters. 

This interval of temperature, that is, the 
range from zero to the boiling point, is taken 
as the unit for comparing temperatures; just 
as a certain length, a foot or a yard for in¬ 
stance, is used as a basis for comparing lengths. 

254. Determination of the fixed points. 
To obtain zero, snow or pounded ice is placed in 
a vessel, in the bottom of which is an aperture 
by which water escapes (fig. 192). The bulb 
and a part of the stem of the thermometer 
are immersed in this for about a quarter of an 
hour, and a mark made at the level of the 
mercury, which represents zero. 

The second fixed point is determined by 
means of the apparatus represented in the 
figures 193 and 194, of which fig. 194 repre¬ 
sents a vertical section. In both, the same 
letters designate the same parts. The whole 
of the apparatus is of copper. A central tube, 



Fig. 192. 


A, open at both ends, is fixed on a cylindrical vessel containing water; 
a second tube, B, concentric with the first, and surrounding it, is 











THERMOMETERS. 


219 


- 254 ] 


fixed on the same vessel, M. In this second cylinder, which is 
clos'd at both ends, there are three tubulures, a, E, D. A cork, in which 
is the thermometer, t, fits in a. To E a glass tube, containing mercury, is 
attached, which serves as a manometer for measuring the pressure of the 
vapour in the apparatus. D is an escape tube for the vapour and con¬ 
densed water. 

The apparatus is placed on a furnace and heated to boiling, the vapour 
produced in M rises in the tube A, and passing through the two tubes in 
the direction of the arrows escapes by the tubulure D. The thermometer 
t y being thus surrounded with vapour, the mercury expands, and when it 
has become stationary the point at which it stops is marked. This is the 



point sought for. The object of the second case, B, is to avoid the cooling 
of the central tubulure by its contact with the air. 

The determination of the point 100 (see next article) would seem to 
require that the height of the barometer during the experiment should 
be 760 millimeters, for when the barometric height is greater or less than 
this quantity, water boils either above or below 100 degrees. But the 
point 100 may always be exactly obtained, by making a correction in¬ 
troduced by M. Biot. He found that, for every 27 millimeters difference 
in height of the barometer, there was a difference in the boiling point of 
1 degree. If, for example, the height of the barometer is 778—that is, 
18 millimeters, or two-thirds of 27, above 760—water would boil at 100 

l 2 


























ON HEAT. 


220 


[ 255 - 


degrees and two-thirds. Consequently 100§ would have to he marked 
at the point at which the mercury stops. 

Gay-Lussac observed that water boils at a somewhat higher tem¬ 
perature in a glass than in a metal vessel; and as the boiling point is 
raised by any salts which are dissolved, it has been assumed that it was 
necessary to use a metal vessel and distilled water in fixing the boiling 
point. M. Rudberg has, however, shown that these latter precautions are 
superfluous. The nature of the vessel, and salts dissolved in ordinary 
water, influence the temperature of boiling water, but not that of the 
vapour which is formed. That is to say, that if the temperature of 
boiling water from any of the above causes is higher than 100 degrees, 
the temperature of the vapour does not exceed 100, provided the pressure 
is not more than 760 millimeters. Consequently the higher point may 
be determined in any kind of a vessel, provided the thermometer is 
quite surrounded by vapour, and does not dip in the water. 

Even with distilled water, the bulb of the thermometer must not dip 
in the liquid ; for it is only the upper layer that really has the tempera¬ 
ture of 100 degrees, since the temperature increases from layer to layer 
towards the bottom in consequence of the increased pressure. 

255. Construction of the scale. —Just as the foot-rule which is 
adopted as the unit of comparison for length is divided into a number of 
equal divisions called inches for the purpose of having a smaller unit of 
comparison, so likewise the unit of comparison of temperatures, the range 
from zero to the boiling point, must be divided into a number of parts 
of equal capacity called degrees. There are three modes in which this is 
done. On the continent, and more especially in France, this space is 
divided into 100 parts, and this division is called the Centigrade or Celsius 
scale ; the latter being the name of the inventor. The Centigrade ther¬ 
mometer is almost exclusively adopted in foreign scientific works, and as 
its use is gradually extending in this country, it has been and will be 
adopted in this book. 

The degrees are designated by a small cipher placed a little above on 
the right of the number which marks the temperature, and to indicate 
temperatures below zero the minus sign is placed before them. Thus, 
-15° signifies 15 degrees below zero. 

In accurate thermometers the scale is marked on the stem itself. It 
cannot be displaced, and its length remains fixed, as glass has very little 
inexpansibility. This is effected by covering the stem with a thin layer 
of wax, and then marking the divisions of the scale, as well as the corre¬ 
sponding numbers with a steel point. The thermometer is then exposed 
for about ten minutes to the vapours of hydrofluoric acid, which attacks 
the glass where the wax has been removed. The rest of the wax is then 
removed, and the stem is found to be permanently etched. 



THERMOMETRIC SCALE. 


221 


- 255 ] 


Besides the Centigrade scale two others are frequently used— Fahren¬ 
heit's scale and Reaumur's scale. 

In Reaumur’s scale the fixed points are the same as on the Centigrade 
scale, but the distance between them is divided into 80 degrees instead 
of into 100. That is to say, 80 degrees Reaumur are equal to 100 de¬ 
grees Centigrade; one degree Reaumur is equal to or f of a degree 
Centigrade, and one degree Centigrade equals T ~ or f degree Reaumur. 
Consequently to convert any number of Reaumur degrees into Centigrade 
degrees (20 for example), it is merely necessary to multiply them by f 
(which gives 25). Similarly, Centigrade degrees are converted into 
Reaumur’s by multiplying them by f. 

The thermometric scale invented by Fahrenheit in 1714 is still much 
used in England, and also in Holland and North America. The higher 
fixed point is like that of the other scales, the temperature of boiling 
water, but the null point or zero is the temperature obtained by mixing 
equal weights of sal-ammoniac and snow, and the interval between the 
two points is divided into 212 degrees. The zero was selected because the 
temperature was the lowest then known, and was thought to represent 
absolute cold. When Fahrenheit’s thermometer is placed in melting 
ice it stands at 32 degrees, and, therefore, 100 degrees on the Centigrade 
scale are equal to 180 degrees on the Fahrenheit scale, and thus 1 degree 
Centigrade is equal to f degree Fahrenheit, and inversely 1 degree 
Fahrenheit is equal to f of a degree Centigrade. 

If it be required to convert a certain number of Fahrenheit degrees (95 
for example), into Centigrade degrees, the number 32 must first be sub¬ 
tracted, in order that the degrees may count from the same part of the 
scale. The remainder in the example is thus 63, and as 1 degree 
Fahrenheit is equal to § of a degree Centigrade, 63 degrees are equal 
j to 63 X | or 35 degrees Centigrade. 

If F be the given temperature in Fahrenheit’s degrees and C the 
i corresponding temperature in Centigrade degrees, the former may be 
I converted into the latter by means of the formula 


(F - 32) f=C. f 


and conversely, Centigrade degrees may be converted into Fahrenheit by 
means of the formula 

f C + 32 = F. 


These formulae are applicable to all temperatures of the two scales, 
provided the signs are taken into account. Thus, to convert the tem¬ 
perature of 5 degrees Fahrenheit into Centigrade degrees we have 


(5-32) |= 


-27 x 5 


= -15 C. 


0 



222 ON HEAT. [ 256 - 

In like manner we liave for converting Reaumur’s into Fahrenheit’s 
degrees the formula 

|R + 32 = F., 

and conversely, for changing Fahrenheit’s into Reaumur’s degrees, the 
formula 

(F —32) | = R. 

256. Displacement of zero. —Thermometers, even when con¬ 
structed with the greatest care, are subject to a source of error which 
must be taken into account; this is, that in course of time the zero 
tends to rise, the displacement sometimes extending to as much as 2 
degrees; so that when the thermometer is immersed in melting ice it 
no longer sinks to zero. 

This is generally attributed to a diminution of the volume of the 
reservoir and also of the stem, occasioned by the pressure of the 
atmosphere. It is usual with very delicate thermometers to fill them 
two or three years before they are graduated. 

Besides this slow displacement, there are often variations in the 
position of the zero, when the thermometer has been exposed to high 
temperatures, caused by the fact that the bulb and stem do not contract 
on cooling to their original volume (248), and hence it is necessary to 
verify the position of zero when a thermometer is used for delicate 
determinations. 

Regnault has found that some mercurial thermometers, which agree 
at 0° and at 100°, differ between these points, and that these differences 
frequently amount to several degrees. Regnault thinks that this is due 
to the unequal expansion of different kinds of glass. 

257. Xiimits to the employment of mercurial thermometers.— 
Of all thermometers in which liquids are used, the one with mercury 
is the most useful, because this liquid expands most regularly, and is. 
easily obtained pure, and because its expansion between — 36° and 100° 
is regular , that is, proportional to the degree of heat. It also has the 
advantage of having a very low specific heat. But for temperatures 
below — 36° C. the alcohol thermometer must be used, for mercury 
solidifies at — 40° C. Above 100 degrees the coefficient of expansion 
increases and the indications of the mercurial thermometers are only 
approximate, the error arising sometimes to several degrees. Mercurial 
thermometers also cannot be used for temperatures above 350°, for this 
is the boiling point of mercury. 

258. Alcohol thermometer.— The alcohol thermometer differs from 
the mercurial thermometer in being filled with coloured alcohol. But as 
the expansion of liquids is less regular in proportion as they are near the 
boiling point, alcohol, which boils at 78° C., expands very irregularly. 
Hence, alcohol thermometers are usually graduated by placing them 
in baths at different temperatures together with a standard mercurial 


THERMOMETERS. 


223 


- 260 ] 

thermometer, and marking on the alcohol thermometer the temperature 
indicated by the mercurial thermometer. In this manner the alcohol 
thermometer is comparable with the mercurial one ; that is to say, it indi¬ 
cates the same temperatures under the same conditions. The alcohol 
thermometer is especially used for low temperatures, for it does not 
solidify at the greatest known cold. 

259. Conditions of the delicacy of a thermometer.— A thermo¬ 
meter may be delicate in two ways. 1. When it indicates very small 
changes of temperature. 2. When it quickly assumes the temperature 
of the surrounding medium. 

The first object is attained by having a very narrow capillary tube 
and a very large bulb, the expansion of the mercury on the stem is then 
limited to a small number of degrees, the 10 to 20 or 20 to 30 for instance, 
so that each degree occupies a great length on the stem, and can be sub¬ 
divided into very small fractions. The second kind of delicacy is obtained 
by making the bulb very small, for then it rapidly assumes the tempe¬ 
rature of the liquid in which it is placed. 

A good mercurial thermometer should answer to the following tests : 
When its bulb and stem, to the top of the column of mercury, are im¬ 
mersed in melting ice, the top of the mercury should exactly indicate 
0° C; and when suspended with its bulb and scale immersed in the steam 
of water boiling in a metal vessel (as in fig. 193), the barometer standing 
at 760 mm., the mercury should be stationary at 100° C. When the instru¬ 
ment is inverted, the mercury should fill the tube, and fall with a metallic 
click, thus showing the complete exclusion of air. The value of the degrees 
should be uniform ; to ascertain this, a little cylinder of mercury may be 
detached from the column by a slight jerk, and on 
inclining the tube it may be made to pass from one 
portion of the bore to another. If the scale be 
properly graduated, the column will occupy an 
equal number of degrees in all parts of the tube. 

260. Leslie's differential thermometer. —Sir 
John Leslie constructed a thermometer for show¬ 
ing the difference of temperature of two neighbour¬ 
ing places, from which it has received the name 
differential thermometer. It consists of two glass 
bulbs containing air, and joined by a bent glass 
tube of small diameter fixed on a frame (fig. 195). 

Before the apparatus is sealed, a coloured liquid 
is introduced in sufficient quantity to fill the hori¬ 
zontal part of the tube, and about half the vertical 
legs. It is important to use a liquid which does 
not give off vapours at ordinary temperatures, and dilute sulphuric acid 
coloured with litmus is generally preferred. The apparatus being 

















224 


ON HEAT. 


[ 260 a- 



closed the air is passed from one bulb into the other by beating them 
unequally until the level of the liquid is the same in both branches. A 

zero is marked at each end of 
the liquid column. To graduate 
the apparatus, one of the bulbs 
is raised to a temperature 10° 
higher than the other. The air 
of the first is expanded and 
causes the column of liquid ba to 
rise in the other leg. When the 
column is stationary, the number 
10 is marked on each side at the 
level of the liquid, the distance 
between zero and 10 being divided 
into 10 equal parts, both above 
and below zero, on each leg. 

260a. IVIatthiessen’s Differ¬ 
ential Thermometer. —Pro¬ 
fessor Matthiessen has devised a 
form of differential thermometer 
which can be used for indicating 
big. 196. the temperature of liquids, and 

which constitutes a valuable addition to our means of illustrating for 
lecture purposes many important experiments in heat. Its construction 

is evident from the annexed figure 
(196). The bulbs are pendent, and 
it can therefore be readily immersed 
in a liquid. In a tube which con¬ 
nects the two limbs there is a stop¬ 
cock, which is very useful as a 
means of adjusting the level of the 
liquids, a rather troublesome task 
with Leslie’s instrument. 

261. Breguet’s metallic ther¬ 
mometer.— Breguet invented a 
thermometer founded on the un¬ 
equal expansion of metals, and re¬ 
markable for its delicacy. It consists 
of three strips of platinum, gold, 
and silver, which are passed through 
lig. 197. a rolling mill so as to form a very 

thin metallic ribbon. This is then coiled in a spiral form, as seen in fig. 
197, and one end being fixed to a support, a light needle is fixed to the 
other, which is free to move round a graduated scale. 





















THERMOMETERS. 


225 


- 262 ] 

Silver, which is the most expansible of the metals, forms the internal 
face of the spiral, and platinum the external. When the temperatnre rises, 
the silver expands more than gold or platinum, the spiral unwinds itself, 
and the needle moves from left to right of the above figure. The contrary 
effect is produced when the temperature sinks. The gold is placed between 
the other two metals, because its expansibility is intermediate between 
that of the silver and the platinum. Were these two metals employed 
alone, their rapid unequal expansion might cause a fracture. Breguet’s 
thermometer is graduated in Centigrade degrees, by comparing it with a 
standard mercurial thermometer. 

262. Rutherford’s maximum and minimum thermometers. —It is 

necessary, in meteorological observations, to know the highest tempe¬ 
rature of the day, and the lowest temperature of the night. Ordinary 
thermometers could only give these indications by a continuous observa¬ 
tion, which would be impracticable. Several instruments have accordingly 
been invented for this purpose, the simplest of which is Rutherford’s. On 
a rectangular piece of plate glass (fig. 198) two thermometers are fixed, 
whose stems are bent horizontally. The one, A, is a mercurial, and the 
other, B, an alcohol thermometer. In A there is a small piece of iron 



wire, A, moving freely in the tube, which serves as an index. The 
thermometer being placed horizontally, when the temperature rises the 
mercury pushes the index before it. But as soon as the mercury con¬ 
tracts, the index remains in that part of the tube to which it has been 
moved, for there is no adhesion between the iron and the mercury. In 
this way the index registers the highest temperature which has been 
attained; in the figure this is 31°. In the minimum thermometer there is 
a small hollow glass tube which serves as index. When it is at the end 
of the column of liquid, and the temperature falls, the column contracts 
and carries the index with it, in consequence of adhesion, until it has 
reached the greatest contraction. When the temperature rises, the 

l 3 














226 


ON HEAT. 


[ 263 - 


alcohol expands, and passing between the sides of the tube and the 
index, does not displace B. The position of the index gives therefore 
the lowest temperature which has been reached: in the figure this was 
9£ degrees below zero. 

263. Pyrometers,— The name pyrometers is given to instruments for 
measuring temperatures so high that mercurial thermometers could not 
be used. The older contrivances for this purpose, Wedgewood’s, 
Darnell's (which in principle resembled the apparatus in fig. 189), 
Brongniart’s, etc., are gone entirely out of use. None of them gives an 
exact measure of temperature. The arrangements now used for the 
purpose are either based on the expansion of gases and vapours, or on 
the electrical properties of bodies, and will be subsequently described. 

264. Different remarkable temperatures.— The following table 
gives some of the most remarkable points of temperature. It may be 
observed that it is easier to produce very elevated temperatures than very 
low degrees of cold. 


Greatest artificial cold produced by a bath of bisulphide of 
carbon and liquid nitrous acid ..... 
Greatest cold produced by ether and liquid carbonic acid . 
Greatest natural cold recorded in Arctic expeditions 

Mercury freezes.. 

Mixture of snow and salt. 

Ice melts. 

Greatest density of water. 

Mean temperature of London. 

Blood heat. 

Water boils .. 

Mercury boils ......... 

Bed heat (just visible) (Daniell) . . . . • 

Silver melts „ 

Cast iron melts .. 

Highest heat of wind furnace „. 


-140° C. 
-110 C. 
-49 
-39-4 
-20 
0 
+4 
9-9 
36-6 
100 
350 
526 
1002 
1530 
1804 


CHAPTEB II. 

EXPANSION OF SOLIDS, 

265. Linear expansion and cubical expansion. Coefficients of 
expansion. —It lias been already explained that in solid bodies the expan¬ 
sion may be according to three dimensions, linear, superficial, and cubical. 
The coefficient of linear expansion is the elongation of the unit of 










EXPANSION OF SOLIDS. 


227 


- 266 ] 

length of a body when its temperature rises from zero to 1 degree; the 
coefficient of superficial expansion is the increase of the surface in being 
heated from zero to 1 degree, and the coefficient of cubical expansion is the 
increase of the unit of volume under the same circumstances. 

These coefficients vary with different bodies, but for the same body 
the coefficient of cubical expansion is three times that of the linear 
expansion , as is seen from the following considerations. Suppose a 
cube, the length of whose side is 1 at zero. Let k be the elongation 
of this side in passing from zero to 1 degree, its length at 1 degree 
will be 1 -\-k, and the volume of the cube, which was 1 at zero, 
will be (1+&) 3 , or l+3&+3& 2 -f & 3 . But as the elongation k is 
always a very small fraction (see table, art. 267), its square k 2 , and its 
cube & 3 , are so small that they may be neglected, and the value at 1 
degree becomes very nearly l-f-3A;. Consequently the increase of 
volume is 3k, or thrice the coefficient of linear expansion. 

In the same manner it may be shown that the coefficient of superficial 
expansion is double the coefficient of linear expansion. 

266. Measurement of the coefficients of linear expansion. 
Lavoisier and Laplace’s method. —The apparatus used by Lavoisier 



Fig. 199. 


and Laplace for determining the coefficients of linear expansion (fig. 199) 
consists of a copper trough, placed on a furnace between four stone 
supports. On the two supports on the right hand, there is a horizontal 
axis, at the end of -which is a telescope ; on the middle of this axis, and 
at right angles to it, is fixed a glass rod, turning with it, as does also the 
telescope. The other two supports are joined by a cross piece of iron, to 
which another glass rod is fixed, also at right angles. The trough, which 
contains oil or water, is heated by a furnace not represented in the figure, 
and the bar -whose dilatation is to be determined is placed in it. 

Fig. 200 represents a section of the apparatus: G is the telescope, 
KH the bar, whose ends press against the two glass rods F and D. 
As the rod F is fixed, the bar can only expand in the direction KH, 


















228 


ON HEAT. 


[ 267 - 


and in order to eliminate the effects of friction it rests on two glass 
rollers. Lastly, the telescope has a cross-wire in the eyepiece, which, 
when the telescope moves, indicates the depression by a corresponding 
number of divisions on a vertical scale, AB, at a distance of 220 yards. 

The trough is first filled with ice, and the bar being at zero, the 
division on the scale AB, corresponding to the wire of the telescope, is 
read off. The ice having been removed, the trough is filled with oil or 
water, which is heated to a given temperature. The bar then expands, 
and when its temperature has become stationary, which is determined 
by means of thermometers, the division of the scale, seen through the 
telescope, is read off. 



Fig. 200. 


From these data the elongation of the bar is determined ; for since it 
has become longer by a quantity, CH, and the optical axis of the 
telescope has become inclined in the direction GB, the two triangles, 
GHC and ABG, are similar, for they have the sides at right angles 
HC GH 

each to each, so that —— = T . In the same way, if HC' were 
’ AB AG 


another elongation, and AB' a corresponding deviation, there,would 
HC' GH 

still be — = ——, from which it follows that the ratio between the 
AB' AG 


elongation of the bar and the deflection of the telescope is constant, 
GrH 

for it is always equal to A preliminary measurement had shown 

that this ratio was =fr. Consequently whence HC = • 

A B 744 


that is, the total elongation of the bar is obtained by dividing the 
length on the scale traversed by the cross-wire by 744. Dividing this 
elongation by the length of the bar, and then by the temperature of the 
bath, the quotient is the dilatation for the unit of length and for a single 
degree—in other words, the coefficient of linear dilatation. 

267. Roy and Ramsden’s method.— Lavoisier and Laplace’s method 
is founded on an artifice which ds frequently adopted in physical deter¬ 
minations, and which consists in amplifying by a known amount 
dimensions which, in themselves, are too small to be easily measured. 
Unfortunately this plan is often more fallacious than profitable, for it is 






















EXPANSION OF SOLIDS. 


229 


-267] 

first necessary to determine the ratio of the motion measured to that 
on which it depends. In the present case it is necessary to know the 
lengths of the arms of the level in the apparatus. But this preliminary 
operation may introduce errors of such importance as partially to 
counterbalance the advantage of great delicacy. The following method, 
which was used by General Roy in 1787, and which was devised by 
Ramsden, depends on another principle. It measures the elongations 
directly, and without amplifying them, but it measures them by means 
of a micrometer, which indicates very small displacements. 

The apparatus (fig. 201) consists of three parallel metal troughs about 
6 feet long. In the middle one there is a bar of the body whose expan¬ 
sion is to be determined, and in the two others are cast iron bars of exactly 
the same length as this bar. Rods are fixed vertically on both sides of 



these three bars. On the rods in the troughs A and B there are rings 
with cross-wires like those of a telescope. On the rods in the trough C 
are small telescopes also provided with cross-wires. 

The troughs being filled with ice, and all three bars at zero, the 
points of intersection of the wires in the disc, and of the wires in the 
telescope, are all in a line at each end of the bar. The temperature in 
the middle trough is then raised to 100° C. by means of spirit lamps 
placed beneath the trough ; the bar expands, but as it is in contact with 
the end of a screw, «, fixed on the side, all the elongation takes place in 



























230 


ON HEAT. 


[267- 

the direction nm, and as tlie cross-wire n remains in position, the cross¬ 
wire m is moved towards B by a quantity equal to the elongation. But 
since the screw a is attached to the bar, by turning it slowly from right 
to left, the bar is moved in the direction mn ) and the cross-wire m 
regains its original position. To effect this, the screw has been turned 
by a quantity exactly equal to the elongation of the bar, and as this 
advance of the screw is readily deduced from the number of turns of 
its thread , the total expansion of the bar is obtained, which, divided by 
the temperature of the bath, and this quotient by the length of the bar 
at zero, gives the coefficient of linear expansion. 


Coefficients of linear expansion for 1° betiveen 0° and 100° C. 


White glass . . . 

0-000008613 

Copper 

.... 0-000017182 

Platinum .... 

0-000008842 

Bronze. 

.... 0000018167 

Untempered steel . 

0-000010788 

Brass . 

.... 0-000018782 

Cast iron .... 

0-000011250 

Silver . 

.... 0-000019097 

Wrought iron . . 

0-000012204 

Tin. . 

.... 0-000021730 

Tempered steel . . 

0 000012395 

Lead . 

.... 0-000028575 

Gold. 

0-000014660 

Zinc . 

.... 0-000029417 


From what has been said about the linear dilatation (265), the co¬ 
efficients of cubical expansion of solids are obtained by multiplying those 
of linear expansion by three. 

The coefficients of the expansion of the metals vary with their physical 
condition, being different for the same metal according as it has been cast, 
hammered and rolled, hardened or annealed. As a general rule, opera¬ 
tions which increase its density increase also the rate of expansion. But 
even for substances in apparently the same condition, different observers 
have found very unequal amounts of expansions; this may arise in the 
case of compound substances such as glass, brass, or steel, from a want of 
uniformity in chemical composition, and in simple bodies from slight dif¬ 
ferences of physical state. 

The expansion of amorphous solids, and of those which crystallise in 
the regular system, is the same for all dimensions, unless they are sub¬ 
ject to a strain in some particular direction. A fragment of such a sub¬ 
stance varies in bulk, but retains the same shape. Crystals not belong¬ 
ing to the regular system exhibit when heated an unequal expansion in 
the direction of their different axes, in consequence of which the magni¬ 
tude of their angles, and therefore their form, is altered. In the dimetric 
system the expansion is the same in the direction of the two equal axes, 
but different in the third. In crystals belonging to the hexagonal system 
the expansion is the same in the direction of the three secondary axes; 
but different from that according to the principal one. In the trimetric 
system it is different in all three directions. 






EXPANSION OF SOLIDS. 


231 


-269] 


268. The coefficients of expansion increase with the tempe¬ 
rature. According to Dr. Matthiessen, who determined the expansion 
of the metals and alloys by weighing them in water at different tem¬ 
peratures, the coefficients of expansion are not quite regular between 0° 
and 100°, He found the following values for the linear expansion be¬ 
tween 0° and 100°: 


Zinc . . 

. L, = 

Lead . . 

. L, = 

Silver . , 

. L,= 

Copper . , 

. L t = 

Gold . . 

. L ( = 


1 + 0-00002741 t + 0-0000000235 t 2 ) 

L, = L 0 (1 + 0-00002726 t -f 0-0000000074 t 2 ) 

L 0 (1 + 0-00001809 t + 0-0000000135 t 2 ) 

L, = L 0 (1 + 0-00001408 t + 0-0000000264 t 2 ) 

L 0 (1 + 0-00001358'* 4- 0-0000000112 t 2 ) 

The same authority has found that alloys expand very nearly according 
to the following law: 1 the coefficients of expansion of an alloy is equal 
to the mean of the coefficients of expansion of the volumes of the metals 
composing it.’ 

269. Formulae relative to the expansion of solids. —Let l be 

the length of a bar at zero, V its length at the temperature t° C., and a 
its coefficient of linear expansion. The tables usually give the expansion 
for 1° between 0° and 100°, as in article 267, or for 100°; in this latter 
case a is obtained by dividing the number by 100. t 

The relation existing between the above quantities is expressed by a 
few simple formulae. 

The elongation corresponding to t° is t times a, or at for a single unit 
of length, or atl for l units. The length of the bar which is l at zero is 
at t°, consequently— 


l' = l + atl = l (1 -f at) 

This formula gives the length of a body l at t° , knowing its length at 
zero, and the coefficient of expansion a •, and by simple algebraical trans¬ 
formations, we can obtain from it formulae for the length at zero, know¬ 
ing the length l' at t°, and also for finding a the coefficient of linear 
expansion, knowing the lengths V and l at t° and zero respectively. 

It is obvious that the formulae for cubical expansion are entirely 
analogous to the preceding. 

The following are examples of the application of these formulae :— 

A metallic bar has a length V at t'° , what will be its length l at t° ? 
From the above formula we first get the length of the given bar at 

zero, which is --; by means of the same formula we pass from 

1 at 

zero to t'° in multiplying by 1 -f- at', which gives for the desired length 
the formula 


J_ l' (1 4- at') 
1 ff- at 





232 


ON HEAT. 


[ 270 - 


The density of a body being d at zero, required its density d' at t°. 

If 1 be the volume of the body at zero, and D its coefficient of cubical 
expansion, the volume at t will be 1 + Dt, and as the density of a body 
is in inverse ratio of the^volume which the body assumes in expanding, 
we get the inverse proportion 

d!id— 1 : 1 + D t, 

1_ ; or d’ = _ — _ 

d 1 Dt 1 -f I)£ 


Consequently, when a body is heated from 0 to t° , its density, and 
therefore its weight for an equal volume, are inversely as the binomial 
expression, 1 + Dt. 

270. Applications of the expansion of solids.— In the arts we meet 
with numerous examples of the influence of expansion, (i.) The bars of 
furnaces must not be fitted tightly at their extremities, but must, at least, 
be free at one end, otherwise, in expanding, they would split the masonry, 
(ii.) In making railways a small space is left between the successive rails, 
for if they touched, the force of expansion would cause them to curve 
or would break the chairs, (iii.) Water pipes are fitted to one another by 
means of telescopic joints, which allow room for expansion, (iv.) If a 
glass is heated or cooled too rapidly it cracks ; this arises from the fact 
that glass being a bad conductor of heat, the sides become unequally 
heated, and consequently unequally expanded, which causes a fracture. 

W T hen bodies have been heated to a high temperature, the force pro¬ 
duced by their contraction on cooling is very considerable ; it is equal to 
the force which is needed to compress or expand the material to the 
same extent by mechanical means. According to Barlow a bar of mal¬ 
leable iron a square inch in section is stretched of its length by a 
weight of a ton ,* the same increase is experienced by about 9° 0. A 
difference of 45° C. between the cold of winter and the heat of summer 
is not unfrequently experienced in this country. In that range a wrought 
iron bar ten inches long will vary in length by ^ of a » inch, and will exert 
a strain, if its ends are securely fastened, of fifty tons. It has been cal¬ 
culated from Joule’s data that the force exerted by heat in expanding a 
pound of iron between 0° and 100° during which it increases about ^ 
of its bulk, is equal to 16,000 foot pounds; that is, it could raise a weight 
of 7 tons through a height of one foot. 

(i.) An application of this contractile force is seen in the mode of 
securing the tires on wheels. The tire being made red hot, and thus 
considerably expanded, is placed on the circumference of the wheel and 
then cooled. The tiro, when cold, embraces the wheel with such force 
as not only to secure itself on the rim, but also to press home the joints 
of the spokes into the felloes and nave, (ii.) Another interesting appli¬ 
cation was made in the case of a gallery at the Conservatoire des Arts 




EXPANSION OF SOLIDS. 


233 


- 271 ] 

et Metiers in Paris, the walls of which had begun to bulge outwards. 
Iron bars were passed across the building and screwed into plates on 
the outside of the walls. Each alternate bar was then heated by means 
of lamps, and when the bar had expanded it was screwed up. The bars 
being then allowed to cool contracted, and in so doing drew the walls 
together. The same operation was performed on the other bars. 

271. Compensation pendulum.— An important application of the 
expansions of metals has been made in the compensation pendulum. This 
is a pendulum in which the elongation, when the temperature rises, is so 
compensated that the distance between the centre of suspension and 
the centre of oscillation (70) remains constant, which, from the laws of 
the pendulum (71), is necessary for 
isochronous oscillations, and in order 
that the pendulum may be used as a 
regulator of clocks. 

In fig. 202, which represents the 
gridiron pendulum, one of the com¬ 
monest forms of compensation pen¬ 
dulums, the ball, L, instead of being 
supported by a single rod, is supported 
by a frame-work, consisting of alter¬ 
nate rods of steel and brass. In the 
figure the shaded rods represent steel; 
including a small steel rod, h, which 
supports the whole of the apparatus, 
there are six of them. The rest of the 
rods, four in number, are of brass. The 
rod, i , which supports the ball, is fixed 
at its upper end to a horizontal cross¬ 
piece ; at its lower end it is free, and 
passes through the two circular holes in 
the lower horizontal cross-pieces. 

Now it is easy to see from the man¬ 
ner in which the vertical rods are fixed 
to the cross-pieces, that the elongation 
of the steel rods can only take place in 
a downward direction, and that of the 
brass rods in an upward direction. Con¬ 
sequently, in order that the pendulum 
may remain of the same length, it is 
necessary that the elongation of the 
brass rods shall tend to make the ball rise by exactly the same quantity 
that the elongation of the steel rod tends to lower it: a result which is 



Fig. 202. 





















234 


ON HEAT. 


[271- 

attained when the sum of the lengths of the steel rods A is to the sum 
of the lengths of the brass rods B in the inverse ratio of the coefficients of 
expansion of steel and brass, a and b, that is, in the proportion A : B=6 : a. 

The elongation of the rod may also be compensated for by means of 
compensating strips. These consist of two blades of copper and iron sol¬ 
dered together and fixed to the pendulum rod, as represented in fig. 203. 
The copper blade, which is more expansible, is below the iron. W hen 




the temperature sinks, the pendulum rod becomes shorter, and the ball 
rises. But at the same time the compensating strips become curved, as 
seen in fig. 204, in consequence of the copper contracting more than 
the iron, and two metallic balls at their extremities become lower. If 
they have the proper size in reference to the pendulum ball, the parts 
which tend to approach the centre of suspension compensate those which 
tend to remove from it, and the centre of oscillation is not displaced. If 
the temperature rises the pendulum ball descends, but at the same time 
the small balls ascend, as shown in fig. 205, so that there is always 
compensation. 

One of the most simple compensating pendulums is the mercury pen¬ 
dulum, invented by an English watchmaker, Graham. The ball of the 
pendulum, instead of being solid, consists of a glass cylinder, containing 
pure mercury, which is placed in a sort of stirrup, supported by a steel rod. 
When the temperature rises the rod and stirrup become longer, and thus 
lower the centre of gravity; but at the same time the mercury expands, 
and, rising in the cylinder, produces an inverse effect, and as mercury is 
much more expansible than steel, a compensation may be effected with¬ 
out making the mercurial vessel of undue dimensions. 

The same principle is applied in the compensating balances of chrono¬ 
meters. The motion here is regulated by a balance or wheel, furnished 
with a spiral spring, and the time of the chronometer depends on the 
force of the spring, the mass of the balance, and on its circumference. 
Now when the temperature rises the circumference increases, and the 
chronometer goes slower j and to prevent this, part of the mass must be 














EXPANSION OF LIQUIDS. 


235 


- 273 ] 


brought nearer the axis. On the circumference of the balance compensat¬ 
ing strips are fixed, of which the more expansible metal is on the outside, 
and at the end of these are small masses of metal which play the same 
part as the balls in the above case. When the radius is expanded by 
heat, the small masses are brought nearer the centre in consequence of the 
curvature of the strips; and as they can be fixed in any position, they 
are easily arranged so as to compensate for the expansion of the balance. 


CHAPTER III. 

EXPANSION OF LIQUIDS. 

272. Apparent and real expansion.— If a flask of thin glass, pro¬ 
vided with a capillary stem, the flask and part of the stem being filled 
with some coloured liquid, be immersed in hot water, the column of liquid 
in the stem at first sinks, but then immediately after rises, and continues 
to do so until the liquid inside has the same temperature as the hot water. 
This first sinking of the liquid is not due to its contraction; it arises from 
the expansion of the glass, which becomes heated before the heat can 
reach the liquid ; but the expansion of the liquid soon exceeds that of the 
glass, and the liquid ascends. 

Hence in the case of liquids we must distinguish between the apparent 
and the real or absolute expansion. The apparent expansion is that 
which is actually observed when liquids contained in vessels are heated ; 
the absolute expansion is that which would be observed if the vessel did 
not expand; or, as this is never the case, is the apparent expansion 
corrected for the simultaneous expansion of the containing vessel. 

As has been already stated, the cubical expansion of liquids is alone 
considered; and as in the case of solids, the coefficient of expansion of a 
liquid is the increase of the unit of volume for a single degree, but a dis¬ 
tinction is here made between the coefficient of absolute expansion and the 
coefficient of apparent expansion. Of the many methods which have been 
employed for determining these two coefficients, we shall describe that of 
Dulong and Petit. 

273. Coefficient of the absolute expansion of mercury. —In order 
to determine the coefficient of absolute expansion of mercury, the influence 
of the envelope must be eliminated. Dulong and Petit’s method depends on 
the hydrostatical principle that in two communicating vessels the heights 
of two columns of liquid in equilibrium are inversely as their densities 
(98), a principle independent of the diameters of the vessels and there¬ 
fore of their expansions. 

The apparatus consists of two glass tubes, A and B (fig. 206), joined by 




23 G 


ON HEAT. 


[273- 


a capillary tube, and kept vertical by an iron support. Each of the tubes 
is surrounded by a metal case, of which the smaller, D, is filled with 
ice, the other containing oil, can be heated by the furnace, which is repre¬ 
sented in section so as to show the case. Mercury is poured into the tubes 
A and B j it remains at the same level in both as long a3 they are at the 
same temperature, but rises in B in proportion as it is heated, and expands. 

Let h and d be the height and density of the mercury in the leg A, at 
the temperate zero, and h' and d' the same quantities in the leg B. From 
the hydrostatical principle previously cited we have had hd — h'd'. Now 


from the problem on page 232, D being the coefficient of ab¬ 

solute expansion of mercury j substituting this value of d' in the equation 


we have 


h'd 


=hd , from which we get D = 


h'—k 


1 + D* ~ ht 

The coefficient of absolute expansion of mercury is obtained from this 
formula, knowing the heights h' and h, and the temperature t of the bath 
in which the tube B is immersed. In Dulong and Petit’s experiment 
this temperature was measured by a weight thermometer, P (275), the 
mercury of which overflowed into the basin, C. The heights h' and h 
were measured by a cathetometer, K (79). 



Fig. 206 . 


Dulong and Petit found by this method that the coefficient of absolute 
expansion of mercury, between 0° and 100° C. is -g—. But they found 
that the coefficient increased with the temperature. Between 100° and 
200° it is 5^5, and between 200° and 300° it is The same obser¬ 

vation has been made in reference to other liquids, showing that their ex¬ 
pansion is not regular. It has been found that this expansion is less regular 
in proportion as liquids are near a change in their state of aggregation, that 
is, approach their freezing or boiling points. Dulong and Petit found 
that the expansion of mercury between — 36° and 100° is practically quite 
uniform. 




























EXPANSION OF LIQUIDS. 


237 


- 276 ] 


Pegnault, who has determined this important physical constant, has 
found that the mean coefficient between 0° and 100° is ^ between 
100° and 200°, and between 200° and 300°, 

2/4. Coefficient of the apparent expansion of mercury,— The co¬ 
efficient of apparent expansion of a liquid varies with the nature of the 
envelope. That of mercury in glass was determined by means of the 
apparatus represented in figure 207. It consists of a glass cylinder to 
which is joined a bent capil¬ 
lary glass tube, open at the end. 

The apparatus is weighed 
first empty, and then when 
filled with mercury at zero; 
the difference gives the weight 
of the mercury, P. It is then 
raised to a known temperature, Pig- 207• 

t ; the mercury expands, a certain quantity passes out, which is received 
in the capsule and weighed. If the weight of this mercury be p , that 
of the mercury remaining in the apparatus will be P— 

When the temperature is again zero, the mercury in cooling produces 
an empty space in the vessel, which represents the contraction of the 
weight of mercury P— p , from t° to zero, or, what is the same thing, the 
expansion of the same weight from 0 to t° , that is, the weight p repre¬ 
sents the expansion of the weight P— p, for t°. If this weight expands 
in glass by a quantity p for t°, a single unit of weight would expand 



for and f p P v for a sin & le degree; consequently, for D', 
(1— p) (t P)* 

the coefficient of apparent expansion of mercury in glass, we have 

D'= ytJ- * Dulong and Petit found the coefficient of apparent expan- 
(P— p)t 

sion of mercury in glass to be 

275. Weight thermometer. —The apparatus represented in fi or, 
207 is called the weight thermometer , because the temperature can be 
deduced from the weight of mercury which overflows. 

The above experiments have placed the coefficient of apparent expan- 


P 


=64 1 80> from 


sion at we have therefore the equation _ 

6480 • * (P— p)t 

which we get t — , a formula which gives the temperature t 

when the weights P and p are known. 

276. Coefficient of the expansion of glass.— As the absolute ex¬ 
pansion of a liquid is the apparent expansion plus the expansion due to 
the envelope, the coefficient of the cubical expansion of glass has been 
obtained by taking the difference between the coefficient of absolute ex- 












238 


ON HEAT. 


[277- 


pansion of mercury in glass, and that of its apparent expansion. That is, 
the coefficient of cubical expansion of glass is 

_L_ l— = . 1 = 0-002584. 

5508 6480 38700 

Regnault has found that the coefficient of expansion varies with differ¬ 
ent kinds of glass, and further with the form of the envelopes. For 
ordinary chemical glass tubes, the coefficient is 0-0000254. 

277. Coefficients of expansion of various liquids. —The apparent 
expansion of liquids may be determined by means of the weight thermo¬ 
meter, and the absolute expansion is obtained by adding to this coefficient 
the expansion of the glass. 


Total apparent expansions of liquids between 0° and 100° C. 
Mercury. 0 01543 Oil of turpentine . . . .0-07 


Distilled water .... 0-0466 Ether.0*07 

Water saturated with salt 0*05 Fixed oils.0-08 

Sulphuric acid .... 0-06 Nitric acid.0-11 

Hydrochloric acid . . .0-06 Alcohol.0-116 


The coefficient of apparent expansion for 1° C, is obtained by dividing 
these numbers by 100 ; but the number thus obtained does not represent 
the mean coefficient of expansion of liquids, for the expansion of these 
bodies increases gradually from zero. The expansion of mercury is prac¬ 
tically constant between — 36° and 100° C, while water contracts from 
zero to 4°, and then expands. 

For many physical experiments a knowledge of the exact expansion 
of water is of great importance. This physical constant has been deter¬ 
mined with great care by Dr. Matthiessen, who has found that between 
4° and 32° it may be expressed by the formula 

Yt= 1-0-00000253 ($-4) 0-0000008389 (t- 4) 3 + 

0-00000007173 (t -4) 3 

and between 32° and 100° by 

V*=0-999695+0-0000054724 £ 2 +0-00000001126 t s 

Many liquids, with low boiling points, especially condensed gases, 
have very high coefficients of expansion. Thilorier found that liquid 
carbonic acid expands four times as much as air. Drion has recently 
confirmed this observation, and has obtained analogous results with 
chloride of ethyle, liquid sulphurous acid, and liquid hyponitrous acid, 

278. Correction of the barometric height.— It has been already 
explained under the Barometer (155), that, in order to make the indica¬ 
tions of this instrument comparable in different places and at different 
times, they must be reduced to a uniform temperature, which is that of 
melting ice. The correction is made in the following manner: 







MAXIMUM DENSITY OF WATER. 


239 


-280] 


Let H be the barometric height at t°, and h its height at .zero, d the 
density of mercury at zero, and d' its density at t°. The heights H and 

.7/ 

h are inversely as the densities d and d r j that is, h — - If we call 

d-‘ 

1 the volume of mercury at zero, its volume at t° will be L-t-D^, L, 
being the coefficient of absolute expansion of mercury. But these 
volumes, 1+D£ and 1, are inversely as the densities d and d' ; that is, 

isr c « nse i ueatl y> h = T&t> whence h = rfw 

placing D by its value -s—. we have h = -—-— * 

F O J 5O087 , — 5508 


d' = 


Re- 


1 + 


t 

5508 


In this calculation, the coefficient of absolute expansion of mercury is 
taken, and not that of apparent expansion: for the value A is the same 
as if the glass did not expand, the barometric height being independent 
of the diameter of the tube, and therefore of its expansion. 

279. Force exerted by liquids in expanding-.— The force which 
liquids exert in expanding is very great, and equal to that which would 
be required in order to bring the expanded liquid back to its original 
volume. Now we know what an enormous force is required to compress 
a liquid to even a very small extent. Thus between 0° and 10°, mercury 
expands by 0-0017905 of its volume at 0°; 
its compressibility is 0-00000295 of its 
volume for one atmosphere; hence a pres¬ 
sure of more than 600 atmospheres would 
be requisite to prevent mercury expanding 
when heated from 0° to 10°. 

280. Maximum density of water.— 

Water presents the remarkable phenome¬ 
non that when its temperature sinks it con¬ 
tracts up to 4°; but from that point, al¬ 
though the cooling continues, it expands 
up to the freezing point, so that 4° represent 
the point of greatest contraction of water. 

Many methods have been used to deter¬ 
mine the maximum density of water. Hope 
made the following experiment. He took 
a deep vessel, perforated by two lateral 
apertures, in which he fixed thermometers 
(fig. 208), and having filled the vessel 
with water at 0°, he placed it in a room 
at a temperature of 15°. As the layers 



Fig. 208 . 


of liquid at the sides of the vessel became heated they sank to the 






















240 


ON HEAT. 


[ 281 - 

bottom, and the lower thermometer marked 4°, while that of the upper 
one was still at zero. Hope then made the inverse experiment; having 
tilled the vessel with water at 15°, he placed it in a room at zero. 
The lower thermometer having sunk to 4°, remained stationary for 
some time, while the upper one cooled down until it reached zero. 
Both these experiments prove that water is heavier at 4° than at 0°, for 
in both cases it sinks to the lower part of the vessel. 

Hallstrom made a determination of the maximum density of water 
in the following manner. He took a glass bulb, loaded with sand, and 
weighed it in water of different temperatures. Allowing for the expan¬ 
sion of glass, he found that 4T° was the temperature at which it lost 
most weight, and consequently this was the temperature of the maximum 
density of water. 

Despretz arrived at the temperature 4° by another method. He took 
a water thermometer, that is to say, a bulbed tube containing water, and 
placing it in a bath, the temperature of which was indicated by an ordinary 
mercury thermometer, found that the water contracted to the greatest 
extent at 4°, and that this is therefore the point of greatest density. 

This phenomenon is of great importance in the economy of nature. In 
winter the temperature of lakes and rivers falls, from being in contact 
with the cold air, and from other causes, such as radiation. The colder 
water sinks to the bottom, and a continual series of currents goes on 
until the whole has a temperature of 4°. The cooling on the surface 
still continues, but the cooled layers being lighter remain on the surface, 
and ultimately freeze. The ice formed thus protects the water below, 
which remains at a temperature of 4°, even in the most severe winters, a 
temperature at which fishes and other inhabitants of the waters are not 
destroyed. 


CHAPTER IV. 

EXPANSION AND DENSITY OF GASES. 

281. Cay-Xiussac's method.—Gases are the most expansible bodies, 
and at the same time the most regular in their expansion. The coeffi¬ 
cients of expansion, too, of the several gases, differ only by very small 
quantities. The cubical expansion of gases need alone be considered. 

Gay-Lussac first determined the coefficient of the expansion of gases 
by means of the apparatus represented in fig. 209. 

In a rectangular metal bath, about 16 inches long, was fitted an air 
thermometer, which consisted of a capillary tube, AB, with a bulb, A, 



EXPANSION OF G ASES . 


241 


- 281 ] 

at one end. The tube was divided into parts of equal capacity, and the 
contents of the bulb ascertained in terms of these parts. This was effected 
by weighing the bulb and tube full of mercury at zero, and then heating 
slightly to expel a small quantity of mercury, which was weighed. The 
apparatus being again cooled down to zero, the vacant space in the tube 
corresponded to the weight of mercury which had overflowed; the 
volume of mercury remaining in the apparatus, and consequently the 
volume of the bulb, was determined by calculations analogous to those 
made for the piezometer (88). 

In order to fill the thermometer with dry air it was first filled with 
mercury, which was boiled in the bulb itself. A tube, C, filled with 
chloride of calcium, was then fixed on to its end by means of a cork. A 
fine platinum wire having then been introduced into the stem AB. through 



Fig. 209. 


the tube C, and the apparatus being sl ightly inclined and agitated from 
time to time, air entered, having been previously well dried by passing 
through the chloride of calcium tube. The whole of the mercury was 
displaced with the exception of a small thread, which remained in the 
tube AB as an index. 

The air thermometer was then placed in the box filled whh melting 
ice, the index moved towards A, and the point was noted at which it 
became stationary. This gave the volume of air at zero: for the capacity 
of the bulb was known. Water or oil was then substituted for the ice, 
and the bath successively heated to different temperatures. The air ex¬ 
panded and moved the index from A towards B. The position, of the 
index in each case was noted, and the corresponding temperature was 
indicated by means of the thermometers D and E. 

Assuming that the atmospheric pressure did not vary during the 
experiment, and neglecting the expansion of the glass as being too sm al l 
in comparison with that of the air, the total expansion of the air is 

x 







242 


ON HEAT. 


[ 282 - 


obtained by subtracting from its volume at a given temperature its volume 
at zero. Dividing this by the given temperature, and then by the num¬ 
ber of units contained in the volume at zero, the quotient is the coefficient 
of expansion for a single unit of volume and a single degree; that is, the 
coefficient of expansion. It will be seen, further on, how corrections for 
pressure and temperature may be introduced. 

By this method Gay-Lussac found that the coefficient of expansion of 
air was 0-00375; and he enunciated the two following laws in reference 
to the expansion of gases : 

I. All gases have the same coefficient of expansion as air. 

II. This coefficient is the same whatever be the pressure supported by 
the gas. 

These simple laws are not, however, rigorously exact (283) ; they only 
express the expansion of gases in an approximate manner. 

282. Problems on the expansion of gases.— Many of the pro¬ 
blems relative to the expansion of gases are similar to those on the 
expansion of liquids. With obvious modifications they are solved in a 
similar manner. In most cases, the pressure of the atmosphere must be 
taken into account in considering the expansion of gases. The following 
is an example of the manner in which this correction is made: 

i. The volume of a gas at t°, and under the pressure H, is V'; what 
will be the volume V of the same gas at zero, and under the normal 
pressure 760 millimeters ? 

Here there are two corrections to be made; one relative to the tem¬ 
perature, and the other to the pressure. It is quite immaterial which 
is taken first. If a be the coefficient of cubical expansion for a single 
degree, by reasoning similar to that in the case of linear expansion (269), 
the volume of the gas at zero, but still under the pressure H, will be 
V' 

p-qp-^. This pressure is reduced to the pressure 760, in accordance 
with Boyle and Mariotte’s law (161), by putting 
V x 760 = —^— x H 

1 + at 


V'H 

whence V=_ __ 

760(1 + at) 

ii. A volume of gas weighs P' at t° j what will be its weight at zero ? 
Let P be the desired weight, a the coefficient of expansion of the gas, 
d' its density at t°, and d its density at zero. As the weights of 

equal volumes are proportional to the densities, we have 

P d 

If 1 be the volume of a gas at zero, its volume at t will be 1 + at ; but 

as the densities are inversely as the volumes, - =_1_, and therefore 

d 1 -p at 





— 2 83 ] 


EXPANSION OF GASES. 


243 


P'_ 1 

P~ 1 + at 

whence P=P'(1 + at) 

From this equation we get P'= which gives the weight at t, 

knowing the weight at zero, and which further shows that the weight 
P / i s inversely as the binomial of expansion Y+at. 

283. Reg-nault’s method.— M. Regnault has successively used four 
different methods for determining the expansion of gases. In some of 
them, the pressure was constant and the volume variable, as in Gay- 
Lussac s method j in others the volume remained the same while the 
pressure varied. The first method will be described. It is the same as 



Fig. 210. 


that used by Rudberg and Dulong, but is distinguished by the care with 
which all sources of error are avoided. 

The apparatus consisted of a pretty large cylindrical reservoir, B (fig. 
210), terminating in a bent capillary tube. In order to fill the reservoir 
with dry air, it was placed in a hot water bath, and the capillary tube 
connected by a caoutchouc tube with a series of drying tubes. These 
tubes were joined to a small air pump, P, by which a vacuum could be 
produced in the reservoir while at a temperature of 100°. The reservoir 
was first exhausted, and air afterwards admitted slowly; this operation 
was repeated a great many times, so that the air in the reservoir became 
quite dry, for the moisture adhering to the sides passed off in vapour at 
100°, and the air which entered became dry in its passage through the 
U tubes. 

The reservoir was then kept for half an hour at the temperature of 

m 2 

























244 


ON HEAT. 


[ 283 - 


boiling water; the air pump having been detached, the drying tubes 
were then disconnected, and the end of the tube hermetically sealed, 
the height, H, of the barometer being noted. When the reservoir B was 
cool, it was placed in the apparatus represented in fig. 211. It was 
there quite surrounded with ice, and the end of the tube dipped in the 
mercury bath, C. After the air in the reservoir B had sunk to zero, the 
point h was broken off by means of a forceps; the air in the interior 
became condensed by atmospheric pressure, the mercury rising to a 
height oG. In order to measure the height of this column, Go, which 
will be called h , a moveable rod, go, was lowered until its point, o, was 

flush with the surface of the mercury in 
the bath ; the distance between the point 
o and the level of the mercury G, was 
measured by means of the cathetometer. 
The point b was finally closed with wax by 
means of the spoon a, and the barometric 
pressure noted at this moment. If this 
pressure be IT, the pressure in the reservoir 
is IV—h. 

The reservoir was now weighed to 
ascertain P, the weight of the mercury 
which it contained. It was then com¬ 
pletely filled with mercury at zero, in order 
to have the weight P 7 of the mercury in the 
reservoir and in the tube. 

If 5 be the coefficient of the cubical ex¬ 
pansion of glass, and I) the density of 
mercury at zero, the coefficient a of the 
cubical expansion of air is determined in 
the following manner. The volume of the 

reservoir and of the tube at zero is 
from the formula P = YD (116); consequently, this volume is ® 

D^C 1 + s 0.(1) 

at the temperature t°, assuming, as is the case, that the reservoir and 
tube expand as if they were solid glass. But from the formula P = YD, 
the volume of air in the reservoir at zero, and under the pressure H 7 — h 
P' — P 

is ——.. At the same pressure, but at t°, its volume would be 



Fig. 211. 


D 


p/ _ p 

— -q— C 1 + «0; 


and, by Boyle and Mariotte’s law (161), at the pressure H, under which 
the tube was sealed, this volume must have been 














- 284 ] 


EXPANSION OF GASES. 


245 


(P' - P) (l + erf) (H' - h) 

dh . 

Now the volumes represented by these formulas, (1) and (2), are each 
equal to the volume of the reservoir and the tube at t°; they are there¬ 
fore equal. Removing the denominators, we have 

P' (1 -t- SO H= (P' - P) (1 + «0 (H' — h) .... (3) 
from which the value of a is deduced. 

The means of a great number of experiments between zero and 100°, 
and for pressures between 300 millimeters and 500 millimeters, gave the 
following numbers for the coefficients of expansion for a single degree. 

Air.0-0036650 Hydrochloric acid . . 0 0036812 

Hydrogen .... 0-0036678 Cyanogen .... 0‘0036821 

Nitrogen. 0*0036682 Carbonic acid . . . 0‘0036896 

Sulphurous acid . . 0-0036606 

These numbers, with which the results obtained by Magnus closely 
agree, show that the coefficients of expansion of the permanent gases differ 
very little; but that they are slightly greater in the case of the condensable 
gases, such as carbonic and sulphurous acids. Regnault has further found, 
that, at the same temperature, the coefficient of expansion of any gas 
increases with the pressure which it supports. Finally he has found 
that the coefficients of expansion of two different gases differ more in 
proportion as they are under greater pressures. 

The number found by Regnault for the coefficient of the expansion of air, 
0-003665, is equal to 27^9 = all nearly; and if we take the coefficient of 
expansion at 0-0036666 ... it may be represented by the fraction 

which is very convenient for purposes of calculation. 

284. Air thermometer.—The air thermometer is based on the ex¬ 
pansion of air. When it is used to measure small differences of tempe¬ 
rature, it has the same form as the tube used by Gay-Lussac in deter¬ 
mining the expansion of air (fig. 209), that is, a capillary tube with a 
bulb at the end. The reservoir being filled with dry air, an index of 
coloured sulphuric acid is passed into the tube; the apparatus is then 
graduated in Centigrade degrees by comparing the positions of the index 
with the indications of a mercurial thermometer. Of course the end of 
the tube must remain open; otherwise, the air above the index con¬ 
densing or expanding at the same time as that in the bulb, the index 
would remain stationary. A correction must be made at each observation 
for the atmospheric pressure. 

When considerable variations of temperature are to be measured, the 
tube has a form like that used in Regnault’s experiments (figs. 210 and 
211). By experiments made as described in paragraph 283, P, P', H, IF, 
and h , may be found, and the coefficients a and 0 being known the tern- 





ON HEAT. 


246 


[ 285 - 


perature t to which the tube has been raised is readily deduced from the 
equation (3). 

Regnault’s researches show that the air and the mercurial thermometer 
agree up to 260°, but above that point mercury expands relatively more 
than air. 

In cases where very high temperatures are to be measured the reser¬ 
voir is made of platinum. The use of an air thermometer is seen in 
Dulong and Petit’s experiment (273) ; it was by such an apparatus that 
Pouillet measured the temperature corresponding to the colours which 
metals take when heated in a fire, and found them to be as follows: 

Incipient red. 525° C. Dark orange ..... 1100° C. 

Dull red. 700 White.1300 

Cherry red. 900 Dazzling white .... 1500 

In the measurement of high temperatures Deville and Troost have 
used, with advantage, the vapour of iodine instead of air. 

285. Density of gases.— The relative density of a gas, or its specific 
gravity , is the ratio of the weight of a certain volume of the gas to 
that of the same volume of air; both the gas and the air being at zero 
and at a pressure of 760 millimeters. 

In order, therefore, to find the specific gravity of a gas, it is necessary 
to determine the weight of a certain volume of this gas, at a pressure of 
760 millimeters, and a temperature of zero, and then the weight of the 
same volume of air under the same conditions. For this purpose a large 
globe of about two gallons capacity is used, the neck of which is pro¬ 
vided with a stopcock, which can be screwed to the air pump. The 
globe is first weighed empty, and then full of air, and afterwards full of 
the- gas in question. The weights of the gas and of the air are obtained 
by subtracting the weight of the exhausted globe from the weight of 
the globes filled, respectively, with air and gas. The quotient, obtained 
by dividing the latter by the former, gives the specific gravity of the gas. 
It is difficult to make these determinations at the same temperature and 
pressure, and therefore all the weights are reduced to zero and the normal 
pressure of 760 millimeters. 

The gases are dried by causing them to pass through drying tubes 
before they enter the globe, and air must also be passed over potash to 
free it from carbonic acid. And as even the best air pumps never produce 
a perfect vacuum, it is necessary to exhaust the globe until the mano¬ 
meter in each case marks the same pressure. 

The globe having been exhausted, dried air is allowed to enter, and 
the process is repeated several times until the globe is perfectly dried. 
It is then finally exhausted until the residual tension, in millimeters, is e. 
The weight of the exhausted globe is p. Air, which has been dried 



DENSITY OF GASES. 


247 


-286] 

and purified by passing through potash and chloride of calcium tubes, is 
then allowed to enter slowly. The weight of the globe full of air is P. 
If H is the barometric height in millimeters, and t° the temperature at 
the time of weighing, P —p is the weight of the globe full of air at the 
temperature t, and the pressure H— e. 

To reduce this weight to the pressure 760 millimeters and the tempera¬ 
ture zero, let a be the coefficient of the expansion of air, and 8 the coef¬ 
ficient of the cubical expansion of glass. From Boyle and Mariotte’s law 
the weight, which is P— p at t°, and a pressure of H— e, would be 

under the pressure 760 millimeters and at the same tem¬ 
perature t°. If the temperature is 0°, the capacity of the globe will 
diminish in the ratio 1 -f- 8t to 1, while the weight of the gas increases 
in the ratio 1 : 1 -f at, as follows from the problems in art. 282. Conse¬ 
quently the weight of the air in the globe at 0°, and at the pressure 760 
millimeters, will be 

CP—p)- 760 ( L + nt ) _.(1) 

Further, let a' be the coefficient of expansion of the gas in question, 
let P' be the weight of the globe full of the gas at the temperature t' and 
the pressure H', and let p be the weight of the globe when it is ex¬ 
hausted to the tension e ; the weight of the gas in the globe at the 
pressure 760 and the temperature of zero will be 

1 P) (H'— e) (l-WT). K ) 

Dividing the latter formula by the former we obtain the density 
p _( F— P') (H — e) (1 4- a'f) (1 + ft) 

(P — p) (IF— e) (1 -f- at) (1 + ct') 

If the temperature and the pressure do not vary during the experiment 
we get D = (* *—**? U + a '*\ and if a = a', D = 

(P— p)(l + at)’ P—p 

286. Regnault’s method of determining- the density of g^ases. — 

M. Regnault has so modified the above method that many of the cor¬ 
rections may be dispensed with. The globe in which the gas is weighed 
is suspended from one pan of a balance, and is counterpoised by means of 
a second globe of the same dimensions, and hermetically sealed, sus¬ 
pended from the other. These two globes expanding at the same time 
always displace the same quantity of air, and consequently variations in 
the temperature and pressure of the atmosphere do not influence the 
weighing. The globe, too, is filled with air or with the gas, while 
placed in a metallic vessel filled with ice. The correction for tempera¬ 
ture is thus useless, as the gas is at the temperature of melting ice. The 










248 


ON HEAT. 


[ 287 - 

only correction necessary is to reduce the weights of the two gases to the 
same pressure 760 millimeters, for the weights of equal volumes are pro¬ 
portional to the pressures. 

287. Bensity of gases which attack metals.— For gases which 
attack the ordinary metals, such as chlorine, a metal stopcock cannot be 
used, and vessels with ground glass stoppers are substituted. The gas is 
introduced by a bent glass tube, the vessel being held either upright or 
inverted, according as the gas is heavier or lighter than air; when the 
vessel is supposed to be full, the tube is withdrawn, the stopper inserted, 
and the weight taken. This gives the weight of the vessel and gas. If 
the capacity of the vessel be measured by means of water, the weight of 
the air which it contains is deduced, for the density of air at 0° C. and 
760 millimeters pressure, is jyt that of distilled water under the same cir¬ 
cumstances. The weight of the vessel full of air, less the weight of the 
contained air, gives the weight of the vessel itself. From these three data 
—the weight of the vessel full of the gas, the weight of the air which it 
contains, and the weight of the vessel alone—the specific gravity of the 
gas is readily deduced, the necessary corrections being made for tempe¬ 
rature and pressure. 

Densities of gases at zero and at a pressure of 760 millimeters, that of air 


being taken as unity. 

Air. 1*0000 Sulphuretted hydrogen . 1T912 

Hydrogen. 0 0693 Hydrochloric acid . . . 12540 

Marsh gas.0 5590 Protoxide of nitrogen. . 1-5270 

Ammoniacal gas . . . 0*5367 Carbonic acid .... 1-5291 

Carbonic oxide .... 0 9670 Cyanogen. 1*8600 

Nitrogen.0-9714 Sulphurous acid . . . 2*2474 

Binoxide of nitrogen . . 1*0360 Chlorine. 3-4400 

Oxygen. 1-1057 Hydriodic acid .... 4-4430 

Regnault has furnished the following determinations of the weight of a 
litre of the most important gases at 0° C. and 760 mm. 

Air. 1293187 grins. Nitrogen . . . 1*256167 grms. 

Oxygen .... 1*429802 Carbonic acid . . 1*977414 

Hydrogen . . . 0 089578 


CHAPTER V. 

CHANGES OF CONDITION. VAPOURS. 

288. Fusion. Its laws.— The only phenomena of heat with which 
we have hitherto been engaged have been those of expansion. In the 
case of solids it is easy to see that this expansion is limited. For in pro- 














CHANGES OF CONDITION. 


249 


- 288 ] 

portion as a body absorbs a larger quantity of heat, the repulsive force 
between the molecules is increased, and ultimately a point is reached at 
which the molecular attraction is not sufficient to retain the body in the 
solid state. A new phenomenon is then produced, fusion takes place j 
that is, the body passes from the solid into the liquid state. 

Some substances, however, such as paper, wood, wool, and certain salts 
do not fuse at a high temperature, but are decomposed. Many bodies 
have long been considered refractory ; that is, incapable of fusion ; but, 
in proportion as it has been possible to produce higher temperatures, their 
number has diminished. Gaudin has succeeded in fusing rock crystal by 
means of a lamp fed by a jet of oxygen ; and more recently Despretz, by 
combining the effects of the sun, the voltaic battery, and the oxy-hydro- 
gen blow-pipe, has melted alumina and magnesia, and softened carbon, 
so as to be flexible, which is a condition near that of fusion. 

It has been experimentally found, that the fusion of bodies is governed 
by the two following laws : 

I. Every substance begins to fuse at a certain temperature , which is in¬ 
variable for each substance if the pressure be constant. 

II. Whatever be the intensity of the source of heat, from the momentfusion 
commences, the temperature of the body ceases to rise , and remains constant 
until the fusion is complete. 


Fusing points of certain substances. 

Mercury.—38*8° Sodium. 90° 

Bromine.— 12-5 Rose’s fusible metal . . 94 

Ice.0 Sulphur.114 

Butter.+33 Tin.228 

Phosphorus.44 Bismuth.264 

Spermaceti.49 Cadmium.321 

Potassium.55 Lead.335 

Margaric acid.57 Zinc.422 

Stearine.60 Antimony.450 

White wax.65 Silver.1000 

Wood’s fusible metal.... 68’5 Gold.1250 

Stearic acid.70 Iron.1500 


Some substances pass from the solid to the liquid state without show¬ 
ing any definite melting point; for example, glass and iron become gra¬ 
dually softer and softer when heated, and pass by imperceptible stages 
from "the solid to the liquid condition. This intermediate condition is 
spoken of as the state of vitreous fusion. Such substances may be said to 
melt at the lowest temperature at which perceptible softening occurs, and 
to be fully melted when the further elevation of temperature does not 
make them more fluid; but no precise temperatures can be given as theii 
melting points. 

\f 3 




















250 


ON HEAT. 


[ 289 - 

The variations which take place in the ordinary atmospheric pressure 
have no perceptible influence on the melting point of substances ; but 
greater variations in pressure have a very appreciable effect. Prof. W. 
Thomson found that pressures of 8T° and 16*8 atmospheres lowered the 
melting point of ice by 0'059° and 0T^6° C. respectively. These results 
justify the theoretical conclusions of Prof. J. Thomson, according to 
which an increase of pressure of n atmospheres lowers the melting point 
of ice by 00074 n° C. 

In the case of some substances, however, the melting point is increased 
by pressure. Thus, Hopkins has found that the melting point of wax, 
which at the ordinary pressure is 64*7°, is 74'7° under a pressure of 520, 
and 80 2° under a pressure of 793 atmospheres; the melting point of 
spermaceti is raised 29° by a pressure of 795 atmospheres. These results 
have been confirmed by Bunsen for lower pressures. 

In general all those substances which expand on liquefying , such as wax, 
sulphur, etc., have their melting point raised by increased pressure: those, 
on the contrary, which contract on liquefying , have their melting points 
lowered by increased pressure. 

289. Alloys. Fluxes. —Alloys are generally more fusible than either 
of the metals of which they are composed; for instance, an alloy of five 
parts of tin and one of lead fuses at 194°. The alloy known as Rose's 
fusible metal, which consists of 4 parts of bismuth, 1 part of lead, and 1 
of tin, melts at 94°, and an alloy of 1 or 2 parts of cadmium with 2 parts 
of tin, 4 parts of lead, and 7 or 8 parts of bismuth, known as Wood's 
fusible metal, melts between 66° and 71° C. Fusible alloys are of extended 
use in soldering and in taking caste. 

Mixtures of the fatty acids melt at lower temperatures than the pure 
acids. A mixture of the chlorides of potassium and of sodium fuses at a 
lower temperature than either of its constituents ; the same is the case 
with a mixture of the carbonates of potass and soda, especially when 
they are mixed in the proportion of their chemical equivalents. 

An application of this property is met with in the case of fluxes, 
which are much used in metallurgical operations. They consist of sub¬ 
stances which, when added to an ore, partly by their chemical action, 
help the reduction of the substance to the metallic state, and, partly by 
presenting a readily fusible medium, promote the formation of a regulus. 

290. Latent heat.— Since, during the passage of a body from the solid 
to the liquid state, the temperature remains constant until the fusion is 
complete, whatever be the intensity of the source of heat, it must be 
concluded that, in changing their condition, bodies absorb a considerable 
amount of heat, the only effect of which is to maintain them in the liquid 
state. This heat, which is not indicated by the thermometer, is called 
latent heat , or latent heat by fusion , an expression which, though not in 


CHANGES OF CONDITION. 


- 292 ] 


251 


strict accordance witli modem ideas, is convenient from the fact of its 
universal recognition and employment. 

An idea of what is meant by latent heat may be obtained from the 
following experiment. If a pound of water at 80° is mixed with a 
pound of water at zero, the temperature of the mixture is 40°. But if a 
pound of pounded ice at zero is mixed with a pound of water at 80°, the 
ice melts, and two pounds of water at zero are obtained. Consequently, 
the mere change of a pound of ice to a pound of water at the same tem¬ 
perature requires as much heat as will raise a pound of water through 
80°. This quantity of heat represents the latent heat of the fusion of 
ice, or the latent heat of water. 

Every liquid has its own latent heat, and in the chapter on Calori¬ 
metry we shall show how this is determined. 

291. Solution.— A body is said to dissolve when it becomes liquid in 
consequence of an affinity between its molecules and those of a liquid. 
Gum arabic, sugar, and most salt3 dissolve in water. 

During solution, as well as during fusion, a certain quantity of heat 
always becomes latent, and hence it is that the solution of a substance 
usually produces a diminution of temperature. In certain cases, how¬ 
ever, instead of the temperature being lowered, it actually rises, as when 
caustic potass is dissolved in water. This depends upon the fact that 
two simultaneous and contrary phenomena are produced. The iirst is 
the passage from the solid to the liquid condition, which always lowers 
the temperature. The second is the chemical combination of the body 
dissolved with the liquid, and which, as in the case of all chemical com¬ 
binations, produces an increase of temperature. Consequently, as the 
one or the other of these effects predominates, or as they are equal, the 
temperature either rises, or sinks, or remains constant. 

292. Solidification. — Solidification or congelation is the passage of a 
body from the liquid to the solid state. This phenomenon is regulated 
by the two following laws:— 

I. Every body , under the same pressure , solidifies at a fixed temperature, 
ivhich is the same as that of fusion. 

II. From the commencement to the end of the solidification, the tempera - 
ture of a liquid remains constant. 

Certain bodies, more especially some of the fats, present an exception 
to the first law, in so far that by repeated fusions they seem to undergo 
a molecular change which alters their melting point. 

The second law is a consequence of the fact that the latent heat ab¬ 
sorbed during fusion becomes free at the moment of solidification. 

Many liquids, such as alcohol, ether, and bisulphide of carbon, do not 
solidify even at the lowest known temperature. But M. Despretz, by the 
cold produced by a mixture of liquid protoxide of nitrogen, solid carbonic 


ON HEAT. 


252 


[293- 


acid, and ether, has reduced alcohol to such a consistence that the vessel 
containing it could be inverted without losing the liquid. 

293. Crystallisation. —Generally speaking, bodies which pass slowly 
from the liquid to the solid state assume regular geometrical forms, 
such as the cube, prisms, rhombohedrons, etc.; these are called crystals. 
If the crystals are formed from a body in fusion, such as sulphur or 
bismuth, the crystallisation is said to take place by the dry way. But if 
the crystallisation takes place from the slow evaporation of a solution of 
a salt, it is said to be by the moist way. Snow, ice, and many salts pre¬ 
sent examples of crystallisation. 

294. Retardation of the point of solidification.— The freezing 
point of pure water can be diminished by several degrees, if the water 
be previously freed from air by boiling and then kept in a perfectly still 
place. In fact, it may be cooled to —15° C., and even below, without 
freezing. But when it is slightly agitated, the liquid soon solidifies. 
The smaller the quantity of liquid the lower the temperature to which 
it can be cooled, and the greater the mechanical disturbance it supports 
without freezing. Fournet has observed the frequent occurrence of mists 
formed of particles of liquid matter suspended in an atmosphere whose 
temperature is 10° or even 15° below zero. 

A very rapid agitation also prevents the formation of ice. The same 
is the case with all actions which, hindering the molecules in their 
movements, do not permit them to arrange themselves in the conditions 
necessary for the solid state. M. Despretz was able to lower the tem¬ 
perature of water contained in fine capillary tubes to —20° without their 
solidifying. This experiment shows how it is that plants in many cases 
do not become frozen, as the sap is contained in very fine capillary 
vessels. Finally M. Mousson has found that a powerful pressure not 
only retards the freezing of water, but prevents its complete solidifica¬ 
tion. In this case the pressure opposes the tendency of the water to 
expand on freezing, and thus virtually lowers the point of solidification. 

If water contains salts or other foreign bodies its freezing point is 
lowered. Sea water freezes at — 2'5° to — 3° C.; the ice which forms is 
quite pure, and a saturated solution remains. In Finland advantage is 
taken of this property to concentrate sea water for the purpose of 
extracting salt from it. If water contains alcohol, precisely analogous 
phenomena are observed: the ice formed is pure, and all the alcohol is 
contained in the residue. 

Dufour has observed some very curious cases of liquids cooled out of 
contact with solid bodies. His mode of experimenting was to place the 
liquid in another of the same specific gravity but of lower melting point, 
and in which it was insoluble. Spheres of water, for instance, suspended 
in a mixture of chloroform and oil, usually solidified between — 4° and 


CHANGES OF CONDITION. 


253 


- 295 ] 

—1$°, while some smaller globules cooled down to -18° or - 20°. Con¬ 
tact with a fragment of ice immediately set up congelation. Globules of 
sulphur (which solidifies at 115°) remained liquid at 40°; and globules of 
phosphorus (solidifying point 42°) at 20°. 

When a liquid solidifies after being cooled below its normal freezing 
point, the solidification takes place very rapidly, and is accompanied by 
a disengagement of heat, often sufficient to raise its temperature from 
the point at which solidification begins up to its ordinary freezing point. 
This is well seen in the case of hyposulphite of soda, which melts in its 
own water of crystallisation at 45°, and when carefully cooled will remain 
liquid at the ordinary temperature of the atmosphere. If it then he made 
to solidify by agitation or by adding a small fragment of the solid salt, the 
rise of temperature is distinctly felt by the hand. In this case the heat 
which had become latent in the process of liquefaction again becomes free. 

295. Change of volume on solidification and liquefaction.— The 
rate of expansion of bodies generally increases as they approach their 
melting points, and is in most cases followed by a further expansion at 
the moment of liquefaction, so that the liquid occupies a greater volume 
than the solid from which it is formed. Phosphorus, for instance, increases 
about 3-4 per cent, on liquefaction : that is, 100 volumes of solid phos¬ 
phorus at 44° (the melting point) become 103*4 at the same temperature 
when melted. Sulphur expands about 5 per cent, on liquefying, and 
stearic acid about 11 per cent. 

Water presents a remarkable exception; it expands on the moment of 
solidifying, or contracts on melting, by about 10 per cent. One volume of 
ice at 0° gives 0*908 of water at 0°, or 1 volume of water at 0° gives 
1-102 of ice at the same temperature. In consequence of this expansion, 
ice floats on the surface of water. 

The increase of volume in the formation of ice is accompanied by an 
expansive for6e which sometimes produces powerful mechanical effects, 
of which the bursting of water pipes and the breaking of jugs containing 
water are familiar examples. The splitting of stones, rocks, and the 
swelling up of moist ground during frost, are caused by the fact that 
water penetrates into the pores and there becomes frozen. 

The expansive force of ice was strikingly shown by some experiments 
of Major Williams in Canada. Having quite filled a 13-inch iron bomb¬ 
shell with water, he firmly closed the touch-hole with an iron plug 
weighing 3 pounds, and exposed it in this state to the frost. After some 
time the iron plug was forced out with a loud explosion, and thrown to a 
' distance of 415 feet, and a cylinder of ice 8 inches long issued from the 
opening. In another case the shell burst before the plug was driven out, 
and in this case a sheet of ice spread out all round the crack. It is pos¬ 
sible that under the great pressure some of the water still remained 


254 


ON HEAT. 


[ 296 - 

liquid up to the time at which the resistance was overcome ; that it then 
issued from the shell in a liquid state, hut at a temperature below 0°, 
and therefore instantly began to solidify when the pressure was removed, 
and thus retained the shape of the orifice whence it issued. 

Cast-iron, bismuth, and antimony expand on solidifying like water, 
and can thus be used for casting ; but gold, silver, and copper contract, and 
hence coins of these metals cannot be cast, but must be stamped with a die. 

296. Freezing- mixtures.— The absorption of heat in the passage of 
bodies from the solid to the liquid state has been used to produce artificial 
cold. This is effected by mixing together bodies which have an affinity 
for each other, and of which one at least is solid, such as water and a 
salt, ice and a salt, or an acid and a salt. Chemical affinity accelerates 
the fusion, the portion which melts robs the rest of the mixture of a large 
quantity of sensible heat, which thus becomes latent. In many cases a 
very considerable diminution of temperature is produced. 

The following table gives the names of the substances mixed, their 
proportions, and the corresponding diminutions of temperature. 



Parts 

Reduction of 

Substances. 

by weight. 

temperature. 

Sulphate of sodium 
Hydrochloric acid 

::: ■ 

. 4-10° to -17° 

Pounded ice or snow . 


. +10° to-18° 

Common salt . . . 

. . . l}* * 

Sulphate of sodium . 
Dilute nitric acid . . 

::: 5}- • 

. +10° to-19° 

Sulphate of sodium . 



Nitrate of ammonium 


. +10° to-26° 

Dilute nitric acid . . 

Phosphate of sodium . 
Dilute nitric acid . . 

. . . 4) 

. . . 91 
... 4 J 

. 4-10° to -29° 


If the substances taken be themselves first previously cooled down, a 
still more considerable diminution of temperature is occasioned. 

Freezing mixtures are frequently used in chemistry, in physics, and in 
domestic economy. The portable ice-making machines which have come 
in use during the last few years, consist of a cylindrical metallic vessel 
divided into four concentric compartments. In the central one is placed 
the water to be frozen j in the next there is the freezing mixture, which 
usually consists of sulphate of sodium and hydrochloric acid ; 6 pounds of 
the former and 5 of the latter will make 5 to 6 pounds of ice in an hour. 
The third compartment also contains water, and the outside one contains 
some badly conducting substance, such as cotton, to prevent the influence 
of the external temperature. The best effect is obtained when pretty 






VAPOURS. 


255 


- 299 ] 

large quantities, 2 or 3 pounds, of the mixture are used, and when they 
are intimately mixed. It is also advantageous to use the machines for 
a series of successive operations. 

VAPOURS. MEASUREMENT OF THEIR TENSION. 

297. Vapours. —We have already seen (137) that vapours are the 
aeriform fluids into which volatile substances, such as ether, alcohol, 
water, and mercury, are changed by the absorption of heat. Volatile 
liquids are those which thus possess the property of passing into the 
aeriform state, and fixed liquids , those which do not form vapours at any 
temperature without undergoing chemical decomposition, such as the 
fatty oils. There are some solids, such as ice, arsenic, camphor, and in 
general all odoriferous solid substances, which can directly form vapours 
without first becoming liquid. 

Vapours are transparent like gases, and generally colourless : there are 
only a few coloured liquids, which also give coloured vapours. 

298. Vaporisation. —The passage of a liquid into the gaseous state 
is designated by the general term vaporisation; the term evaporation 
especially refers to the slow production of vapour at the free surface of a 
liquid, and boiling to its rapid production in the mass of the liquid itself. 
We shall presently see (311) that at the ordinary atmospheric pressure, 
ebullition, like fusion, takes place at a definite 
temperature. This is not the case with evapora¬ 
tion, which takes place even with the same liquid 
at very different temperatures, although the for¬ 
mation of a vapour seems to cease below a certain 
point. Mercury, for example, gives no vapour 
below —10°, nor sulphuric acid below 30°. 

299. Elastic force of vapours. —Like gases, 
vapours have a certain elastic force, in virtue of 
which they exert pressures on the sides of vessels 
in which they are contained. The tension of 
vapours may be demonstrated by the following 
experiment. A quantity of mercury is placed in 
a bent glass tube (fig. 212), the shorter leg of 
which is closed; a few drops of ether are then 
passed into the closed leg and the tube immersed 
in a water bath at a temperature of about 45°. 

The mercury then sinks slowly in the short 
branch, and the space ab is filled with a gas 
which has all the appearance of air, and whose 
elastic force counterbalances the pressure of the 
column of mercury cf?,and the atmospheric pressure 
on d. This gas is the vapour of ether. If the 



Fig. 212. 








256 


ON HEAT. 


[ 300 - 

water be cooled, or if tbe tube be removed from the bath, the vapour 
which fills the space ah disappears, and the drop of ether is reproduced. 
If, on the contrary, the bath be heated still higher, the level of the 
mercury descends below b, indicating an increased tension. 

300. Formation of vapours in a vacuum. —In the previous expe¬ 
riment the liquid changed very slowly into the vaporous condition; the 
same is the case when a liquid is freely exposed to the air. In both cases 
the atmosphere is an obstacle to the vaporisation. In a vacuum there is no 
resistance, and the formation of vapours is instantaneous, as is seen in the 

following experiment. Four barometer 
tubes, filled with mercury, are immersed 
in the same trough (fig. 213). One of 
them, A, serves as a barometer, and a 
few drops of water, alcohol, and ether 
are respectively introduced into the 
tubes, B, C, D. When the liquids reach 
the vacuum a depression of the mercury 
is at once produced. And as this de¬ 
pression cannot be produced by the 
weight of the liquid, which is an in¬ 
finitely small fraction of the weight of 
the displaced mercury, it must be due to 
the formation of some vapour whose 
elastic force has depressed the mercurial 
column. 

The experiment also shows that the de¬ 
pression is not the same in all the tubes ; 
it is greater in the case of alcohol than 
of water, and greater with ether than 
with alcohol. We consequently obtain 
the two following laws for the formation 
of vapours. 

I. In a vacuum all volatile liquids are 
instantaneously converted into vapour. 

II. At the same temperature the vapours of different liquids have dffe- 
rent elastic forces. 

For example, at 20°, the tension of ether vapour is 25 times as great as 
that of aqueous vapour. 

301. Saturated vapours. Maximum of tension.— When a small 
quantity of a volatile liquid, such as ether, is introduced into a barometer 
tube it is at once completely vaporised, and the mercurial column is not 
depressed to its full extent, for if some more ether be introduced the 
depression increases. By continuing the addition of ether, it finally ceases 


























TENSION OF VAPOURS. 


257 


- 302 ] 

to vaporise, and remains in the liquid state. There is, therefore, for a 
certain temperature a limit to the quantity of vapour which can be 
formed in a given space. This space is accordingly said to be saturated. 
Further, when the vaporisation of the ether ceases, the depression of the 
mercurial column stops. And hence there is a limit to the tension of the 
vapour, a limit which, as we shall presently see (304), varies with the 
temperature, but which for a given temperature is independent of the 
pressure. 

To show that, in a closed space, saturated with vapour and contain¬ 
ing liquid in excess, the temperature remaining constant, there is a 
maximum of tension which the vapour cannot exceed, a barometric tube 
is used dipping in a deep bath (fig. 214). This 
tube is filled with mercury, and then so much 
ether is added as to be in excess after the Tor¬ 
ricellian vacuum is saturated. The height of 
the mercurial column is next noted by means 
of the scale graduated on the tube itself. Now, 
whether the tube be depressed, which tends to 
compress the vapour, or whether it be raised, 
which tends to expand it, the height of the 
mercurial column is constant. The tension of 
the vapour remains constant in the two cases, 
for the depression neither increases nor di¬ 
minishes it. Hence it is concluded that when 
the saturated vapour is compressed, a portion 
returns to the liquid state ; that when, on the 
other hand, the pressure is diminished, a por¬ 
tion of the excess of liquid vaporises, and the 
space occupied by the vapour is again saturated; 
but in both cases the tension and the density 
of the vapour remain constant. 

302. Non-saturated vapours. — From 
what has been said, vapours present two very 
different states, according as they are saturated 
or not. In the first case, where they are 
saturated and in contact with the liquid, they 
differ completely from gases, since for a given 
temperature they can neither be compressed 
nor expanded; their elastic force and their 
density remain constant. 

In the second case, on the contrary, where they are not saturated, they 
exactly resemble gases. For if the experiments (fig. 214) be repeated 
only a small quantity of ether being introduced, so that the vapour is not 











258 


ON HEAT. 


[ 303 - 


saturated, and if the tube be then slightly raised, the level of the mer¬ 
cury is seen to rise, which shows that the elastic force of the vapour has 
diminished. Similarly, by immersing the tube still more, the level of 
the mercury sinks. The vapour consequently behaves just as a gas 
would do, its tension diminishes when the volume increases, and vice 
versa; and as in both cases the volume of the vapour is inversely as the 
pressure, it is concluded that non-saturated vapours obey Boyle and 
Mariotte’s law. 

When a non-saturated vapour is heated, its volume increases like 
that of a gas: and the number 000366, which is the coefficient of the 
expansion of air, may be taken for that of 
vapours. 

Hence we see that the physical properties 
of unsaturated vapours are comparable with 
those of permanent gases, and that the for¬ 
mulae for the compressibility and expansibility 
of gases (161 and 281) also apply to unsaturated 
vapours. But it must not be forgotten that 
there is always a limit of pressure or of cool¬ 
ing at which unsaturated vapours pass into a 
state of saturation, and that they have then a 
maximum of tension and density which can 
only be exceeded when the temperature rises 
while they are in contact with the liquid. 

303. Tension of aqueous vapour below 
zero. —For the sake of measuring the elastic 
force of aqueous vapour below zero, Gay- 
Lussac used two barometer tubes filled with 
mercury, and placed in the same bath (fig. 
215). The straight tube, A, serves as a 
barometer; the other, B, is bent, so that part 
of the Torricellian vacuum can be surrounded 
by a freezing mixture (296). When a little 
W water is admitted into the bent tube, the level 
of the mercury sinks below that in the tube 
A, to an extent which varies with the tem¬ 
perature of the freezing mixture. 



Fig. 215. 


At 0° the depression is 

„ -io° „ „ • 

,, — 20 ° ,, „ 

„ -30° 


4’60 millimeters. 
1-96 
0-84 
0-36 


V 

V 
1) 


These depressions, which must be due to the tension of aqueous 





















-304] 


TENSION OF VAPOURS. 


259 


vapour in the space BC, show that even at low temperatures there is 
aqueous vapour in the atmosphere. 

Although in the above experiment the part B and the part C are not 
both immersed in the freezing mixture, we shall presently see that when 
two communicating vessels are at different temperatures, the tension 
of the vapour is the same in both, and always corresponds to the lowest 
temperature. 

That water evaporates even below zero follows from the fact, that wet 
linen exposed to the air during frost first 
becomes stiff and then dry, showing that 
the particles of water evaporate even after 
the latter has been converted into ice. 

304. Tension of aqueous vapour 
between zero and one hundred de¬ 
grees. —i. Dalton's method .—Dalton mea¬ 
sured the elastic force of aqueous vapour 
between 0° and 100°, by means of the 
apparatus represented in fig. 216. Two 
barometer tubes, A and B, are filled with 
mercury, and inverted in an iron bath full 
of mercury, and placed on a furnace. 

The tube A contains a small quantity of 
water. The tubes are supported in a 
cylindrical vessel full of water, the tem¬ 
perature of which is indicated by the 
thermometer. The bath being gradually 
heated, the water in the cylinder becomes 
heated too ; the water which is in the tube 
A vaporises, and in proportion as the 
tension of its vapour increases, the mercury 
sinks. The depressions of the mercury j 
corresponding to each degree of the ther- ! 
mometer are indicated on the scale E, and 
in this manner a table of the elastic forces 
between zero and 100° has been constructed. 



Fig. 216. 


ii. Regnault's method. —Dalton’s method is wanting in precision, for 
the liquid in the cylinder has not everywhere the same temperature, and 
consequently the exact temperatnre of the aqueous vapour is not indicated. 
Regnault’s apparatus is a modification of that of Dalton. The cylindrical 
vessel is replaced by a large cylindrical zinc drum, MN (fig. 217), in the 
bottom of which are two tubulures. The tubes A and B pass through 
these tubulures, and are fitted by caoutchouc collars. The tube containing 
vapour, B, is connected with a flask, a, by means of a copper three-way 





















260 


ON HEAT. 


[ 305 - 



tube, 0. The third limb of this tube is connected with a drying tube, 
D, containing pumice impregnated with sulphuric acid, which is connected 
with the air pump. 

When the flask a contains some water, a small portion is distilled into 
B by gently heating the flask. Exhausting then by means of the air 

pump, the water distils con¬ 
tinuously from the flask and 
from the barometric tube 
towards D, which condenses 
the vapours. After having 
vaporised some quantity of 
water, and it is thought that 
the air in the tube is with¬ 
drawn, the capillary tube 
which connects B with the 
three-way tube is sealed. 
The tube B being thus closed, 
it is experimented with as in 
Dalton’s method. 

The drum MN being filled 
with water is gently heated 
by a spirit lamp, which is 
separated from the tubes by a 
wooden screen. By means of a 
stirrer K all parts of the liquid 
are kept at the same tempera¬ 
ture. In the side of the drum is 
a glass window through which 
the height of the mercury in 
the tubes can be read off by 
means of a cathetometer; from 
the difference in these heights, 
reduced to zero, the tension 
Fig. 217. of vapour is deduced. By 

means of this apparatus, the elastic force of vapour between 0° and 50° 
has been determined with accuracy. 

305. Tension of aqueous vapour above one hundred degrees.— 
Two methods have been employed for determining the tension of aqueous 
vapour at temperatures above 100°, the one by Dulong and Arago, in 
1830, and the other by Regnault, in 1844. 

Fig. 218 represents a vertical section of the apparatus used by Dulong 
and Arago. It consisted of a copper boiler, k, with very thick sides, and 
of about 20 gallons capacity. Two gun barrels, a, of which only one is 




































TENSION OF VAPOURS. 


261 



- 306 ] 

seen in the drawing, were firmly fixed in the sides of the boiler, and 
plunged in the water. The gun barrels were closed below, and contained 
mercury, in which were placed thermometers t, indicating the tem¬ 
perature of the water and of the vapour. The tension of the vapour was 
measured by means of a manometer with compressed air, m, previously 
graduated (164) and fitted into an iron vessel, d, filled with mercury. 
In order to see the height of the mercury in the vessel, it was connected 
above and below with a glass tube, n , in which the level was always the 
same as in the bath. A copper tube, i, connected the upper part of the 

#1 


Fig. 218. 

vessel d with a vertical tube, c, fitted in the boiler. The tube i, and the 
upper part of the bath d, were filled with water, which was kept cool by 
means of a current of cold water flowing from a reservoir and circulating 
through the tube b. 

The vapour which was disengaged from the tube c, exercised a pres¬ 
sure on the water of the tube i ; this pressure was transmitted to the 
water and to the mercury in the bath d, and the mercury rose in the 
manometer. By noting on the manometer the pressures corresponding to 
each degree of the thermometer, Dulong and Arago were able to make a 
direct measurement of the tension up to 24 atmospheres, and the tension 
from thence to 50 atmospheres was determined by calculation. 

306. Tension of vapour below and above one hundred degrees.— 
Regnault has devised a method by which the tension of vapour may be 
measured at temperatures either below or above 100°. It depends on the 




























262 


ON HEAT. 


[ 306 - 

principle that when a liquid boils, the tension of the vapour is equal to 
the pressure it supports (314). If, therefore, the temperature and the 
corresponding pressure are known, the question is solved, and the method 
merely consists in causing water to boil in a vessel under a given pressure, 
and measuring the corresponding temperature. 

The apparatus consists of a copper retort, C (fig. 219) hermetically 
sealed, and about two-thirds full of water. In the cover there are four 
thermometers, two of which just dip into the water, and two descend 



almost to the bottom. By means of a tube, AB, the retort C is connected 
with a glass globe, M, of about 6 gallons capacity, and full of air. The 
tube AB passes through a metallic cylinder, D, through which a current 
of cold water is constantly flowing from the reservoir, E. To the upper 
part of the globe a tube with two branches is attached, one of which is 
connected with a manometer, 0 ; the other tube, HIE, which is of lead, 
can be attached either to an exhausting or a condensing air pump, accord- 
ing as the air in the globe is to be rarefied or condensed. The reservoir, 
K, in which is the globe, contains water of the temperature of the sur¬ 
rounding air. 









































TENSION OF VAPOURS. 


263 


- 306 ] 

If the elastic force of aqueous vapour below 100° is to be measured, 
the end H' of the leaden pipe is connected with the plate of the air pump, 
and the air in the globeM, and consequently that in the retort, C, is rarefied. 
The retort being gently heated, the water begins to boil at a temperature 
below 100°, in consequence of the diminished pressure. And since the 
vapour is condensed in the tube AB, which is always cool, the pressure 
originally indicated by the manometer does not increase, and therefore 
the tension of the vapour during ebullition remains equal to the pressure 
on the liquid. 

A little air is then allowed to enter ; this alters the pressure, and the 
liquid boils at a new temperature j both these are read off, and the ex¬ 
periment repeated as often as desired up to 100°. 

In order to measure the tension above 100°, the tube H' is connected 
with a condensing pump, by means of which the air in the globe M, and 
that in the vessel C, are exposed to successive pressures, higher than the 
atmosphere. The ebullition is retarded (314), and it is only necessary to 
observe the difference in the height of the mercury in the two tubes of 
the manometer, O, and the corresponding temperature, in order to obtain 
the tension for a given temperature. 

The following tables by M. Regnault give the tension of aqueous 
vapour from - 10° to 101°. 


Tensions of aqueous vapour from —10° to 101° C. 


c3 

u . 

<D in 
P* ? 

s U 

<V - 4 — > 

Eh 

Tensions 

in 

milli¬ 

meters. 

Tempera¬ 

tures. 

Tensions 

in 

milli¬ 

meters. 

Tempera¬ 

tures. 

Tensions 

in 

milli¬ 

meters. 

Tempera¬ 

tures. 

Tensions 

in 

milli¬ 

meters. 

-10° 

2-078 

12° 

10-457 

29° 

29-782 

85° 

433-41 

8 

2-456 

13 

11-062 

30 

31-548 

90 

525-45 

6 

2-890 

14 

11-906 

31 

33-405 

91 

545-78 

4 

3-387 

15 

12-699 

32 

35-359 

92 

566-76 

2 

3-955 

16 

13-635 

33 

37-410 

93 

588-41 

0 

4-600 

17 

14-421 

34 

39-565 

94 

610-74 

+ 1 

4-940 

! 18 

15-357 

35 

41-827 

95 

633-78 

2 

5-302 

19 

16-346 

40 

54-906 

96 

657-54 

3 

5-687 

20 

17-391 

45 

71-391 

97 

682-03 

4 

6-097 

21 

18-495 

50 

91-982 

98 

707-26 

5 

6-534 

22 

19-659 

55 

117-478 

98-5 

720-15 

6 

6-998 

23 

20-888 

60 

148-791 

99-0 

733-21 

7 

7-492 

24 

22-184 

65 

186-945 

99-5 

746-50 

8 

8-017 

25 

23-550 

70 

233-093 

100-0 

760-00 

9 

8-574 

26 

24-998 

75 

288-517 

i 100-5 

773-71 

10 

9-165 

27 

26-505 

80 

354-643 

i 101-0 

787-63 

11 

9-792 

28 

28-101 



































264 


ON HEAT. 


[307- 

In the second table the numbers were obtained by direct observation 
up to 24 atmospheres ; the others were calculated by the aid of a formula 
of interpolation. 


Tension in atmospheres from 100 3 to 230 , 9°. 


Temperature. 

. Number of 
atmospheres. 

Temperature. 

Number of 
atmospheres. 

Temperature. 

Number of 

atmospheres. 

Temperature. 

Number of 

atmospheres. 

100-0° 

1 

170-8° 

8 

198-8° 

15 

217-9° 

22 

112-2 

4 

175-8 

9 

201-9 

16 

220-3 

23 

120-6 

2 

180-3 

10 

204-9 

17 

222-5 

24 

133-9 

3 

184-5 

11 

207-7 

18 

224-7 

25 

144-0 

4 

188-4 

12 

210-4 

19 

226-8 

26 

152-2 

5 

192-1 

13 

2130 

20 ! 

228-9 

27 

159-2 

6 

195-5 

14 

215-5 

21 

230-9 

28 

165-3 

7 





i 



These tables show that the elastic force increases much more rapidly 
than the temperature. The law which regulates this increase is not 
accurately’ known. 

307. Tension of the vapours of different liquids. —Regnault has 
determined the elastic force at various temperatures of a certain number 
of liquids which are given in the following table:— 


Liquids. 

Tempera¬ 

ture. 

Tensions in 
millimeters. 

Liquids. 

Tempera¬ 

ture. 

Tensions in | 
millimeters. 

| 

Mercury . 

Alcohol . 

Bisulphide J 
of carbon J 

50° 

100 

0 

50 

100 

-20 

0 

60 

100 

Oil 

0-74 

18 
220 
1685 | 

43 

132 

1164 

3329 

1 Ether . . -j 

j Sulphurous J 
acid 

Ammonia 

-20° 

0 

60 

100 

I -20 

0 

60 

-30 

-20 

0 

9 

182 

1728 

4920 

479 

1165 

8124 

441 

4373 

7709 

i 


308. Tension of the vapours of mixed liquids,— Regnault’s expe¬ 
riments on the tension of the vapour of mixed liquids prove that (i.) when 
two liquids exert no solvent action on each other—such as water and 
















































TENSION OF VAPOURS. 


205 


-309] 

bisulphide of carbon, or water and benzole —the tension of the vapour which 
rises from them is nearly equal to the sum of the tensions of the two sepa¬ 
rate liquids at the same temperature ; (ii.) with water and ether, which 
partially dissolve each other, the tension of the mixture is much less than 
the sum of the tensions of the separate liquids, being scarcely equal to 
that of the ether alone ; (iii.) when two liquids dissolve in all proportions, 
as ether and bisulphide of carbon, or water and alcohol, the tension of the 
vapour of the mixed liquid is intermediate between the tensions of the 
separate liquids. 

Wiillner has shown that the tension of aqueous vapour emitted from a 
saline solution, as compared with that of pure water, is diminished by an 
amount proportional to the quantity of anhydrous salt dissolved, when 
the salt crystallises without water or yields efflorescent crystals; when the 
salt is deliquescent, or has a powerful attraction for water, the reduction 
of tension is proportional to the quantity of crystallised salt. 



Fig. 220. 


309. Tension in two communicating: vessels at different tem¬ 
peratures. —When two vessels containing the same liquid, but at dif- 
i ferent temperatures, are connected with each other, the elastic force is 
not that corresponding to the mean of the two temperatures, as would 
naturally be supposed. Thus, if there are two globes, fig. 220, one, A, 
containing water kept at zero by means of melting ice, the other, B, con¬ 
taining water at 100°, the tension, as long as the globes are not connected, 
is 4 to 6 millimeters in the first, and 760 millimeters in the second. But 
j when they are connected by opening the stopcock, C, the vapour in the 
globe B, from its greater tension, passes into the other globe, and is there 
condensed, so that the vapour in B can never reach a higher temperature 

ST 




















ON HEAT. 


266 


[ 310 - 



than that in the globe A. The liquid simply distils from B towards A 
without any increase of tension. 

From this experiment the general principle may be deduced that when 
two vessels containing the same liquid, but at different temperatures, are con¬ 
nected, the tension is identical in both vessels, and is the same as that corre¬ 
sponding to the lower temperature. An application of this principle has 
been made by Watt in the condenser of the steam engine. 

310. Evaporation. Causes which accelerate it. — Evaporation , as 
has been already stated (298), is the slow production of vapour at the 
surface of a liquid. It is in consequence of this evaporation that wet 
clothes dry when exposed to the air, and that open vessels containing 
water become emptied. The vapours which, rising in the atmosphere, 
condense, and becoming clouds fall as rain, are due to the evaporation 
from the seas, lakes, rivers, and the soil. 

Four causes influence the rapidity of the evaporation of a liquid : i. 
the temperature; ii. the quantity of the same vapour in the surround¬ 
ing atmosphere; iii. the renewal of this atmosphere ; iv. the extent of 
the surface of evaporation. 

Increase of temperature accelerates the evaporation by increasing the 
elastic force of the vapours. 

In order to understand the in¬ 
fluence of the second cause, it is to 
be observed that no evaporation 
could take place in a space already 
saturated with vapour of the same 
liquid, and that it would reach its 
maximum in air completely freed 
from this vapour. It therefore fol¬ 
lows that between these two ex¬ 
tremes the rapidity of evaporation 
varies according as the surrounding 
atmosphere is already more or less 
charged with the same vapour. 

The effect of the renewal of this 
atmosphere is similarly explained; 
for if the air or gas, which surrounds 
the liquid, is not renewed, it soon 
becomes saturated, and evaporation 
ceases. 

The influence of the fourth cause 
is self-evident. 

311. Laws of ebullition. — Ebullition, or boiling, is the rapid production 
of elastic bubbles of vapour in the mass of a liquid itself. 






TENSION OF VAPOURS. 


267 


- 312 ] 


When a liquid, water for example, is heated at the lower part of a 
vessel, the first bubbles are due to the disengagement of air which had 
previously been absorbed. Small bubbles of vapour then begin to 
rise from the heated parts of the sides, but as they pass through the 
upper layers, the temperature of which is lower, they condense before 
reaching the surface. The formation and successive condensation of 
these first bubbles occasion the singing noticed in liquids before they 
begin to boil. Lastly, large bubbles rise and burst on the surface, and 
this constitutes the phenomenon' of ebullition (fig. 221). 

The laws of ebullition have been determined experimentally, and are 
as follows: 

I. The temperature of ebullition , or the boiling point, increases with the 
pressure. 

II. For a given pressure ebullition commences at a certain temperature, 
which varies in different liquids , but which, for equal pressures, is always 
the same in the same liquid. 

III. Whatever be the intensity of the source of heat, as soon as ebulli¬ 
tion commences, the temperature of the liquid remains stationary. 


Boiling points under the pressure 760 millimeters. 


Sulphurous acid .... —10° Turpentine.160° 

Chloride of ethyl©. . . . +11 Butyric acid .157 

Ether.37 Phosphorus.290 

Bisulphide of carbon ... 48 Strong sulphuric acid . . . 325 

Bromine.63 Mercury ....... 320 

Alcohol.78 Sulphur.447 

Distilled water.100 Cadmium.860 

Acetic acid.117 Zinc . ..1040 


There are many causes which influence the boiling point of a liquid, 
such as the substances dissolved, the nature of the vessel, and the pres¬ 
sure. We shall illustrate the effects of these different causes, more par¬ 
ticularly on water. 

Kopp has pointed out that in analogous chemical compounds the same 
difference in chemical composition frequently involves the same difference 
of boiling points; and he has endeavoured to show that in a very ex¬ 
tensive series of compounds the difference of CH 2 is attended by a dif¬ 
ference of 19° C. in the boiling point. 

312. Influence of substances in solution on the boiling: point.— 
The ebullition of a liquid is the more retarded, the greater the quantity 
of any substance it may contain in solution, provided that the substance be 
not volatile, or, at all events, be less volatile than the liquid itself. Water 
which boils at 100° when pure boils at the following temperatures when 
saturated with different salts : 

n 2 













268 


ON HEAT. 


[ 312 - 


Water saturated with common salt . . boils at 109° 

„ „ nitrate of potassium „ 116 

„ „ carbonate of potassium „ 135 

„ „ chloride of calcium „ 179 

Acids in solution present analogous results; but substances merely 
mechanically suspended, such as earthy matters, bran, wooden shavings, 
etc., do not affect the boiling point. 

Dissolved air exerts a very marked influence on the boiling point of 
water. Deluc first observed that water freed from air by ebullition, 
and placed in a flask with a long neck, could be raised to 112° without 
boiling. M. Donny found that water deprived of air and sealed up in a 
lono- glass tube may be heated at one end as high as 138° without boiling, 
and is then suddenly and violently thrown to the other by a burst of vapour. 

When a liquid is suspended in another of the same specific gravity, 
but higher boiling point, it may be raised far beyond its boiling point 
without the formation of a trace of vapour. Dufour has made a number 
of valuable experiments on this subject; he used in the case of water 
a mixture of oil of cloves and linseed oil, and placed in it globules of 
water, and then gradually heated the oil; in this way ebullition rarely 
set in below 110° or 115°, very commonly globules of 10 millimeters 
diameter reached a temperature of 120° or 130°, while very small 
globules of 1 to 3 millimeters reached the temperature of 175°, a tem¬ 
perature at which the tension of vapour on a free surface is 8 or 9 
atmospheres. 

At these high temperatures the contact of a solid body, or the produc¬ 
tion of gas bubbles in the liquid, occasioned a sudden vaporisation of the 
globule, accompanied by a sound like the hissing of a hot iron in water. 

Saturated aqueous solutions of sulphate of copper, chloride of sodium, 
etc., remained liquid at a temperature far beyond their boiling point, when 
immersed in melted stearic acid. In like manner, globules of chloroform 
(which boils at 61°) suspended in a solution of chloride of zinc could be 
heated to 97° or 98° without boiling. 

It is a disputed question as to what is the temperature of the vapour 
from boiling saturated saline solutions. It has been stated by Itudberg 
to be that of pure water boiling under the same pressure ; the most recent 
experiments of Magnus seem to show, however, that this is not the case, 
but that the vapour of boiling solutions is hotter than that of pure 
water; and that the temperature rises as the solutions become more 
concentrated, and therefore boil at higher temperatures. Nevertheless, 
the vapour was always found somewhat cooler than the mass of the 
boiling solution, and the difference was greater at high than at low 
temperatures. 



EBULLITION. 


269 


- 314 ] 

313. Influence of the nature of the vessel on the boiling: 
point. —Gay-Lussac observed that water in a glass vessel required a 
higher temperature for ebullition than in a metal one. Taking the tem¬ 
perature of boiling water in a copper vessel at 100°, its boiling point 
in a glass vessel was found to be 101°; and if the glass vessel had 
been previously cleaned by means of sulphuric acid and of potass.the 
temperature would rise to 105° or even to 106° before ebullition com¬ 
menced. A piece of metal placed in the bottom of the vessel was 
always sufficient to lower the temperature to 100°, and at the same time 
to prevent the violent concussions which accompany the ebullition of 
saline or acid solutions in glass vessels. Whatever be the boiling point 
of water, the temperature of its vapour is uninfluenced by the substance 
of the vessels. 

314. Influence of pressure on the boiling: point.— We see from 
the table of tensions (306) that at 100°, the temperature at which 
water boils under a pressure of 
760 millimeters, aqueous vapour 
has a tension exactly equal to 
this pressure. This principle is 
general, and may be thus enun¬ 
ciated : A liquid boils when the 
tension of its vapour is equal to the 
pressure it supports.' Consequently 
as the pressure increases or dimi¬ 
nishes, the tension of the vapour, 
and therefore the temperature 
necessary for ebullition, must 
increase or diminish. 

In order to show that the boil¬ 
ing point is lower under dimi¬ 
nished pressure, a small dish 
containing water at 30° is placed 
under the receiver of an air pump, 
which is then exhausted. The 
liquid soon begins to boil, the 
vapour formed being pumped out 
as rapidly as it is generated. 

A paradoxical but very simple experiment also well illustrates the 
dependence of the boiling point on the pressure. In a glass flask water 
is boiled for some time, and when all air has been expelled by the steam 
the flask is closed by a cork and inverted as shown in fig. 222. If the 
bottom is then cooled by a stream of cold water from a sponge, the 
water begins to boil again. This arises from the condensation of the 









ON HEAT. 


270 


[ 315 - 


steam above the surface of the water, by which a partial vacuum is 
produced. 

It is in consequence of this diminution of pressure that liquids boil on 
high mountains at lower temperatures. On Mont Blanc, for example, 
water boils at 84°, and at Quito at 90°. 

On the more rapid evaporation of water under feeble pressures is 
based the use of the air pump in concentrating those solutions which 
either cannot bear a high degree of heat, or which can be more 
cheaply evaporated in an exhausted space. Mr. Howard made a 
most important and useful application of this principle in the 
manufacture of sugar. The syrup, in his method, is enclosed in an air¬ 
tight vessel, which is exhausted by a steam engine. The evaporation 
consequently goes on at a lower temperature, which secures the syrup 
from injury-. The same plan is adopted in evaporating the juice of 
certain plants used in preparing medicinal extracts. 

On the other hand, ebullition is retarded by increasing the pressure; 
under a pressure of two atmospheres, for example, water only boils at 
120 - 6 °. 


315. Pranklin's experiment.— The influence of pressure on ebul¬ 
lition may further be illustrated by means of an experiment of 
Franklin’s. The apparatus consists of a bulb, a, and a tube, b, 
joined by a tube of smaller dimensions (fig. 223). The tube b is 

drawn out, and the apparatus 
filled with water, which is 
then in great part boiled 
away by means of a spirit 
lamp. When it has been 
boiled sufficiently long to 
expel all the air, the tube 
b is sealed. There is then 
a vacuum in the apparatus, 
or rather there is a pres¬ 
sure due to the tension of 
aqueous vapour, which at ordinary temperatures is very small. Con¬ 
sequently, if the bulb a be placed in the hand the heat is sufficient to 
produce a tension which drives the water into the tube b, and causes a 
brisk ebullition. 



Fig. 223. 


316. Measurement of heights by the boiling point.— From 
the connection between the boiling point of water and the pressure, the 
heights of mountains may be measured by the thermometer instead of 
by the barometer. Suppose, for example, it is found that water boils on 
the summit of a mountain -at 90°, and at its base at 98°; at these 
temperatures the elastic force or tension of the vapour is equal to that 







EBULLITION. 


271 


-317] 

of the pressure on the liquid, that is, to the pressure of the atmosphere 
at the two places respectively. Now the tensions of aqueous vapour for 
various temperatures have been determined, and accordingly the tensions 
corresponding to the above temperatures are sought in the tables. 
These numbers represent the atmospheric pressures at the two places : in 
other words, they give the barometric heights, and from these .the 
height of the mountain may be calculated by the method already 
given (160). An ascent of about 1080 feet produces a diminution of 
1° C. in the boiling point. 

The instruments used for this purpose are called thermo-barometers , 
or hypsometers , and were first applied by Wollaston. They consist 
essentially of a small metallic vessel for boiling water, fitted with 
very delicate thermometers, which are only graduated from 80° to 
100°; so that, each degree occupying a considerable space on the scale, 
the lOths and even the lOOths of a degree may be estimated, and thus it 
is possible to determine the height of a place by means of the boiling 
point to within about 10 feet. 

317. Formation of vapour in a closed tube. —We have hitherto 
considered vapours as being produced in an indefinite space, or where 
they could expand freely, and it is only under this condition that 
ebullition can take place. In a closed vessel the vapours produced 
finding no issue, their tension and their density increase with the 
temperature, but the rapid disengagement of vapour which constitutes 
ebullition is impossible. Hence while the temperature of a liquid 
in an open vessel can never exceed that of ebullition, in a closed vessel 
it may be much higher. The liquid state has, nevertheless, a limit ; for, 
according to experiments by Cagniard-Latour, if either water, alcohol, 
or ether be placed in strong glass tubes, which are hermetically sealed 
after the air has been expelled by boiling, when these tubes are 
exposed to a sufficient degree of heat, a moment is reached at which 
the liquid suddenly disappears, and is converted into vapour at 200°, 
occupying a space less than double its volume in the liquid state, and 
that the tension was then 38 atmospheres. 

Alcohol which half fills a tube is converted into vapour at 207° C. 
If a glass tube about half filled with water, in which some carbonate of 
soda has been dissolved, to diminish the action of the water in the glass, be 
heated, it is completely vaporised at about the temperature of melting zinc. 

When chloride of ethyle was heated in a very thick sealed tube, the 
upper surface ceased to be distinct at 170°, and was replaced by an 
ill-defined nebulous zone. As the temperature rose this zone increased in 
width in both directions, becoming at the same time more transparent; 
after a time the liquid was completely vaporised, and the tube became 
transparent and seemingly empty. On cooling, the phenomena were 


ON HEAT. 


272 


[ 318 - 


reproduced in the opposite order. Similar appearances were observed on 
heating ether in a sealed tube at 190°. 

Andrews has observed that when liquid carbonic acid was heated to 
31° C. the surface of demarcation between the liquid and the gas became 
fainter, lost its curvature, and gradually disappeared. The space was then 
occupied by a homogeneous fluid, wdiich, when the pressure was suddenly 
diminished, or the temperature slightly lowered, exhibited a peculiar 
appearance of moving or flickering striae throughout its whole mass. 
Above 30° no apparent liquefaction of carbonic anhydride, or separation 
into two distinct forms of matter, could be effected, even when the pressure 
of 400 atmospheres was applied. It would thus seem that there exists 
for every liquid a temperature at which no amount of pressure is capable 
of retaining it in the liquid form. It is not surprising, therefore, that 
mere pressure, however intense, should fail to liquefy many of the bodies 
which usually exist as gases. 

318. Papin’s digester. —Papin, a French physician, appears to have 
been the first to study the effects of the production of vapour in closed 
vessels. The apparatus which bears his name consists of a cylindrical 
iron vessel (fig. 224) provided with a cover, which is firmly fastened 
down by the screw B. In order to close the vessel hermetically, sheet 

lead is placed between the edges of 
the cover and the vessel. At the 
bottom of a cylindrical cavity, which 
traverses the cylinder, S, and the 
tubulure, o, the cover is perforated 
by a small orifice in which there is 
a rod, n. This rod presses against 
a lever, A, moveable at a , and 
the pressure may be regulated by 
means of a weight moveable on this 
lever. The lever is so weighted, 
that when the tension in the in¬ 
terior is equal to 6 atmospheres, for 
example, the valve rises and the 
vapour escapes. The destruction of 
the apparatus is thus avoided, and 
the mechanism has hence received 
the name of safety valve. The di¬ 
gester is filled about two-thirds 
with water, and is heated on a fur¬ 
nace. The water may thus be 
raised to a temperature far above 
100°, and the tension of the vapour increased to several atmospheres, ac¬ 
cording to the weight on the lever. 





















LATENT HEAT OF VAPOUR. 


273 


- 319 ] 

We have seen that water boils at much lower temperatures on high 
mountains (314); the temperature of water boiling in open vessels in 
such localities is not sufficient to soften animal fibre completely and 
extract the nutriment, and hence Papin’s digester is used in the pre¬ 
paration of food. 

Papin’s digester is used in extracting gelatine. When bones are 
digested in this apparatus they are softened so that the gelatine which 
they contain is dissolved. 

319. Latent heat of vapour. —As the temperature of a liquid 
remains constant during ebullition whatever be the source of heat (311), 
it follows that a considerable quantity of heat becomes absorbed in 
ebullition, the only effect of which is to transform the body from the 
liquid to the gaseous condition. And conversely when a saturated 
vapour passes into the state of liquid, it gives out an amount of heat. 

These phenomena were first observed by Black, and he described 
them by saying that during vaporisation a quantity of sensible heat 
became latent, and that the latent heat again became free during conden¬ 
sation. The quantity of heat which a liquid must absorb in passing 
from the liquid to the gaseous state, and which it gives out in passing 
from the state of vapour to that of liquid, is spoken of as the latent heat 
of evaporation. 

The analogy of these phenomena to those of fusion will be at once 
seen; the modes of determining them will be described in the chapter on 
Calorimetry; but the following results which have been obtained for the 
latent heats of evaporation of a few liquids may be here given :— 




Bisulphide of carbon . . 

. . 87 

Alcohol. 

... 208 

Turpentine. 

. . 74 

Acetic acid . . . . 

... 102 

Bromine ...... 

. . 46 

Ether. 

... 90 

Iodine. 

. . 24 


The meaning of these numbers is, in the case of water, for instance, 
that it requires as much heat to convert a pound of water from the state 
of liquid at the boiling point to that of vapour at the same temperature, 
as would raise a pound of water through 540 degrees, or 540 pounds of 
waterthrough one degree ; or that the conversion of one pound of vapour 
of alcohol at 78° into liquid alcohol of the same temperature would heat 
208 pounds of water through one degree. 

Watt, who made some investigations on the subject, found that the 
whole quantity of heat necessary to raise a given weight of water from zero 
to any temperature, and then to evaporate it entirely , is a constant quantity. 
His experiments showed that this quantity is 640. Hence the lower the 
temperature, the greater the latent heat, and, on the other hand, the 
higher the temperature the less the latent heat.- The latent heat of the 

n 3 









274 


ON HEAT. 


[320- 

vapour of water evaporated at 100° would be 540, while at 50° it would 
be 590. At higher temperatures the latent heat of aqueous vapour 
would go on diminishing. Water evaporated under a pressure of 15 
atmospheres at a temperature of 200°, would have a latent heat of 440, 
and if it could be evaporated at 640° it would have no latent heat at all. 

Experiments by Southern and Creighton in 1803 led to a different 
conclusion: namely, that the latent heat of evaporation is a constant quantity 
for all temperatures , and that the total quantity of heat necessary to evaporate 
water, is the sensible heat plus this constant, which they found in round 
numbers to be 540; consequently, to evaporate water at 100°, 640 
thermal units (340) would be needed, while it would require 200 + 540 
= 740 thermal units to evaporate it at 200°. 

Regnault, who examined this question with great care, arrived at 
results which differed from both these laws. He found that the total 
quantity of heat necessary for the evaporation of water increases with the 
temperature, and is not constant, as Watt had supposed. It is repre¬ 
sented by the formula 

Q = 606-5 + 0 305 T 

in which Q is the total quantity of heat, and T the temperature of the 
water during evaporation, while the numbers are constant quantities. 
The total quantity of heat necessary to evaporate water at 100° is 
606-5 4- (0-305 x 100) = 637, at 120° it is 643, at 150° it is 651, and at 
180° it is 661. 

320. Cold due to evaporation. Mercury frozen,— Whatever be 
the temperature at which a vapour is produced, an absorption of heat 
always takes place. If, therefore, a liquid evaporates, and does not 
receive from without a quantity of heat equal to that which is expended 

in producing the vapour, its temperature 
sinks, and the cooling is greater in propor¬ 
tion as the evaporation is more rapid. 

Leslie succeeded in freezing water by 
means of rapid evaporation. Under the 
receiver of the air pump is placed a vessel 
containing strong sulphuric acid, and above 
it a thin metallic capsule (fig. 225) contain¬ 
ing a small quantity of water. By ex¬ 
hausting the receiver the water begins to 
boil (314), and since the vapours are ab¬ 
sorbed by the sulphuric acid as fast as 
they are formed, a rapid evaporisation is 
produced, which quickly effects the freezing 
of the water. 

This experiment is best performed by using, instead of the thin 



Fig. 225. 





COLD DUE TO EVAPORATION. 


275 


- 320 ] 

metallic vessel, a watch-glass, coated with lampblack and resting on 
a cork. The advantage of this is twofold; firstly, the lampblack is 
a very bad conductor, and secondly, it is not moistened by the liquid, 
which remains in the form of a globule not in contact with the 
glass. 

Carre has constructed an apparatus which is based upon Leslie’s ex¬ 
periment, and by which considerable quantities of water may be frozen 
in a very short time. It consists of a horizontal brass cylinder, about 
fifteen inches in length and four in diameter, lined on the inside with an 
alloy of antimony and lead, so as to resist the action of strong sulphuric 
acid, with which it is about half filled. In the top of the cylinder, and 
at one end, is fitted a brass tube, bent twice at right angles, and con¬ 
structed in such a manner that a flask containing water can be easily 
fitted on air-tight. At the other end of the cylinder, also at the top, 
there is a somewhat wide upright tube B. This is connected with a simple 
air pump, specially devised for the purpose, and there is an arrangement 
so that the motion which works the pump works also a stirrer, which 
keeps the acid in continual agitation. A fresh surface is thus continually 
absorbing aqueous vapour; and as the space to be exhausted is small, 
and the pump very effective, soon after its working commences the water 
first boils and then freezes. These apparatus have been introduced for 
industrial purposes ; and where there is a continual demand and use for 
dilute sulphuric acid, there seems no reason why this should not be an 
economical mode of making ice. 

By using liquids more volatile than water, more particularly liquid 
sulphurous acid, which boils at —10°, a degree of cold is obtained suffi¬ 
ciently intense to freeze mercury. The experiment may be made by 
covering the bulb of a thermometer with cotton wool, and after having 
moistened it with liquid sulphurous acid, placing it under the receiver of 
the air pump. When a vacuum is produced the mercury is quickly 
frozen. 

Thilorier, by directing a jet of liquid carbonic acid on the bulb of an 
alcohol thermometer, obtained a cold of -100° without freezing the 
alcohol. We have already seen, however (292), that, with a mixture of 
solid carbonic acid, liquid protoxide of nitrogen, and ether, M. Despretz 
obtained a sufficient degree of cold to reduce alcohol to the viscous state. 

By means of the evaporation of bisulphide of carbon the formation of 
ice may be illustrated without the aid of an air pump. A little water is 
dropped on a small piece of wood, and a capsule of thin copper foil, con¬ 
taining bisulphide of carbon, is placed on the water. The evaporation ot 
the bisulphide is accelerated by means of a pair of bellows, and after a 
few minutes the water freezes round the capsule, so that the latter ad¬ 
heres to the wood. 


270 


ON HEAT. 


[320a - 

The cold produced by evaporation is used in hot climates to cool water 
by means of alcarrazas. These are porous earthen vessels, through which 
water percolates, so that on the outside there is a continual evaporation, 
which is accelerated when the vessels are placed in a current of air. For 
the same reason wine is cooled by wrapping the bottles in wet cloths and 
placing them in a draught. 

In Harrison’s method of making ice artificially, a steam engine is used 
to work an air pump, which produces a rapid evaporation of some ether, 
in which is immersed the vessel containing the water to be frozen. The 
apparatus is so constructed that the vaporised ether can be condensed and 
used again. 

The cooling effect produced by a wind or draught does not necessarily 
arise from the wind being cooler, for it may, as shown by the thermo¬ 
meter, be actually warmer; but arises from the rapid evaporation it causes 
from the surface of the skin. We have the feeling of oppression, even 
at moderate temperatures, when we are in an atmosphere saturated by 
moisture in which no evaporation takes place. 

320a. Carre’s apparatus for freezing water. —We have already 
seen that when any liquid is converted into vapour it absorbs a consider¬ 
able quantity of sensible heat; this furnishes a source of cold which is the 
more abundant the more volatile the liquid and the greater its heat of 
vaporisation. 

This property of liquids has been utilised by M. Carre, in freezing 
water by the distillation of ammonia. The apparatus consists of a cylin¬ 
drical boiler C (figs. 226, 227) and of a slightly conical vessel A, which 
is the freezer. These two vessels are connected by a tube m, and a brace 
n binds them firmly. They are made of strong galvanised plate, and can 
resist a pressure of seven atmospheres. 

The boiler C, which holds about two gallons, is three parts filled with 
strong solution of ammonia. In a tubulure in the upper part of the 
boiler some oil is placed, and in this a thermometer t indicating tem¬ 
peratures from 100° to 150°. The freezer A consists of two concentric 
envelopes, in such a manner that its centre being hollow, a metal 
vessel G, containing the water to be frozen, can be placed in this 
space. Hence only the annular space between the sides of the freezer is 
in communication with the boiler by means of the tube m. In the 
upper part of the freezer there is a small tubulure, which can be closed 
by a metal stopper, and by which the solution of ammonia is introduced. 

The formation of ice comprehends two distinct operations. In the 
first, the boiler is placed in a furnace F, and the freezer in a bath of 
cold water of about 12°. The boiler being heated to 130° the am- 
moniacal gas dissolved in the water of the boiler is disengaged, and, 
in virtue of its own pressure, is liquefied in the freezer, along with 


277 


—320rt] carre’s apparatus for freezing water. 

about a tenth of its weight of water. This distillation of C towards 
A lasts about an hour and a quarter, and when it is finished the 
second operation commences; this consists in placing the boiler in the 
cold-water bath (fig. 227), and the freezer outside, care being taken to 
surround it with very dry flannel. The vessel G, about three quarters 
full of water, is placed in the freezer. As the boiler cools, the ammonia- 
cal gas with which it is filled is again dissolved ; the pressure thus being 
diminished the ammonia which has been liquefied in it is converted into 
the gaseous form, and now distils from A towards C, to redissolve in the 
water which has remained in the boiler. During this distillation the 
ammonia which is rarefied absorbs a great quantity of heat, which is 
withdrawn from the vessel G and the water it contains. Hence it is 
that this water freezes. In order to have better contact between the 



Fig. 226. ^g. 227. 


sides of the vessel G and the freezer, alcohol is poured between them. 
In about an hour and a quarter a perfectly compact cylindrical block of 
ice can be taken from the vessel G. 

This apparatus gives about four pounds of ice in an hour, at a price of 
about a farthing a pound : large continuously working apparatus have, 
however, been constructed, which produce as much as 800 pounds of 
ice in an hour. 











































278 


ON HEAT. 


[ 321 - 


LIQUEFACTION OF VAPOURS AND GASES. 

321. Liquefaction of vapours.— The liquefaction or condensation of 
vapours is their passage from the aeriform to the liquid state. Conden¬ 
sation may be due to three causes—cooling, compression, or chemical 
affinity. For the first two causes the vapours must be saturated (301), 
while the latter produces the liquefaction of the most rarefied vapours. 
Thus, a large number of salts absorb and condense the aqueous vapour in 
the atmosphere, however small its quantity. 

When vapours are condensed, their latent heat becomes free, that is, it 
affects the thermometer. This is readily seen when a current of steam 
at 100° is passed into a vessel of water at the ordinary temperature. 
The liquid becomes rapidly heated, and soon reaches 100°. The quantity 
of heat given up in liquefaction is equal to the quantity absorbed in pro¬ 
ducing the vapour. 

322. Distillation. Stills. —Distillation is an operation by which a 
volatile liquid may be separated from substances which it holds in 



Fig. 228 . 

solution, or by which two liquids of different volatilities may be 
separated. The operation depends on the transformation of liquids into 
vapours by the action of heat, and on the condensation of these vapours 
by cooling. 






































LIQUEFACTION OF VAPOURS. 


279 


-323] 


The apparatus used in distillation is called a still. Its form may vary 
greatly, hut consists essentially of three parts: 1st, the body, A (fig. 228), 
a copper vessel containing the liquid, the lower part of which fits in the 
furnace : 2nd, the head, B, which fits on the body, and from which a 
lateral tube, C, leads to, 3rd, the worm, S, a long spiral tin or copper tube, 
placed in a cistern kept constantly full of cold water. The object of the 
worm is to condense the vapour, by exposing a greater extent of cold 
surface. 

To free ordinary well water from the many impurities which it contains, 
it is placed in a still and heated. The vapours disengaged are condensed 
in the worm, and the distilled water arising from the condensation is col¬ 
lected in the receiver, I). The vapours in condensing rapidly heat the 
water in the cistern, which must, therefore, be constantly renewed. For 



Fig. 229. 


this purpose a continual supply of cold water passes into the bottom of 
the cistern, while the lighter heated water rises to the surface and escapes 
by a tube in the top of the cistern. 

323. I.iebig-’s condenser. —In distilling smaller quantities of liquid, 
or in taking the boiling point of a liquid, so as not to lose any of it, the 
apparatus known as Liebig’s condenser is extremely useful. It consists of 
a glass tube, tt, fig. 229, about 30 inches long, fitted in a copper or tin 
tube by means of perforated corks. A constant supply of cold water from 
the vessel a passes into the space between the two tubes, being conveyed 


























280 


ON HEAT, 



to the lower part of the condenser by a funnel and tube f t and flowing 
out from the upper part by the tube g. The liquid to be distilled is con¬ 
tained in a retort, the neck of which is placed in the tube; the condensed 
liquid drops quite cold into a vessel placed to receive it at the other ex¬ 
tremity of the condensing tube. 

323 a. Apparatus for determining- the alcoholic value of wines. 

—One of the forms of this apparatus consists of a glass flask resting on 



Fig. 230. 


a tripod, and heated by a spirit lamp (fig. 230). By means of a caout¬ 
chouc tube this is connected with a serpentine placed in a copper vessel 
filled with cold water, and below which is a test-glass for collecting the 
distillate. On this are three divisions, one a , which measures the quan¬ 
tity of wine taken; the two others indicating one-half and one-third of 
this volume. 

The test-glass is filled with the wine up to «, this is then poured into 
the flask, which, having been connected with the serpentine, the dis¬ 
tillation is commenced. The liquid which distils over is a mixture of 
alcohol and water; for ordinary wines, such as clarets and hecks, about 
one-third is distilled over, and for wines richer in spirit, such as sherries 
and ports, one-half must be distilled ; experiment has shown that under 
these circumstances all the alcohol passes over in the distillate. The 
measure is then filled up with distilled water to a ; this gives a mixture 
of alcohol and water of the same volume as the wine taken, free from all 
solid matters, such as sugar, colouring matter, and acid, but containing 
all the alcohol. The specific gravity of this distillate is then taken bv 


















LIQUEFACTION OF VAPOURS. 


281 


- 324 ] 


means of an alcoholometer (119) and the number thus obtained corre¬ 
sponds to a certain strength of alcohol as indicated by the tables. 

324. Safety- tube. — In preparing gases and collecting them over 
mercury or water, it occasionally happens that these liquids rush back 
into the generating vessel, and destroy the operation. This arises from 
an excess of atmospheric pressure over the tension in the vessel. If a gas, 
sulphurous acid, for example, be generated in the flask m (fig. 231), and 
passed into water in the vessel A, as long as 
the gas is given ofl* freely, its tension exceeds 
the atmospheric pressure and the weight 
of the column of water on, so that the 
water in the vessel cannot rise in the tube, 
and absorption is impossible. But if the 
tension decreases either through the flask 
becoming cooled, or the gas being disen¬ 
gaged too slowly, the external pressure 
prevails, and when it exceeds the internal 
tension by more than the weight of the 
column of water co, the water rises into the 
flask and the operation is spoiled. This accident is prevented by means 
of safety tubes. 

These are tubes which prevent absorption by allowing air to enter in 
proportion as the internal tension decreases. The simplest is a tube Co 



Tig. 231. 



s 



Fig. 232. Fig. 233. 

fig. 232, passing through the cork which closes the flask M, in which 
the gas is generated and dipping in the liquid. When the tension of the 
gas diminishes in M, the atmospheric pressure on the water in the bath 


















282 


ON HEAT. 


[325- 


E causes it to rise to a certain height in the tube DA; but this pressure, 
acting also on the liquid in the tube Co, depresses it to the same extent, 
assuming that this liquid has the same density as the water in E. Now, 
as the distance or is less than the height DH, air enters by the aperture 
o, before the water in the bath can rise to A, and no absorption takes 
place. 

Fi«\ 233 represents another kind of safety tube. It has a bulb a, con¬ 
taining a certain quantity of liquid, as does also id. When the tension 
of the gas in the retort M exceeds the atmospheric pressure, the level in 
the leg id rises higher than in the bulb, a ; if the gas has the tension of 
one atmosphere, the level is the same in the tube as in the bulb. Lastly, 
if the tension of the gas is less than the atmospheric pressure the level 
sinks in the leg di ; and, as care is taken that the height ia is less than 
bh, as soon as the air which enters through c reaches the curved part i, it 
raises the column ia, and passes into the retort before the water in the 
cylinder can reach b ; the tension in the interior is then equal to the 
exterior, and no absorption takes place. 

325. liquefaction of gases.— We have already seen that a saturated 
vapour, the temperature of which is constant, is liquefied by increasing 
the pressure, and that, the pressure remaining constant, it is brought into 
the liquid state by diminishing the temperature. 

Unsaturated vapours behave in all respects like gases. And it is natural 
to suppose that what are ordinarily called permanent gases are really un¬ 
saturated vapours. For the gaseous form is accidental, and is not inherent 
in the nature of the substance. At ordinary temperatures sulphurous 
acid is a gas, while in countries near the poles it is a liquid; in temperate 
climates ether is a liquid, at a tropical heat it is a gas. And just as un¬ 
saturated vapours may be brought to the state of saturation and then 
liquefied by suitably diminishing the temperature or increasing the 
pressure, so by the same means gases may be liquefied. But as they 
are mostly very far removed from this state of saturation great cold 
and pressure are required. Some of them may indeed be liquefied 
either by cold or by pressure; for the majority, however, both processes 
must be simultaneously employed. Few gases can resist these com¬ 
bined actions, and probably those which have not yet been liquefied, 
hydrogen, oxygen, nitrogen, binoxide of nitrogen, and carbonic oxide, 
would become so if submitted to a sufficient degree of cold and 
pressure. 

Faraday was the first to liquefy some of the gases. His method 
consists in enclosing in a bent glass tube (fig. 234) substances by 
whose chemical action the gas to be liquefied is produced, and then 
sealing the shorter leg. In proportion as the gas is disengaged its 
pressure increases, and it ultimately liquefies and collects in the shorter 


LIQUEFACTION OF GASES. 


283 


-326] 

leg, more especially if its condensation is assisted by placing the 
shorter leg in a freezing mixture. A small manometer may be placed in 
the apparatus to indicate the tension. 

Cyanogen gas is readily liquefied by 
heating cyanide of mercury in a bent tube 
of this description; and carbonic acid by 
heating bicarbonate of soda; other gases 
have been condensed by taking advantage 
of special reactions, the consideration of 
which belongs rather to chemistry than to 
physics. For example, chloride of silver 
absorbs about 200 times its volume of am- 
moniacal gas; when the compound thus 
formed is placed in a condensing tube and gently heated, while the 
shorter leg is immersed in a freezing mixture, a quantity of liquid 
ammoniacal gas speedily collects in the shorter leg. 

326. Apparatus to liquefy and solidify gases.— Thilorier first 
constructed an apparatus by which considerable quantities of carbonic 
acid could be liquefied. Its principle is the same as that used by Faraday 
in working with glass tubes; the gas is generated in an iron cylinder, 
and passes through a metallic tube into another similar cylinder, where it 
condenses. The use of this apparatus is not free from danger; many 
accidents have already happened with it, and it has been superseded by 
an apparatus constructed by Natterer, of Vienna, which is both convenient 
and safe. 

A vertical section of the apparatus, as modified by M. Bianchi, is re¬ 
presented in fig. 235, and on a larger scale in fig. 236. It consists of a 
wrought-iron reservoir A, of something less than a quart capacity, which 
can resist a pressure of more than 600 atmospheres. A small force pump 
is screwed on the lower part of this reservoir. The piston rod t is moved 
by the crank rod E, which is worked by the handle M. As the com¬ 
pression of the gas and the friction of the piston produce a considerable 
disengagement of heat, the reservoir A is surrounded by a copper vessel 
in which ice of a freezing mixture is placed. The water arising from the 
melting or the ice passes by a tube, m, into a cylindrical copper case, C, 
which surrounds the force pump, from whence it escapes through the 
tube n , and the stopcock o. The whole arrangement rests on an iron 
frame, PQ. 

The gas to be liquefied is previously collected in air-tight bags, R, from 
whence it passes into a bottle, V, containing some suitable drying sub¬ 
stance ; it then passes into the. condensing pump through the vulcanised 
india rubber tube H. After the apparatus has been worked for some time, 
the reservoir A can be unscrewed from the pump without any escape of 



284 


ON HEAT, 


[ 326 - 

the liquid, for it is closed below by a valve, S (fig. 235). In order to 
collect some of the liquid gas the reservoir is inverted, and on turning 
the stopcock r, the liquid escapes by a small tubulure x. 

When carbonic acid has been liquefied, and is allowed to escape into the 
air, a portion only of the liquid volatilises, in consequence of the heat 



absorbed by this evaporation, the rest is so much cooled as to solidify in 
white flakes like snow or anhydrous phosphoric acid. 

Solid carbonic acid evaporates very slowly. By means of an alcohol 
thermometer its temperature has been found to be about - 90°. A small 










MIXTURES OF GASES AND VAPOURS. 


285 


- 327 ] 

quantity placed on the hand does not produce the sensation of such great 
cold as might he expected. This arises from the imperfect contact. But 
if the solid he mixed with ether the cold produced is so intense that when 
a little is placed on the skin all the effects of a severe hurn are produced. 
A mixture of these two substances solidifies four times its weight of mer¬ 
cury in a few minutes. When a tube containing liquid carbonic acid is 
placed in this mixture the liquid becomes solid, and looks like a transpa¬ 
rent piece of ice. 

The most remarkable liquefaction obtained by this apparatus is that of 
protoxide of nitrogen. The gas once liquefied only evaporates slowly, and 
produces a temperature of 88° below zero. Mercury placed in it in small 
quantities instantly solidifies. The same is the case with water; it 
must be added drop by drop, otherwise its latent heat being much greater 
than that of mercury, the heat given up by the water in solidifying would 
be sufficient to cause an explosion of the protoxide of nitrogen. 

Protoxide of nitrogen is readily decomposed by heat, and has the pro¬ 
perty of supporting the combustion of bodies with almost as much bril¬ 
liancy as oxygen; and evfen at low temperatures it preserves this property. 
When a piece of incandescent charcoal is thrown on liquid protoxide of 
nitrogen it continues to bum with a brilliant light. 

The cold produced by the evaporation of ether has been used by MM. 
Loir and Drion in the liquefaction of gases. By passing a current of air 
from a blowpipe bellows through several tubes into a few ounces of ether, 
a temperature of — 34° C. can be reached in five or six minutes, and may 
be kept up for fifteen or twenty minutes. By evaporating liquid sul¬ 
phurous acid in the same manner a greater degree of cold, — 50° C., is 
obtained. At this temperature ammoniacal gas may be liquefied. By 
rapidly evaporating liquid ammonia under the air-pump, in the presence 
of sulphuric acid, a temperature of - 87° is attained, which is found 
sufficient to liquefy carbonic acid under the ordinary pressure of the 
atmosphere. 

By means of a bath of ether and of solid carbonic acid, and by using 
very high pressures, Andrews succeeded in reducing air to gfg of its bulk, 
oxygen to —, hydrogen to , carbonic oxide to » an( ^ nitric oxide 
to ^ of its original volume, but without producing liquefaction. Hy¬ 
drogen and carbonic oxide departed less from Boyle and Mariotte’s law 
than oxygen and nitric oxide. 

MIXTURES OF GASES AND VAPOURS. 

327. Laws of the mixture of grases and vapours. —Every mixture 
of a gas and a vapour obeys the following two laws :— 


286 


ON HEAT. 


[ 327 - 


I. The tension , and, consequently , the quantity of vapour which saturates 
a given space are the same for the same temperature, whether this space con¬ 
tains a gas or is a vacuum. 

II. The tension of the mixture of a gas 
and a vapour is equal to the sum of the tensions 
which each would possess if it occupied the 
same space alone. 

These are known as Dalton's laivs, from 
their discoverer, and are demonstrated by 
the following apparatus, which was invented 
by Gay-Lussac. It consists of a glass tube 
A (fig. 237), to which two stopcocks, h and 
d, are cemented. The lower stopcock is pro¬ 
vided with a tubulure, which connects the 
tube A with a tube B of smaller diameter. 
A scale between the two tubes serves to 
measure the heights of the mercurial 
columns in these tubes. 

The tube A is filled with mercury, and 
the stopcocks b and d are closed. A glass 
globe, M, filled with dry air or any other 
gas, is screwed on by means of a stopcock 
in the place of the funnel C. All three 
stopcocks are then opened, and a little 
mercury is allowed to escape, which is re¬ 
placed by the dry air of the globe. The 
stopcocks are then closed, and as the air in 
the tube expands on leaving the globe the 
pressure on it is less than that of the atmo¬ 
sphere. Mercury is accordingly poured into 
the tube B until it is at the same level 
in both tubes. The globe is then removed, and replaced by a funnel C, 
provided with a stopcock a , of a peculiar construction. It is not perfo¬ 
rated, but has a small cavity, as represented in n, on the left of the figure. 
Some of the liquid to be vaporised is poured into C, and the height of the 
mercury, k , having been noted, the stopcock b is opened, and a turned, so 
that its cavity becomes filled with liquid ; being again turned, the liquid 
enters the space A and vaporises. The liquid is allowed to fall drop by 
drop until the air in the tube is saturated, which is the case when the 
level k of the mercury ceases to sink (301). 

As the tension of the vapour produced in the space A is added to that 
of the air already present, the total volume of gas is increased. It may 
easily be restored to its original volume by pouring mercury into B. 



Tig. 237. 



















MIXTURES OF GASES AND VAPOURS. 


287 


-328] 


When the mercury in the large tube has been raised to the level k, there 
is a difference, Bo, in the level of the mercury in the two tubes, which 
obviously represents the tension of the vapour; for as the air has re¬ 
sumed its original volume, its tension has not changed. Now if a few 
drops of the same liquid be passed into the vacuum of a barometric tube 
a depression exactly equal to Bo is produced, which proves that, for the 
same temperature, the tension of a saturated vapour is the same in a gas 
as in a vacuum; from which it is concluded that at the same temperature 
the quantity of vapour is also the same. 

The second law is likewise proved by this experiment, for when the 
mercury has regained its level, the mixture supports the atmospheric pres¬ 
sure on the top of the column B, in addition to the weight of the column 
of mercury Bo. But of these two pressures, one represents the tension of 
the dry air, and the other the tension of the vapour. The second law is, 
moreover, a necessary consequence of the first. 

Experiments can only be made with this apparatus at ordinary tempe¬ 
ratures : but M. Begnault, by means of an apparatus which can be used 
at different temperatures, has investigated the tensions of the vapours of 
water, ether, bisulphide of carbon, and benzole, both in vacuo and in air. 
He has found that the tension in air is less than it is in vacuo, but the 
differences are so small as not to invalidate Dalton’s law. M. Begnault 
is even inclined to consider this law as theoretically true, attributing the 
differences which he observed to the hygroscopic properties of the sides 
of the tube. 

328. Problems on mixtures of gases and vapours.— I. A volume 
of dry air V, at the pressure H, being given, what will be its volume V', 
when it is saturated with vapour, the temperature and the pressure re¬ 
maining the same ? 

If F be the elastic force of the vapour which saturates the air, the 
latter, in the mixture, only supports a pressure equal to H—F (327). 
But by Boyle and Mariotte’s law the volumes V and V' are inversely as 
their pressures, consequently 


V' 

V 


H^F’ whence v ' = 


VH 

H - F 


II. Let V be a given volume of saturated air at the pressure H, and 
the temperature t, what will be its volume V', also saturated, at the 
pressure H', and the temperature t' ? 

If/be the maximum tension of aqueous vapour at t°, and f its maxi¬ 
mum tension at t’°, the air alone in each of the mixtures V and V' will 
be respectively under the pressures H—/ and H ' —f '; consequently, 
assuming first that the temperature is constant, we obtain 

V' _ H -/ 

V H'-/ 




288 


ON HEAT. 


[329- 


But as the volumes V' and V of air, at the temperatures t' and £, are in 
the ratio of 1 + ut' to 1 + at , a being the coefficient of the expansion of 
air, the equation becomes 

V IP - / I + at 

III. What is the weight P of a volume of air V, saturated with aqueous 
vapour at the temperature t, and pressure H P 

If we call F the maximum tension of the vapour at t°, the tension of 
the air alone will be H—F, and the problem reduces itself to finding : 
1 st, the weight of V cubic inches of dry air at t, and under the pressure 
H—F ; and 2nd, the weight of V cubic inches of saturated vapour at t° 
under the pressure. 

To solve the first part of the problem we know that a cubic inch of 
dry air atO° and the pressure 700 millimeters weighs 0*31 grains, and that 

at t°, and the pressure H—F, it weighs 9-F) (282), conse¬ 
nt + at) 750 

quently V cubic inches of dry air weigh 
0-31 (H-F) V 

(1 + at) 760 . w 


To obtain the weight of the vapour, the weight of the same volume of 
dry air at the same temperature and pressure must be sought, and this 
is to be multiplied by the relative density of the vapour. Now as V 

cubic inches of dry air at t°, and the pressure F, weigh 0 *>1 x VF 
J J ^ ° (1 + at) 760 

Y cubic inches of aqueous vapour, whose density is £ of that of air 
(338), weigh 


0 31 x VF 5 
(1 -j- at) 760 8 


( 2 ) 


and as the weight P is equal to the sum of the weights (1) and (2) we 
have 


P = Q-31 x V (H-F) f O-31 x V F 51 0-31 x Y m 

(1 + at) 760 " r L(l+«*)760 8 J (1 -M) 760 { 8} 


SPHEROIDAL CONDITION. 

329. Zieidenfrost’s phenomenon. Boutigny’s experiments.— 

When liquids are thrown upon incandescent metallic surfaces they 
present remarkable phenomena, which were first observed by Leiden- 
frost a century ago, and have been named after their discoverer. They 
have since then been studied by other physicists, and more especially 
by M. Boutigny, to whom our present knowledge of the subject is 
mainly due. 








SPHEROIDAL CONDITION. 


289 


- 329 ] 

When a tolerably thick silver or platinum dish is heated to redness, 
and a little water, previously warmed, dropped into the dish by means of 
a pipette, the liquid does not spread itself out on the dish, and does not 
moisten it, as it would at the ordinary temperature, but assumes the 
form of a flattened globule, which fact M. Boutigny expresses by saying 
that it has passed into the spheroidal state. It rotates rapidly round on 
the bottom of the dish, taking sometimes the form of a star, and not only 
does it not boil, but its evaporation is only about one-fifth as rapid as 
if it boiled. As the dish cools, a point is reached at which it is not hot 
enough to keep the water in the spheroidal state; it is accordingly 
moistened by the liquid, and a violent ebullition suddenly ensues. 

All volatile liquids can assume the spheroidal condition ; the lowest 
temperature at which it can be produced varies with each liquid, and is 
more elevated the higher the boiling point of the liquid. For water, the 
dish must have at least a temperature of 200°; for alcohol, 134°; and for 
ether, 61°. 

The temperature of a liquid in the spheroidal state is always below its 
boiling point. This temperature has been measured by M. Boutigny by 
means of a very delicate thermometer; but his method is not free from 
objections, and it is probable that the temperatures he obtained were too 
high. He found that of water to be 95°; alcohol, 75° ; ether, 34°; and 
liquid sulphurous acid, —11°. But the temperature of the vapour which 
is disengaged appears to be as high as that of the vessel itself. 

This property of liquids in the spheroidal state remaining below their 
boiling point has been applied by M. Boutigny in a remarkable experi¬ 
ment, that of freezing water in a red-hot crucible. He heated a platinum 
dish to bright redness, and placed a small quantity of liquid sulphurous 
acid in it. It immediately assumed the spheroidal condition, and its 
evaporation was remarkably slow. Its temperature, as has been stated, 
was about —11°, and when a small quantity of water was added it 
immediately solidified, and a small piece of ice could be thrown out of 
the red-hot crucible. In a similar manner Faraday, by means of a mix¬ 
ture of solid carbonic acid and ether, succeeded in freezing mercury in 
a red-hot crucible. 

In the spheroidal state the liquid is not in contact with the vessel. 
M. Boutigny proved this by heating a silver plate placed in a horizon¬ 
tal position, and dropping on it a little dark coloured water. The 
liquid assumed the spheroidal condition, and the flame of a candle placed 
at some distance could be distinctly seen between the drop and the plate. 
If a plate perforated by several fine holes be heated, a liquid will assume 
the spheroidal state when projected upon it. This is also the case with 
a flat helix of platinum wire pressed into a slightly concave shape. An 
experiment of another class, due to Mr. A. H. Church, also illustrates 

o 


290 


ON HEAT. 


[ 329 - 

the same fact. A polished silver disli is made red hot, and a few drops 
of a solution of sulphide of sodium are projected on it. The liquid 
passes into the spheroidal condition, and the silver undergoes no 
alteration. But if the dish is allowed to cool, the liquid instantly 
moistens it, producing a dark spot, due to the formation of sulphide of 
silver. In like manner nitric acid assumes the spheroidal state when 
projected on a heated silver plate, and does not attack the metal so long 
as the plate remains hot. 

Similarly liquids may he made to roll upon liquids, and solid bodies 
which vaporise without becoming liquid also assume a condition analo¬ 
gous to the spheroidal state of liquids when they are placed on a surface 
whose temperature is sufficiently high to vaporise them rapidly. This 
is seen when a piece of carbonate of ammonium is placed in a red-hot 
platinum crucible. 

The phenomena of the spheroidal state seem to prove that the liquid 
globule rests upon a sort of cushion of its own vapour, produced by the 
heat radiated from the hot surface against its under side. As fast as 
this vapour escapes from under the globule, its place is supplied by a 
fresh quantity formed in the same way, so that the globule is constantly 
buoyed up by it, and does not come in actual contact with the heated 
surface. When, however, the temperature of the latter falls, the for¬ 
mation of vapour at the under surface becomes less and less rapid, until 
at length it is not sufficient to prevent the globule touching the hot 
metal or liquid on which it rests. As soon as contact occurs heat is rapidly 
imparted to the globule, it enters into ebullition, and quickly boils away. 

These experiments on the spheroidal state explain the fact that the 
hand may be dipped into melted lead, or even melted iron, without in¬ 
jury. It is necessary that the liquid metal be heated greatly above its 
solidifying point. Usually the natural moisture of the hand is sufficient, 
hut it is better to wipe it with a damp cloth. In consequence of the 
great heat, the hand becomes covered with a layer of spheroidal fluid, 
which prevents the contact of the metal with the hand. Radiant heat 
alone operates, and this is principally expended in forming aqueous 
vapour on the surface of the hand. If the hand is immersed in boiling 
water, the water adheres to the flesh, and consequently a scald is pro¬ 
duced. 

The tales of ordeals by fire during the middle ages, of men who could 
run barefooted over red-hot iron without being injured, are possibly 
true in some cases, and would find a ready explanation in the preceding 
phenomena. 


-330] 


DENSITY OF VAPOURS. 


291 


DENSITY OF VAPOURS. 

330. Gay-X<ussac's method.— The density of a vapour is the relation 
between the weight of a given volume of this vapour and of that of the 
same volume of air at the same temperature and pressure. 

Two methods principally are used in determining the density of 
vapours : Gay-Lussac’s, which serves for liquids which boil at about 100°, 
and Dumas’, which can be used up to 350°. 

Figure 238 represents the apparatus used by Gay-Lussac. It consists 
of an iron vessel containing mercury, in 
which there is a glass cylinder, M. This 
is filled with water or oil, and the tem¬ 
perature is indicated by the thermometer, 

T. In the interior of the cylinder is a 
graduated glass jar, C, which, at first, is 
filled with mercury. 

The liquid whose vapour density is to 
be determined is placed in a small bulb, A, 
represented on the left of the figure. The 
bulb is then sealed and weighed; the 
weight of the liquid taken is obviously the 
weight of the bulb when filled, minus its 
weight while empty. The bulb is then 
introduced into the jar C, and the liquid in 
M gradually heated somewhat higher than 
the boiling point of the liquid in the bulb. 

In consequence of the expansion of this 
liquid the bulb breaks, and the liquid be¬ 
coming converted into vapour the mercury 
is depressed, as represented in the figure. 

The bulb must be so small that all the 
liquid in it is vaporised. The volume of 
the vapour is given by the graduation on the jar. Its temperature is 
indicated by the thermometer T, and the pressure is indicated by the 
difference between the height of the barometer at the time of the 
observation, and the height of the column of mercury in the gas jar. It 
is only necessary then to calculate the weight of a volume of air equal 
to that of the vapour under the same conditions of temperature and 
pressure. The quotient, obtained by dividing the weight of the-vapour 
by that of the air, gives the required density of the vapour. 

Letjt? be the weight of the vapour in grains, v its volume in cubic 
inches, and t its temperature; if H be the height of the barometer, and 

o 2 



Fig. 238. 















ON HEAT. 


292 


[ 331 - 


li that of the mercury in the gas jar, the pressure on the vapour will be 
H— h. 

It is required to find the weight p' of a volume of air v, at the tem¬ 
perature t, and under a pressure H— h. At zero, under the pressure 
760 millimeters, a cubic inch of air weights 031 grains; consequently, 
under the same conditions v cubic inches will weigh 0*31 v grains. And 
therefore the weight of v cubic inches of air, at t° and the pressure 760 
millimeters, is 

03Ty g ra i ng r2g2 ? prob. ii.]. 
l-+-a£ 

As the weight of a volume of air is proportional to the pressure, the 
above weight may be reduced to the pressure H— h by multiplying by 
H — h ,. , . 

“MP ™ hlch glves 

0-31 v (H — h) 

(1 + at) 760 

for the weight p' of the volume of air v, at the pressure H — h, and at t°. 
Consequently, for the desired density we have 
—P — P (I + at ) 760 
p f 031 v (H - h) 

331. Dumas’ method. —The method just described cannot be applied 
to liquids whose boiling point exceeds 150° 
or 160°. In order to raise the oil in the 
cylinder to this temperature it would be 
necessary to heat the mercury to such a 
degree that the mercurial vapours would 
be dangerous to the operator. And, 
moreover, the tension of the mercurial 
vapours in the graduated jar would increase 
the tension of the vapour of the liquid, and 
so far vitiate the result. 

The following method, devised by 
M. Dumas, can be used up to the tem¬ 
perature at which glass begins to soften; 
that is, about 400°. A glass globe 
is used with the neck drawn out to a 
fine point (fig. 239). The globe, having 
been dried externally and internally, is 
weighed, the temperature t and barometric 
height h being noted. This weight W is 
the weight of the glass O in addition to p, the weight of the air it con¬ 
tains. The globe is then gently warmed, and its point immersed in 



Fig. 239. 













DENSITY OF VAPOURS. 


293 


- 331 ] 


the liquid whose vapour density is to he determined ; on cooling, the 
air contracts, and a quantity of liquid enters the globe. The globe is 
then immersed in a bath, either of oil or fusible metal, according to 
the temperature to which it is to be raised. In order to keep the globe 
in a vertical position a metallic support, on which a moveable rod slides, 
is fixed on the side of the vessel. This rod has two rings, between 
which the globe is placed, as shown in the figure. There is another 
rod, to which a weight thermometer, D, is attached. 

The globe and thermometer having been immersed in the bath, 
the latter is heated until slightly above the boiling point of the liquid 
in the globe. The vapour which passes out by the point expels all 
the air in the interior. When the jet of vapour ceases, which is the 
case when all the liquid has been converted into vapour, the point of 
the globe is hermetically sealed, the temperature of the bath t', and 
the barometric height h', being noted. When the globe is cooled, it is 
carefully cleaned and again weighed. This weight, W', is that of the 
glass, G, plus p ', the weight of the vapour which fills the globe at the 
temperature f and pressure h ', or W' = G + p'. To obtain the weight 
of the glass alone, the weighty of air must be known, which is deter¬ 
mined in the following manner: The point of the globe is placed under 
mercury and the extremity broken off with a small pair of pincers : the 
vapour being condensed, a vacuum is produced, and mercury rushes 
up, completely filling the globe, if, in the experiment, all the air has 
been completely expelled. The mercury is then poured into a care¬ 
fully graduated measure, which gives the volume of the globe. From 
this result, the volume of the globe at the temperature t' may be easily 
calculated, and consequently the volume of the vapour. From this 
determination of the volume of the globe the weight p of the air 
at the temperature t and pressure h is readily calculated, and this 
result subtracted from W gives G, the weight of the glass. Now the 
weight of the vapour/?' is W'—G. We now know the weight p r of a 
given volume of vapour at the temperature t' and pressure h', and it is 
only necessary to calculate the weight p" of the same volume of air 
under the same conditions, which is easily accomplished. The quotient 
/ 

aL is the required density of the vapour. 


Densities of Vapours. 


Air. 1-0000 

Vapour of water .... 0*6235 

„ alcohol .... 1*6138 

,, ether .... 2*5860 

„ bisulphide of carbon 2*6447 


Vapour of phosphorus . 4*3256 
,, turpentine . 5*0130 

„ sulphur . . 6*6542 

„ mercury . . 6*9760 

,, iodine. . . 8*7160 



294 


ON HEAT. 


[332- 


The density of aqueous vapour, when a space is saturated with it, is at 
all temperatures f, or, more accurately, 06225, of the density of air at 
the same temperature and pressure. 

332. Seville and Troost’s method.— Deville and Troost have modi¬ 
fied Dumas’ method so that it can he used for determining the vapour 
density of liquids with very high boiling points. The globe is heated in 
an iron cylinder in the vapour of mercury or of sulphur, the temperatures 
of which are constant respectively at 350° and 460°. In other respects 
the determination is the same as in Dumas’ method. 

For determinations at higher temperatures, Deville and Troost have 
employed the vapour of zinc, the temperature of which is 1040°. As 
glass vessels are softened by this heat, they use porcelain globes with 
finely drawn out necks, which are sealed by means of the oxyhydrogen 
flame. 

333. Relation between the volume of a liquid and that of its 
vapour. —The density of vapour being known, we can readily calculate 
the ratio between the volume of a vapour in the saturated state at a 
given temperature, and that of its liquid at zero. We may take, as an 
example, the relation between water at zero and steam at 100°. 

The ratio between the weights of equal volumes of air at zero, and 
the normal barometric pressure, and of water under the same circum¬ 
stances, is as 1 : 773. But from what has been already said (282), the 
density of air at zero is to its density at 100° as 1 + at : 1. Hence the 
ratio between the weights of equal volumes of air at 100° and water at 


0°, is 


773, or 073178 : 773. 


1 0003605 x 104 

Now from the above table the density of steam at 100° C., and the 
normal pressure, compared with that of air under the same circumstances, 
is as 0-6225 : 1. Hence the ratio between the weights of equal volumes 
of steam at 100°, and water at 0°, is 


0-73178 x 0-6225 : 773 or 0-4555 : 773 or 1 : 1698. 


Therefore, as the volumes of bodies are inversely as their densities 
one volume of water at zero expands into 1698 volumes of steam at 100° 
C. The practical rule that a cubic inch of water yields a cubic foot of 
steam, though not quite accurate, expresses the relation in a convenient 
form. 



-335] 


HYGROMETRY. 


295 


CHAPTER VI. 

HYGROMETRY. 

334. Object of faygrrometry. —The object of hyyrometry is to deter¬ 
mine the quantity of aqueous vapour contained in a given volume of 
air. This quantity is very variable ; but the atmosphere is never com¬ 
pletely saturated with vapour, at any rate, in our climates. Nor is it 
ever completely dry; for if hygrometric substances , that is to say, sub¬ 
stances with a great affinity for water, such as chloride of calcium, sul¬ 
phuric acid, etc., be at any time exposed to the air, they absorb aqueous 
vapour. 

335. Hygrometric state. —As in general the air is never saturated, 
the ratio of the quantity of aqueous vapour actually present in the 
atmosphere, to that which it would contain if it were saturated, the tem¬ 
perature remaining the same, is called the hygrometric state , or degree of 
saturation. 

The degree of moisture does not depend on the absolute quantity of 
aqueous vapour present in the air, but on the greater or less distance of 
the air from its point of saturation. When the air is cold, it may be 
moist with very little vapour, and, on the contrary, when it is warm, very 
dry, even with a large quantity of vapour. In summer the air usually 
contains more aqueous vapour than in winter, notwithstanding which it 
is less moist, because, the temperature being higher, the vapour is farther 
from its point of saturation. When a room is warmed, the quantity of 
moisture is not diminished, but the humidity of the air is lessened, because 
its point of saturation is raised. The air may thus become so dry as to 
be injurious to the health, and it is hence usual to place vessels of water 
on the stoves used for heating. 

As Mariotte’s law applies to nonsaturated vapours as well as to gases 
(302), it follows that, with the same temperature and volume, the 
weight of vapour in a nonsaturated space increases with the pressure, and 
therefore with the tension of the vapour itself. Instead, therefore, of the 
ratio of the quantities of vapour, that of the corresponding tensions may 
be substituted, and it may be said that the hygrometric state is the ratio 
of the tension of the aqueous vapour which the air actually contains, to the 
tension of the vapour which it would contain at the same temperature if it 
wet'e saturated. 


296 


ON HEAT. 


[ 336 - 

If / is the actual tension of aqueous vapour in the air, and F that of 
saturated vapour at the same temperature, and E the hygrometric state, 

f 

we have E = whence / = F X E. 

As a consequence of this second definition, it is important to notice 
that the temperature having varied, the air may contain the same 
quantity of vapour and yet not have the same hygrometric state. For, 
when the temperature rises, the tension of the vapour which the air 
would contain if saturated increases more rapidly than the tension of 
the vapour actually present in the atmosphere, and hence the ratio 
between the two forces, that is to say, the hygrometric state, becomes 
smaller. 

It will presently be explained (343) how the weight of the vapour 
present in a given volume of air may be deduced from the hygrometric 
state. 

336. Different kinds of hygrometers. —Hygrometers are instru¬ 
ments for measuring the hygrometric state of the air. There are 
numerous varieties of them—chemical hygrometers, condensing hygro¬ 
meters and psychrometers. 

337. Chemical hygrometer. —The method of the chemical hygro¬ 
meter consists in passing a known volume of air over a substance which 
readily absorbs moisture—chloride of calcium, for instance. The sub¬ 
stance having been weighed before the passage of the air, and then 
afterwards, the increase in weight represents the amount of aqueous 
vapour present in the air. By means of the apparatus represented in 
fig. 240, it is possible to examine any given volume. Two brass reser¬ 
voirs A and B, of the same size and construction, act alternately as 
aspirators, by being fixed to the same axis, about which they can turn. 
They are connected by a central tubulure, and by means of two tubulures 
in the axis the lower reservoir is always in connection with the atmo¬ 
sphere, while the upper one, by means of a caoutchouc tube, is connected 
with two tubes M and N, filled either with chloride of calcium, or 
with pumice stone impregnated with sulphuric acid. The first absorbs 
the vapour in the air drawn through, while the other M stops any 
vapour which might diffuse from the reservoirs to the tube N. 

The lower reservoir being full of water, and the upper one of air, the 
apparatus is inverted so that the liquid flows slowly from A to B. A 
vacuum being formed in A, air enters by the tubes NM, in the first of 
which all the vapour is absorbed. When all the water has run into B 
it is turned; the same flow recommences, and the same volume of air is 
drawn through the tube N. Thus, if each reservoir holds a gallon, for 
example, and the apparatus has been turned five times, 5 gallons of air 
have traversed the tube N, and have been dried. If then, before the 


HYGROMETRY. 


297 


-339] 

experiment, tlie tube with its contents has been weighed, the increase 
in weight gives the weight of aqueous vapour present in 5 gallons of air 
at the time of the experiment. 

338. Condensing: hygrometers. —When a body gradually cools 
in a moist atmosphere, the layer of air in immediate contact with 
it cools also, and a point is ultimately reached at which the vapour 
present is j ust sufficient to saturate the air: the least diminution of 
temperature then causes a precipitation of moisture on the body in the 
form of dew. When the temperature rises again, the dew disappears. 


Fig. 240. 



The mean of these two temperatures is taken as the dew point , and the 
object of condensating hygrometers is to observe this point. DanielFs 
and Regnault’s hygrometers belong to this class. 

339. Daniell’s hygrometer. —This consists of two glass bulbs at the 
extremities of a glass tube bent twice (fig. 241). The bulb A is two- 
thirds’full of ether, and a very delicate thermometer plunges in it; the 
rest of the space contains nothing but the vapour of ether, the ether 
having been boiled before the bulb B was sealed. The bulb B is covered 
with muslin, and ether is dropped upon it. The ether in evaporating 
cools the bulb, and the vapour contained in it is condensed. The 
internal tension being thus diminished, the ether in A forms vapours 

o 3 

























298 


ON HEAT. 


[ 340 - 

which condense in the other bulb B. In proportion as the liquid distils 
from the lower to the upper bulb, the ether becomes cooler, and 

ultimately the temperature of the 
air in immediate contact with A sinks 
to that point at which its vapour is 
more than sufficient to saturate it, and 
it is, accordingly, deposited on the out¬ 
side as a ring of dew corresponding to 
the surface of the ether. The tempera¬ 
ture of this point is noted by means of 
the thermometer in the inside. The 
addition of ether to the bulb B is then 
discontinued, the temperature of A 
rises, and the temperature at which the 
dew disappears is noted. In order to 
render the deposition of dew more per¬ 
ceptible, the bulb A is made of black 
glass. 

These two points having been de¬ 
termined, their mean is taken as 
that of the dew point. The tempera¬ 
ture of the air at the time of the 
experiment is indicated by the ther¬ 
mometer on the stem. The tension 
f, corresponding to the temperature of the dew point, is then 
found in the table of tensions (306). This tension is exactly that of 
the vapour present in the air at the time of the experiment. The 
tension F of vapour saturated at the temperature of the atmosphere 
is found by means of the same table; the quotient obtained by 
dividing / by F, represents the hygrometric state of the air (335). 
For instance, the temperature of the air being 15°, suppose the dew point 
is 5°. From the table the corresponding tensions are/= 6*534 milli¬ 
meters, and F = 12*699 millimeters, which gives 0*514 for the ratio off 
to F, or the hygrometric state. 

There are many sources of error in Daniell’s hygrometer. The 
principal are: 1st, that as the evaporation in the bulb A only cools 
the liquid on the surface, the thermometer dipping on it does not 
exactly give the dew point; 2nd, that the observer standing near the 
instrument modifies the hygrometric state of the surrounding air, as 
well as its temperature; the cold ether vapour too flowing from the 
upper bulb may cause inaccuracy. 

340. Regnault’s hygrometer. —Regnault’s hygrometer is free from 
the sources of error incidental to the use of DanielTs. It consists of two 



Fig. 241. 






















hygrometry. 


299 


-340] 

veiy thin polished silver thimbles 1’75 inch in height, and 0 75 inch in 
diameter (fig. 242). In these are fixed two glass tubes, D and E, in each 
of which is a thermometer. A bent tube, A, open at both ends, passes 
through the cork of the tube D, and reaches nearly to the bottom of 
the thimble. There is a tubulure on the side of D, fitting in a brass 
tube which forms a support for the apparatus. The end of this tube 
is connected with an aspirator G. The tube E is not connected with 
the aspirator; its thermometer simply indicates the temperature of the 
atmosphere. 

The tube T) is then half filled with ether, and the stopcock of the 
aspirator opened. The water contained in it runs out, and just as much 



Fig. 242. 

air enters through the tube A, bubbling through the ether, and causing 
it to evaporate. This evaporation produces a diminution of temperature, 
so that dew is deposited on the silver just as on the bulb in Daniells 
hygrometer, the thermometer T is then instantly to be read, and the 
stream from the aspirator stopped. The dew will soon disappear again, 
and the thermometer T is again to be read; the mean of the two 
readings is taken : the thermometer t gives the corresponding temperature 
of the air, and hence there are all the elements necessary for calculating 
the hygrometric state. 




























300 ON HEAT. [ 341 - 

As in this instrument, all the ether is at the same temperature in 
consequence of the agitation, and the temperatures are read off at a 
distance by means of a telescope, the sources of error in Daniell’s hygro¬ 
meter are avoided. 

A much simpler form of the apparatus may be constructed out of a 
common test tube containing a depth of l£ inch of ether. The tube is 
provided with a loosely fitting cork in which is a delicate thermometer 
and a narrow bent tube dipping in the ether. On blowing through the 
ether, by a caoutchouc tube of considerable length, a diminution of tem¬ 
perature is caused, and after a little practice the whole process can be 
conducted almost as well as in Regnault’s complete instrument. The 
temperature of the air is indicated by a free thermometer. 

341. Psychrometer. Wet bulb hygrometer, —A moist body 
evaporates in the air more rapidly in proportion as the air is drier, and in 
consequence of this evaporation the temperature of the body sinks. The 
psychrometer or wet bulb hygrometer is based on this principle, the ap¬ 
plication of which, to this purpose, was first suggested 
by Leslie. The form usually adopted in this country is 
due to Mason. It consists of two delicate thermometers 
placed on a wooden stand (fig. 243). One of the bulbs is 
covered with muslin, and is kept continually moist by 
being connected with a reservoir of water by means of a 
string. Unless the air is saturated with moisture the wet 
bulb thermometer always indicates a lower temperature 
than the other, and the difference between the indications 
of the two thermometers is greater in proportion as the air 
can take up more moisture. The tension e of the aqueous 
vapour in the atmosphere may be calculated from the 
indications of the thermometer by means of the follow¬ 
ing empirical formula: 

e — e' —0’00077 (t — t') h } 

in which e r is the maximum tension corresponding to the 
temperature of the wet bulb thermometer, h is the baro¬ 
metric height, and t and t' the respective temperatures 
of the dry and wet bulb thermometers. If, for example, 
h = 750 millimeters, t = 15° C., t'= 10° C.; according to 
the table of tensions (306), e' = 9T65, and we have 
e = 9T65 — 0-00077 x 5 x 750 = 6-278. 

This tension corresponds to a dew point of about 4-5° C. If the air had 
been saturated, the tension would have been 12-699, and the air is there¬ 
fore about half saturated with moisture. 

' This formula expresses the result with tolerable accuracy, but the 

















HYGROMETRY, 


301 


- 342 ] 


above constant 0’00077 requires to be controlled for different positions 
of tbe instrument; in small closed rooms it is 0-00128, in large rooms 
it is 0’00100, and in tbe open air without wind it is 0’00090: tbe 
number 0 00077 is its value in a large room with open windows. 
Regnault found that tbe difference in temperature of the two bulbs 
depends on tbe rapidity of tbe current of air; be also found that at 
a low temperature, and in very moist air, tbe results obtained with 
the psychrometer differed from those yielded by bis hygrometer. It is 
probable that tbe indications of tbe psychrometer are only true for mean 
and high temperatures, and when the atmosphere is not too moist. 

A formula frequently used in this country is that given by Dr. 
Apjohn. It is 


F — f _Ax or F = f ——x A 

1 88*30 1 96 30 


in which d is the difference of the wet and dry bulb thermometers in 
Fahrenheit degrees, h the barometric height in inches ; f the tension of 
vapour for the temperature of the wet bulb, and F the elastic force of 
vapour at the dew point, from which the dew point may if necessary be 
found from the tables. The constant coefficient 88, for the specific heats 
of air and steam, is to be used when the reading of the wet bulb is above 
32° F. and 96 when it is below. 

According to Glaisher the temperature of the dew point may be ob¬ 
tained by multiplying the difference between the temperatures of the 
wet and dry bulb by a constant depending on the temperature of the air 
at the time of observation, and subtracting the product thus obtained 
from this last named temperature. The following are the numbers : 


Dry Bulb 
Temperature F.° 

Factor 

Dry Bulb 
Temperature F.° 

Factor 

Below 24° 

8-5 

34 to 35 

2-6 

24 to 25 

7-3 

35—40 

2-5 

25—26 

6-4 

40—45 

2-3 

26—27 

6-1 

45—50 

2-1 

27—28 

5-9 

50—55 

2-0 

28—29 

5-7 

55—60 

1-8 

29—30 

5-0 

60—65 

1*8 

30—31 

4-6 

65—70 

1*7 

31—32 

3-6 

70—75 

1-5 

32—33 

3-1 

75—80 

1-3 

33—34 

2-8 

80—85 

1-0 


These are often known as Glaisher 1 s factors. 

342. Hygrometers of absorption. —These hygrometers are based on 








302 ON HEAT. [ 343 - 

the property which organic substances have, of elongating when moist, 
and of again contracting as they become dry. The most common form is 
the hair or Saussure's hygrometer . 

It consists of a brass frame (fig. 244), on which is fixed a hair, c, 
fastened at its upper extremity in a clamp, a, provided with a screw, d. 

This clamp is moved by a screw h. The lower part 
of the hair passes round a pulley, o, and supports a 
small weight, p. On the pulley there is a needle, 
which moves along a graduated scale. When the 
hair becomes shorter the needle rises, when it be¬ 
comes longer the weight p makes it sink. 

The scale is graduated by calling that point zero 
at which the needle would stand if the air were com¬ 
pletely dry, and 100 the point at which it stands in 
air completely saturated with moisture. The dis¬ 
tance between these points is divided into 100 equal 
degrees. 

Kegnault has devoted much study in order to 
render the hair hygrometer scientifically useful, but 
without success. And the utmost that can be claimed 
for it is that it can be used as a hygroscope ; that is, an 
instrument which shows approximately whether the 
air is more or less moist, without giving any indica¬ 
tion as to the quantity of moisture present. To this 
class belong the chimney ornaments, one of the most 
common forms of which is that of a small male and 
female figure, so arranged in reference to a little house, with two doors, 
that when it is moist the man goes out and the woman goes in, and vice 
versa when it is fine. They are founded on the property which twisted 
strings or pieces of catgut possess, of untwisting when moist, and of 
twisting when dry. 

As these hygroscopes only change slowly, their indications are always 
behindhand with the state of the weather; nor are they, moreover, very 
exact. 

343. Problem on hygrometry. —To calculate the weight P of a 
volume of moist air V, the hygrometric state of which is E, the tem¬ 
perature t, and the pressure H, the density of the vapour being £ that of 
air. 

From the second law of the mixture of gases and vapours, it will be 
seen that the moist air is nothing more than a mixture of V cubic inches 
of dry air at t°, under the pressure H minus that of the vapour, and of V 
cubic inches of vapour at f and the tension given by the hygrometric 
state ; these two values must, therefore, be found separately. 



Fig. 244. 
















HYGROMETFY. 


303 


- 344 ] 


The formula/= F x E (335) gives the tension / of the vapour in 
the air, for E has been determined, and F is found in the tables. The 
tension / being known, if f is the tension of the air, / + / = H, from 
which / = H — / = H — FE. 


The question consequently resolves itself into calculating the weight 
of V cubic inches of dry air at t°, and the pressure H — FE, and then 
that of V cubic inches of vapour also at t°, but under the pressure FE. 

Now \ cubic inches of dry air under the given conditions weigh 
0*31 V fH_FE') 

—(F+^/760 —’ anC * We reac ^y 8ee f rom problem III. art. 328 

that V cubic inches of vapour at t °, and the pressure FE, weigh 
5 0’31 V FE 

8 X (1 -f c/) 760' f^ese two weights, and reducing, we get 


p _ 031 V (H - | FE) 
(1 + at) 760 


If the air were saturated we should have E = 1, and the formula would 
thus be changed into that already found for the mixture of gases and 
saturated vapours (328). 

This formula contains, besides the weight P, many variable quantities 
V, E, H, and t, and, consequently, by taking successively each of these 
quantities as unknown, as many different problems might be proposed. 

344. Correction for the loss of weight experienced by bodies 
weighed in the air. —It has been seen in speaking of the balance, that 
the weight which it indicates is only an apparent weight, and is less 
than the real weight. The latter may be deduced from the former when 
it is remembered that every body weighed in the air loses a weight equal 
to that of the displaced air (168). This problem is however very com¬ 
plicated, for not only does the weight of the displaced air vary with the 
temperature, the pressure, and the hygrometric state, but the volume of 
the body to be weighed, and that of the weights, vary also with the tem¬ 
perature ; so that a double correction has to be made; one relative to the 
weights , the other to the body weighed. 

Collection relative to the weights .—In order to make this correction let 
P be their weight in air, and n their real weight in vacuo ; further, let V 
be the volume of these weights at 0°, D the density of the substance of 
which they are made, and K its coefficient of linear expansion. 

The volume V becomes V (1 -f 3Ki) at t°, hence this is the volume of 
air displaced by the weights. If ^ be the weight of a cubic inch of air at 
t, and the pressure H at the time of weighing, we have 
P = n — V (1 + 3K*) 

From the formula P = VD (105) V may be replaced by =? and the 





304 


ON HEAT. 


[ 345 - 


formula becomes 

T = n [l — ^- 3 —] . . . (1) 

which gives the value, in air, of a weight n, when jx is replaced by its 
value. But since fx is the weight of a cubic inch of air more or less moist, 
at the temperature t and the pressure H, its value may be calculated by 
means of the formula in the foregoing paragraph. 

Correction relative to the hodg weighed .—Let p be the apparent weight 
of the body to be weighed, tt its real weight in vacuo, d its density, k its 
coefficient of expansion, and t its temperature, by the same reasoning as 
above we have 

, = .[1 _££ + !*] . . . . (2> 


By using the method of double weighing, and of a counterpoise whose 
apparent weight is p\ the real weight tt', the density d', and the coefficient 
k ', and assuming that the pressure does not change, which is usally the 
case, we have again 

= d + 3 *0] . . . . (3) 

If a and b are the two arms of the beam, we have in the first weighing 
ap = bp ' and in the second «P = bp, whence p — P. Replacing P and 
p by their value deduced from the above quantities, we have 

t J-j _Kl+3to)j =n j-j _ K 1+3KQ J 

whence _ D 

7r “ 1 _ m(1->-3 kt) 

d 

which solves the problem. 


CHAPTER VII. 

CONDUCTIVITY OF SOLIDS, LIQUIDS, AND GASES. 

345. Transmission of heat.— When we stand at a little distance 
from a fire or other source of heat we experience the sensation of warmth. 
The heat is not transmitted by the intervening air ; it passes through it 
without raising its temperature, for if we place a screen before the fire the 
sensation ceases to be felt. The heat from the sun reaches us in the 
same manner. The heat, which, as in this case, is transmitted to a body 











- 346 ] CONDUCTIVITY OF SOLIDS. 305 

from the source of heat without affecting the temperature of the inter¬ 
vening medium, is said to he radiated. 

Heat is transmitted in another way. When the end of a metal bar is 
heated, a certain increase of temperature is presently observed along the 
bar. Where the h eat is transmitted in the mass of the body itself, as in 
this case, it is said to be conducted. We shall first consider the trans¬ 
mission of heat by conduction. 

346. Conductivity of solids.— Bodies conduct heat with different 
degrees of facility. Good conductors are those which readily transmit 
heat, such as are the metals; while bad 
conductors, to which class belong the resins, 
glass, wood, and more especially liquids and 
gases, offer a greater or less resistance to the 
transmission of heat. 

In order to compare roughly the con¬ 
ducting power or conductivity of different 
solids, Ingenhousz constructed the apparatus 
which bears his name, and which is repre¬ 
sented in fig. 245. It is a metallic trough, 
in which, by means of tubulures and corks, 
are fixed rods of the same dimensions, but of different materials; for 
instance, iron, copper, wood, glass. These rods extend to a slight 
distance in the trough, and the parts outside are coated with wax, which 
melts at 61°. The box being filled with boiling water, it is observed 
that the wax melts to a certain distance on the metallic rods, while 
on the others there is no trace of fusion. The conducting power is evi¬ 
dently greater in proportion as the wax has fused to a greater distance. 
The experiment is sometimes modified by attaching glass balls or marbles 
to the ends of the rods by means of wax. As the wax melts, the balls 
drop off, and this in the order of their respective conductivities. The 
quickness with which melting takes place is however only a measure of 
the conducting power in case the metals have the same or nearly the 
same specific heat. 

M. Despretz has compared the conducting powers of solids by means 
of the apparatus represented in fig. 246. It is a bar in which small 
cavities are made at intervals of 4 inches: these cavities contain mercury, 
and a delicate thermometer is placed in each of them. This bar is 
exposed at one end to a constant source of heat; the thermometers gra¬ 
dually rise until they indicate fixed temperatures, which are less accord¬ 
ing as the thermometers are further from the source of heat. By this 
method Despretz verified the following law: If the distances from the 
source of heat increase in arithmetical progression, the excess of temperature 
over that of the surrounding air decreases in geometrical progression. 



Tig. 245. 











306 


ON HEAT. 


[ 346 - 

This law, however, only prevails in the case of very good conductors, 
such as gold, platinum, silver, and copper; it is only approximately 
true for iron, zinc, lead, and tin, and does not apply at all to non- 
metallic bodies, such as marble, porcelain, etc. 

Taking the conducting power of gold at 1000, Despretz has con¬ 
structed the following table of conductivities : 


Platinum . . . 

.... 981 

Tin. 

... 304 

Silver .... 

.... 973 

Lead. 

... 179 

Copper .... 

.... 897 

Marble. 

... 23 

Iron. 

.... 374 

Porcelain . . . 


Zinc. 

. ... 363 

Brick earth. . . . 

... 11 



Wiedemann and Franz have made some valuable investigations on 
the conductivity of heat in metals. By making cavities in the bars, as 
in Despretz’s method, their form is altered, and the continuity partially 
destroyed. Wiedemann and Franz have avoided this source of error by 
measuring the temperature of the bars in different places by applying to 
them the junction of a thermo-electric couple. 

The metallic bars were made as regular as possible; one of the ends 
was heated to 100°, the rest of the bar being surrounded by air at a con¬ 
stant temperature. The thermo-electric couple was of small dimensions, 
in order not to extract too much heat. 

By this method Wiedemann and Franz obtained results which differ 
considerably from those of Despretz. Representing the conductivity of 
silver by 100, they found for the other metals the following numbers: 






























-348] 

CONDUCTIVITY 

OF LIQUIDS. 

307 

Silver . . . 

.100-0 

Steel . 

. . . 11*6 

Copper . . 


Lead. 

... 8-5 

Gold . . . 

.53-2 

Platinum .... 

... 8-4 

Tin . . . 

.14-5 

Rose’s alloy . . . 

... 2-8 

Iron . . . 

.11-9 

Bismuth .... 

... 1-8 


Organic substances conduct beat badly. De la Rive and de Candolle 
have shown that woods conduct better in the direction of their fibres 
than in a transverse direction $ and have remarked upon the influence 
which this feeble conducting power, in a transverse direction, exerts in 
preserving a tree from sudden changes of temperature, enabling it to 
resist alike a sudden abstraction of heat from within, and the sudden 
accession of heat from without. Tyndall has also : shown that this 
tendency is aided by the low conducting power of the bark, which is in 
all cases less than that of the wood. 

Cotton, wool, straw, bran, etc., are all bad conductors. 

347. Senarmont’s experiment. —It is only in homogeneous bodies 
that heat is conducted with equal ^facility in all directions. If an aper¬ 
ture be made in a circular piece of ordinary glass covered with a thin 
layer of wax, and a platinum wire ignited by a voltaic current be held 
through the aperture, the wax will be melted round the hole in a circular 
form. Senarmont has made, on this principle, a series of experiments on 
the conductivity of heat in crystals. A plate cut from a crystal of the 
regular system was covered with wax, and a heated metallic point was 
held against it. The part melted had a circular form ; but when plates 
of crystals belonging to other systems were investigated in a similar 
manner, it was found that the form of the line of equal temperature, that 
is, the limit of the melted part, varied with the different systems and 
with the position of the axes. In plates of uniaxial crystals cut 
parallel to the principal axis it was an ellipse, the major axis of which 
was in the direction of the principal axis. In plates cut perpendicular to 
the principal axis it is a circle. In biaxial crystals the line was always 
an ellipse. 

348. Conductivity of liquids.— The conductivity of liquids is very 
small, as is seen from the following experiment. A delicate thermoscope, 
B, consisting of two glass bulbs joined by a tube, m, in which there is a 
small index of coloured liquid, is placed in a large cylindrical glass 
vessel, I) (fig. 247). This vessel is filled with water at the ordinary 
temperature, and a tin vessel, A, containing oil at a temperature of two 
or three hundred degrees, is dipped in it. The bulb near the vessel 
A is only very slightly heated, and the index m moves through a very 
small distance. Other liquids give the same result. That liquids 
conduct very badly is also demonstrated by a simpler experiment. A 












308 


ON HEAT. 


[ 349 - 

long test tube is half tilled with water and some ice so placed in it 
that it cannot rise to the surface. By inclining the tube and heating the 
surface of the liquid by means of a spirit lamp, the liquid at the top 
may be made to boil, while the ice at the bottom remains unmelted. 

Despretz made a series of experiments with an apparatus analogous to 
that which has been described, but he maintained the liquid in the 
vessel A, at a constant temperature, and arranged a series of thermometers 
one below the other in the vessel D. In this manner he found that the 
conductivity of heat in liquids obeys the same laws as in solids, but is 
much more feeble. For example, the conductivity of water is that 
of copper. 

349. Manner in which liquids are heated.— When a column of 
liquid is heated at the bottom, ascending and descending currents are 
produced. It is by these that heat is mainly distributed through the 
liquid, and not by its conductivity. These currents arise from the ex- 



Fig. 247. 



Fig. 248. 


pansion of the inferior layers, which, becoming .less dense, rise in the 
liquid, and are replaced by colder and denser layers. They may be made 
visible by projecting bran or wooden shavings into water, which rise 
and descend with the currents. The experiment is arranged as shown in 
fig. 248. The mode in which heat is propagated in liquids and in gases 
is said to be by convection. 

350. Conductivity of gases.— It is a disputed question whether gases 
have a true conductivity; but certainly when they are restrained in their 
motion their conductivity is very small. All substances, for instance, 
between whose particles air remains stationary, offer great resistance to 



















CONDUCTIVITY OF GASES. 


309 


- 351 ] 

the propagation of heat. This is well seen in straw, eider down, and furs. 
The propagation of heat in a gaseous mass is effected hy means of the 
ascending and descending currents formed in it, as is the case with 
liquids. 

The following experiment originally devised hy Grove is considered 
to prove that gases have a certain conductivity. In a glass vessel 
provided with delivery tubes by which any gases can be introduced, or by 
which it can be exhausted, is a platinum wire which can be heated to 
redness by a voltaic battery. When the vessel is exhausted the plati¬ 
num wire is gradually raised to a bright redness; on then allowing 
air to enter the luminosity is greatly diminished, and if the vessel be ex¬ 
hausted and then hydrogen admitted, the luminosity quite disappears. 
This greater chilling of the wire in hydrogen than in air is considered 
by Magnus to be an effect of conduction; while Tyndall ascribes it to 
the greater mobility of the particles of hydrogen. 

351. Applications. —The greater or less conductivity of bodies 
meets with numerous applications. If a liquid is to be kept warm for 
a long time, it is placed in a vessel and packed round with non-conduct¬ 
ing substances, such as shavings, straw, bruised charcoal. For this 
purpose water pipes and pumps are wrapped in straw at the approach of 
frost. The same means are used to hinder a body from becoming heated. 
Ice is transported in summer by packing it in bran, or folding it in 
flannel. 

Double walls constructed of thick planks having between them any 
finely divided materials such as shavings, sawdust, dry leaves, etc., retain 
heat extremely well ; and are likewise advantageous in hot countries, for 
they prevent its access. During the night the windows are opened, while 
during the day they are kept close. Pure silica in the state of rock crystal 
is a better conductor than lead, but in a state of powder it conducts very 
badly. If a layer of asbestos is placed on the hand a red-hot iron ball 
can be held without inconvenience. Ped-hot cannon balls can be 
wheeled to the gun’s mouth in wooden barrows partially tilled with sand. 
Lava has been known to flow over a layer of ashes underneath which 
was a bed of ice, and the nonconducting power of the ashes has prevented 
the ice from fusion. 

The clothes which we wear are not warm in themselves; they only 
hinder the body from losing heat, in consequence of their spongy texture 
and the air they enclose. The warmth of bed covers and of counterpanes 
is explained in a similar manner. Double windows are frequently used in 
cold climates to keep a room warm—they do this by the non-conducting 
laver of air interposed between them. It is for the same reason that 
two shirts are warmer than one of the same material but of double the 
thickness. Hence too the warmth of furs, eider down, etc. 


310 


ON HEAT. 


[ 352 - 

That water boils more rapidly in a metallic vessel than in one of porce¬ 
lain of the same thickness; that a burning piece of wood can be held 
close to the burning part with the naked hand, while a piece of iron 
heated at one end can only be held at a great distance, are easily ex¬ 
plained by reference to their various conductivities. 

The sensation of heat or cold which we feel when in contact with 
certain bodies is materially influenced by their conductivity. If their 
temperature is lower than ours, they appear colder than they really are, 
because from their conductivity heat passes away from us. If, on the 
contrary, their temperature is higher than that of our body, they appear 
warmer from the heat which they give up at different parts of their 
mass. Hence it is clear why carpets, for example, are warmer than 
wooden floors, and why the latter are warmer than stone floors. 


CHAPTER VIII. 

RADIATION OF HEAT. 

352. Radiant heat. —It has been already stated (345) that heat could 
be transmitted from one body to another without altering the temperature 
of the intervening medium. If we stand in front of a fire we experience 
a sensation of warmth which is not due to the temperature of the air, 
for if a screen be interposed the sensation immediately disappears, which 
would not be the case if the surrounding air had a high temperature. 
Hence bodies can send out rays which excite heat, and which penetrate 
through the air without heating it, as rays of light through transparent 
bodies. Heat thus propagated is said to be radiated ; and we shall use 
the terms ray of heat, or thermal or calorific ray, in a similar sense to that 
in which we use the term ray of light or luminous ray. 

We shall find that the property of radiating heat is not confined to 
luminous bodies, such as a fire or a red-hot ball, but that bodies of all 
temperatures radiate heat. It will be convenient to make a distinction 
between luminous and obscure rays of heat. 

353. lavs of radiation. —The radiation of heat is governed by 
three laws. 

I. Radiation takes place in all directions round a body. If a ther¬ 
mometer be placed in different positions round a heated body, it indicates 
everywhere a rise in temperature. 

II. In a homogeneous medium, radiation takes place in a right line. 




RADIATION OF HEAT. 


311 


- 354 ] 

For, if a screen be placed in the right line which joins the source of heat 
and the thermometer, the latter is not affected. 

But in passing obliquely from one medium into another, as from air 
into a glass, calorific-like luminous rays become deviated, an effect known 
as refraction. The laws of this phenomenon are the same for heat as 
for light, and they will be more fully discussed under the latter sub¬ 
ject. 

III. Radiant heat is propagated in vacuo as well as in air. This is 
demonstrated by the following experiment. 

In the bottom of a glass flask a thermometer is fixed in such 
a manner that its bulb occupies the centre of the flask (fig. 

249). The neck of the flask is then carefully narrowed by 
means of the blowpipe, and then the apparatus having been 
suitably attached to an air pump, a vacuum is produced 
in the interior. This having been done, the tube is sealed at 
the narrow part. On immersing this apparatus in hot water, 
or on bringing near it some hot charcoal, the thermometer 
is at once seen to rise. This could only arise from radia¬ 
tion through the vacuum in the interior, for glass is so 
bad a conductor, that the heat could not travel with this 
rapidity through the sides of the flask, and the stem of 
the thermometer. 

354. Causes which modify the intensity of radiant heat.— By 

the intensity of radiant heat is understood the quantity of heat received 
on the unit of surface. Three causes are found to modify this intensity; 
the temperature of the source of heat, its distance, and the obliquity of 
the calorific rays in reference to the surface which emits them. The 
laws which regulate these modifications may be thus stated : 

I. The intensity of radiant heat is proportional to the temperature of the 
source. 

II. The intensity is inversely as the square of the distance. 

III. The intensity is less , the greater the obliquity of the rays with respect 
to the radiating surface. 

The first law is demonstrated by placing a metallic box containing 
water at 10°, 20°, or 30°, successively at equal distances from the bulb of 
a differential thermometer. The temperatures indicated by the latter 
are then found to be in the same ratio as those of the box: for instance, 
if the temperature of that corresponding to the box at 10° be 2°, those of 
the others will be 4° and 6° respectively. 

The second law is demonstrated experimentally by placing the differ¬ 
ential thermometer at a certain distance from the source of heat, 
and then removing it to double the distance. In the latter case, the 


/ 



Fig. 249. 







ON HEAT. 


312 


[ 354 - 


temperature is found to be one-fourth of what it was in the former 
case. 

The truth of the second law also follows 
from the geometrical principle that the sur¬ 
face of a sphere increases as the square of its 
radius. Suppose a hollow sphere, ab (fig. 
250), of any given radius, and a source of 
heat, C, in its centre ; each unit of surface in 
the interior receives a certain quantity of 
heat. Now, a sphere, ef \ of double the radius 
will present a surface four times as great; its 
internal surface contains, therefore, four times 
as many units of surface, and as the quantity 
of heat emitted is the same, each unit will receive one-fourth the quantity. 

The third law is demonstrated by means of the following experiment, 
devised by Leslie : a flat cylindrical tin canister, mn, is placed before a 
concave mirror (fig. 251). The box turns on a horizontal axis; there is 
a tubulure at the top, by which it may be filled with hot water, and its 




Fig. 251. 


anterior face is covered with lampblack. Between this box and the 
mirror there are two screens with equal apertures, H and K, so as to 
allow a pencil of parallel rays to fall on the surface of the mirror. 

A differential thermometer having been placed in the focus of the 
mirror the canister is adjusted in the vertical position represented by 
the dotted lines, and is kept in that position until the thermometer has 
become stationary. The canister is then inclined in the position mn r and 


























REFLECTION OF HEAT. 


313 


- 356 ] 

the thermometer is still found to indicate the same temperature, which 
demonstrates the law. For in the first case, the portion of the surface of 
the box which sends rays towards the mirror is represented by a circle 
whose diameter is ac, and which is consequently equal to the aperture 
of the screens; in the second case, the surface is an ellipse, the major 
axis of which is ab , and the minor axis the diameter of the screens, that 
is, ac. The second surface is larger than the first, and it therefore sends 
more rays to the mirror. But as the action on the thermometer is no 
greater than in the first case, it follows that in the second case, where 
the rays are oblique, the intensity is less than in the first case, where 
they are perpendicular. 

In order to express this in a formula, let i be the intensity of the rays 
emitted perpendicularly to the surface, and i' that of the oblique rays. 
These intensities are necessarily inversely as the surfaces ab and ac, for 
the effect is the same in both cases, and therefore i f x surface ab = i x 

surface ac; hence i' = i 8ur ~ = i ~ = i cos bac : which signifies that 
surf, ab ab 

the intensity of oblique rays is proportional to the cosine of the angle which 
these rays form with the normal to the surface; for this angle is equal to 
the angle bac. This law is known as the law of the cosine ; it is, how¬ 
ever, not general; MM. Desains and De la Provostaye have shown that 
it is only true within very narrow limits, that is, only with bodies which, 
like lampblack, are entirely destitute of reflecting power (362). 

355. Mlobile equilibrium. Theory of exchanges.— Prevost of 
Geneva suggested the following hypothesis in reference to radiant heat, 
known as Prevost’s theory of exchanges, which is now universally admitted. 
All bodies, whatever their temperature, constantly radiate heat in all 
directions. If we imagine two bodies at different temperatures placed 
near one another, the one at a higher temperature will experience a loss 
of heat, its temperature will sink because the rays it emits are of greater 
intensity than those it receives; the colder body, on the contrary, will 
rise in temperature because it receives rays of greater intensity than 
those which it emits. Ultimately the temperature of both bodies be¬ 
comes the same, but heat is still exchanged between them, only each 
receives as much as it emits, and the temperature remains constant. 
This state is called the mobile equilibrium of temperature. 

356. KTewton’s law of cooling'. —A body placed in a vacuum is only 
cooled or heated by radiation. In the atmosphere it becomes cooled 
or heated by its contact with the air according as the latter is colder or 
hotter than the radiating body. In both cases the velocity of cooling or 
of heating—that is, the quantity of heat lost or gained in a second — is 
greater according as the difference of temperature is greater. 

Newton has enunciated the following law in reference to the cooling 

p 



314 


ON HEAT. 


[357- 

or heating of a body: The quantity of heat lost or gained by a body in a 
second is proportional to the difference between its temperature and that of 
the surrounding medium. Dulong and Petit have proved that this law is 
not so general as Newton supposed, and only applies where the differences 
of temperature do not exceed 15° to 20°. Beyond that, the quantity of 
heat lost or gained is greater than that required by this law. 

Two consequences follow from Newton’s law: 

i. When a body is exposed to a constant source of heat, its tempera¬ 
ture does not increase indefinitely, for the quantity which it receives in 
the same time is always the same; while that which it loses, increases 
with the excess of the temperature over that of the surrounding medium. 
Consequently a point is reached, at which the quantity of heat emitted 
is equal to that absorbed, and the temperature then remains stationary. 

ii. Newton’s law, as applied to the differential thermometer, shows 
that its indications are proportional to the quantities of heat which it 
receives. If one of the bulbs of a differential thermometer receives rays 
of heat from a constant source, the instrument exhibits first increasing 
temperatures, but afterwards becomes stationary. In this case, tl 
quantity of heat which it receives is equal to that which it emits. But 
the latter is proportional to. the excess of the temperature of the bulb 
above that of the surrounding atmosphere, that is, to the number o r 
degrees indicated by the thermometer; consequently, the temperature 
indicated by the differential thermometer is proportional to the quantity 
of heat it receives. 


REFLECTION OF HEAT. 

357. Laws of reflection.— When thermal rays fall upon a body they 
are, speaking generally, divided into two 
parts, one of which penetrates the body, 
while the other rebounds as if repelled 
from the surface like an elastic ball. This 
is said to be reflected. 

If mn be a plane reflecting surface (fig. 
252), CB an incident ray , BD a line perpen¬ 
dicular to the surface called the normal, and 
BA the reflected ray, the angle CBD is 



B 

Pig. 252. 


called the angle of incidence, and DBA the angle of reflection. The 
reflection of heat, like that of light, is governed by the two following 
laws: 

I. The angle of reflection is equal to the angle of incidence. 

II. Both the incident and the reflected ray are in the same plane with the 
normal to the reflecting surface. 




-• 358 ] REFLECTION OF HEAT. 315 

These laws may be proved, as we shall see, by means of concave mirrors 
'358). 

358. Reflection from concave mirrors. — Concave mirrors , or re¬ 
flectors. , are polished spherical or parabolic surfaces of metal or of glass, 
which are used to concentrate luminous or calorific rays in the same 
point. 

We shall only consider the case of spherical mirrors. Fig. 254 repre¬ 
sents two of these mirrors; fig. 253 gives a medial section, which is called 
the principal section. The centre C of the sphere to which the mirror 
belongs is called the centre of curvature ; the point A, the middle of the 
reflector, is the centre of the figure ; the straight line AB passing through 
these points, is the principal axis of the mirror. 

In order to apply to spherical mirrors the laws of reflection from plane 
surfaces, they are considered to be composed of an infinite number of in¬ 
finitely small plane surfaces, each belonging to the corresponding tangent 
plane, the normals to these small surfaces are all radii of the same sphere, 
and therefore meet at its centre, the centre of curvature of the mirror. 



Suppose now, on the axis AB of the mirror MN, a source of heat so 

distant that the rays EK, PH.which emanate from it may be 

considered as a parallel. From the hypothesis that the mirror is composed 
of an infinitude of small planes, the ray EK is reflected from the plane 
K just as from a plane mirror; that is to say, CK being the normal to 
this plane, the reflected ray takes a direction such that the angle CKF 
is equal to the angle CKE. The other rays PH, GI.are re¬ 

flected in the same manner, and all converge approximately towards the 
same point F, on the line AC. There is then a concentration of the rays 
in this point, and consequently a higher temperature than at any other 
point. This point is called the focus, and the distance from the focus to 
the mirror at A is the focal distance. 

In the above figure the heat is propagated along the lines EKF, LDF. 
in the direction of the arrows; but, reciprocally, if the heated body be 

p 2 


















ON HEAT. 


316 


[359- 


placed at F, the heat is propagated along the lines FKE, FDL, so that 
the rays emitted from the locus are nearly parallel after reflection. 

359. Demonstration of the laws of reflection. —The following ex¬ 
periment, which was made for the first time by Pictet and Saussure, and 
which is known as the experiment of the conjugate mirrors , demonstrates 
not only the existence of the foci, but also the laws of reflection. Two 
reflectors, M and N (fig. 254), are arranged at a distance of 4 to 5 yards, 
and so that their axes coincide. In the focus of one of them, A, is placed 
a small wire basket containing a red-hot iron ball. In the focus of the 
other is placed B, an inflammable body, such as gun-cotton or phosphorus. 
The rays emitted from the focus A are first reflected from the mirror M, 
in a direction parallel to the axis (358), and impinging on the other 



Fig. 254. 


mirror, N, are reflected so that they coincide in the focus B. That this 
is so, is proved by the fact that the gun-cotton in this point takes fire, 
which is not the case if it is above or below it. 

The experiment also serves to show that light and heat are reflected 
in the same manner. For this purpose a lighted candle is placed in the 
focus of A, and a ground glass screen in the focus of B, when a lumi¬ 
nous focus is seen on it exactly in the spot where the gun-cotton ignites. 
Hence, the luminous and the calorific foci are produced at the same 
point, and the reflection takes place in both cases according to the same 












REFLECTION OF HEAT. 


317 


- 362 ] 

laws, for it will be afterwards shown that for light the angle of reflection 
is equal to the angle of incidence, and that both the incident and the 
' reflected ray are in the same plane perpendicular to the plane reflecting 
li surface. 

In consequence of the high temperature produced in the foci of con¬ 
cave mirrors they have been called burning mirrors. It is stated that 
Archimedes burnt the Roman vessels before Syracuse by means of such 
mirrors. BufFon constructed burning mirrors of such power as to prove 
that the feat attributed to Archimedes was possible. The mirrors were 
made of a number of silvered plane mirrors about 8 inches long by 5 broad. 
They could be turned independently of each other in such a manner that 
the rays reflected from each coincided in the same point. With 128 
mirrors and a hot summer’s sun BufFon ignited a plank of tarred wood at 
a distance of 70 yards. 

360. Reflection in a vacuum. —Heat is reflected in a vacuum as well 
as in air, as is seen from the following experiment, due to Sir Humphrey 
Davy. Two small concave reflectors were placed opposite each other 
under the receiver of an air pump. In the focus of one was placed a 
delicate thermometer, and in the focus of the other a platinum wire made 
incandescent by means of a galvanic current. The thermometer was im¬ 
mediately seen to rise several degrees, which could only be due to reflected 
heat, for the thermometer did not show any increase of temperature if it 
were not exactly in the focus of the second reflector. 

361. Apparent reflection of cold. —If two mirrors are arranged as 
represented in fig. 254, and a piece of ice is placed in one of the foci 
instead of the red-hot ball, the surrounding temperature being greater 
than zero, a differential thermometer placed in the focus of the second 
reflector would exhibit a decrease in temperature of several degrees. 
This appears at first to be caused by the emission of frigorijic rays from 
ice. It is, however, easily explained from what has been said about the 
mobile equilibrium of temperature (355). There is still an exchange of 
temperature, but here the thermometer is the warmest body. As the 
rays which the thermometer emits are more intense than those emitted 
by the ice, the former gives out more heat than it receives, and hence its 
temperature sinks. 

The sensation of cold experienced when we stand near a plaster or a 
stone wall whose temperature is lower than that of our body, or when we 
stand in front of a wall of ice, is explained in the same way. 

362. Reflecting: power. —The reflecting power of a substance is its 
property of throwing off a greater or less proportion of incident heat. 

This power varies in different substances. In order to study this 
power in different bodies without having recourse to as many reflectors, 
Leslie arranged his experiments as shown in fig. 255. The source of 


318 


ON HEAT. 


[362- 

heat is a cubical canister, M, now known as a Leslie's cube , filled with 
hot water. A plate, «, of the substance to be experimented upon is 
placed on the axis of a reflecting mirror between the focus and the 
mirror. In this manner the rays emitted by the source are first reflected 
from the mirror and impinge on the plate a, where they are again re¬ 
flected and converge to a focus between the plate and the mirror, in which 
point a differential thermometer is placed. The reflector and the ther¬ 
mometer are always in the same position, and the water of the cube is 
always kept at 100°, but it is found that the temperature indicated by 
the thermometer varies with the nature of the plate. This method gives 


Tig. 255. 



a means of determining, not the absolute reflecting power of a body, but 
its power relatively to that of some body taken as a standard of com¬ 
parison. For, from what has been said on the application of Newton’s 
law to the differential thermometer, the temperatures which this instru¬ 
ment indicates are proportional to the quantities of heat which it re¬ 
ceives. Hence, if in the above experiment, a plate of glass causes the 
temperature to rise 1°, and a plate of lead 6°, it follows that the 
quantity of heat reflected by the latter is six times as great as that re¬ 
flected by the former. For the heat emitted by the source remains the 
same, the concave reflector receives the same portion, and the difference 
can only arise from the reflecting power of the plates a. 



















REFLECTION OF HEAT. 


319 


- 363 ] 


By this method Leslie determined the reflecting powers of the fol¬ 
lowing substances, relatively to that of brass, taken as 100 : 


Polished brass.100 


Silver.90 

Polished tin.80 

Steel.70 

Lead.60 


Indian ink.13 

Amalgamated tin .... 10 

Glass.10 

Oiled glass.5 

Lampblack.0 


as compared 


The numbers only represent the relative reflecting power 
with that of brass. Their absolute power is the relation of the quantity of 
heat reflected to the quantity of heat received. Melloni first determined the 
absolute reflecting power of a certain number of bodies. Desains and De 
la Provostaye, who also examined it for certain metals, obtained the fol¬ 
lowing results by means of Melloni’s thermo-multiplier (373), the heat 
being reflected at an angle of 50° : 

Silver plate.0-97 Steel.0-82 

Gold.0-95 Zinc.0-81 

Brass.0-93 Iron.0-77 

Platinum.0'83 Cast iron.0*74 


We shall presently see (366) what are the causes which modify the 
reflecting power. 

363. Absorbing power.— The absorbing power of a body is its pro¬ 
perty of allowing a greater or less quantity of incident heat to pass into 
its mass. Its absolute value is the ratio of the quantity of heat absorbed 
to the quantity of heat received. 

The absorbing power of a body is always inversely as its reflecting 
power; a body which is a good absorbent is a bad reflector, and vice versa. 
It was formerly supposed that the two powers were exactly complemen¬ 
tary, that the sum of the reflected aud absorbed heat was equal to the 
total quantity of incident heat. This is not the case ; it is always less; 
the incident heat is divided into three parts—1st, one which is absorbed; 
2nd, another which is reflected regularly—that is, according to laws 
previously demonstrated (358); 3rd, and a third, which is irregularly 
reflected in all directions, and which is called scattered or diffused heat. 

In order to determine the absorbing power of bodies, Leslie used the 
apparatus which he employed in determining the reflecting powers (362). 
But he suppressed the plate a , and placed the bulb of the thermometer 
in the focus of the reflector. This bulb being then covered successively 
with lampblack, or varnish, or with gold, silver, or copper foil, etc., the 
thermometer exhibited a higher temperature under the influence of the 
source of heat, M, according as the substance with which the bulb was 
covered absorbed more heat. Leslie found in this way that the absorb¬ 
ing power of a body is greater the less its reflecting power. In these 
















320 


ON HEAT. 


[ 364 - 

experiments, however, the relation of the absorbing powers cannot be 
deduced from that of the temperatures indicated by the thermometer, 
for Newton’s law is not exactly applicable in this case, as it only pre¬ 
vails for bodies whose substance does not vary, and here the covering of 
the bulb varied with each observation. But we shall presently show 
(365) how the comparative absorbing powers may be deduced from the 
ratios of the emissive powers. 

Taking as a source of heat a canister filled with water at 100°, 
Melloni found by means of the thermo-multiplier the following relative 


absorbing powers : 

Lampblack.100 Indian ink.85 

White lead.100 Shellac.72 

Isinglass.91 Metals.13 


364. Radiating- power.— The radiating or emissive powet' of a body is 
its capability of emitting at the same temperature and with the same 
extent of surface greater or less quantities of heat. 

The apparatus represented in fig. 255 was also used by Leslie in deter¬ 
mining the radiating power of bodies. For this purpose the bulb of the 
thermometer was placed in the focus of the reflector, and the faces of 
the canister M were formed of different metals, or covered with different 
substances, such as lampblack, paper, etc. The cube being filled with 
hot water at 100°, and all other conditions remaining the same, Leslie 
turned each face of the cube successively towards the reflectors, and 
noted the temperature each time. That face which was coated with 
lampblack caused the greatest elevation of temperature, and the metal 
faces the least. Applying Newton’s law, and representing the heat 
emitted by lampblack as 100, Leslie formed the following table of 


radiating powers • 

Lampblack.100 Isinglass.80 

White lead.100 Tarnished lead.45 

Paper.08 Mercury.20 

Sealing wax.95 Polished lead.19 

Ordinary white glass ... 90 Polished iron.15 

Indian ink.88 Tin, gold, silver, copper, etc.. 12 


It will be seen that, in this table, the order of the bodies is exactly 
the reverse of that in the table of reflecting powers. 

The radiating powers of several substances were determined by 
Melloni by means of the thermo-multiplier, and more exactly by 
Desains and De la Provostaye, who used the same instrument, but 
avoided certain sources of error incidental to previous methods. They 
found in this manner the following numbers compared with lampblack 
as 100: 


















ABSORPTION OF HEAT. 


321 


- 365 ] 


Platinum foil.10 80 

Burnished platinum . . . 9-50 

Silver deposited chemically 5-36 

Copper foil.4-90 

Gold leaf.4*28 


Pure silver laminated . . . 3*00 

„ burnished . . . 2-50 

,, deposited chemi¬ 

cally and bur¬ 
nished . . . 225 


It appears, therefore, that the radiating power found by Leslie for the 
metals is too large. 

365. Identity of the absorbing and radiating- powers.— The 

absorbing power of a body cannot be accurately deduced from its 
reflecting power, because the two are not exactly complementary. 
But the absorbing power would be determined if it could be shown 
that in the same body it is equal to the radiating power. This con¬ 
clusion has been drawn by Dulong and Petit from the following experi¬ 
ments. In a large glass globe, blackened on the inside, was placed a 
thermometer at a certain temperature, 15° for example : the globe was 
kept at zero by surrounding it with ice, and having been exhausted by 
means of a tubulure connected with the air pump, the time was noted 
which elapsed while the thermometer fell through 5°. The experiment 
was then made in the contrary direction; that is, the sides of the globe 
were heated to 15°, while the thermometer was cooled to zero; the 
time was then observed which the thermometer occupied in rising 
through 5°. It was found that this time 
was exactly the same as that which the 
thermometer had taken in sinking through 
5°, and it was thence concluded that the 
radiating power is equal to the absorbing 
power for the same body, and for the same 
difference between its temperature and the 
temperature of the surrounding medium, 
because the quantities of heat emitted or 
absorbed in the same time are equal. 

This point may also be demonstrated by 
means of the following apparatus devised 
by Bitchie. Fig. 256 represents what is 
virtually a differential thermometer, the 
two glass bulbs of which are replaced by 
two cylindrical reservoirs B and C, of 
metal, and full of air. Between them is 
a third and larger one A, which can be 
filled with hot water by means of a tubu¬ 
lure. 



Fig. 256. 

The faces of B and of A, which face the right, are coated with 
lampblack; those of C and A, which face the left, are either painted 


p 3 

















322 


ON HEAT. 


[366- 

white’or are coated with silver foil. Thus of the two faces opposite each 
other, one is black and the other white ; hence when the cylinder A is 
filled with hot water, its white face radiates towards the black face of 
B, and its black face towards the white face of C. Under these 
circumstances the liquid in the stem does not move, indicating that 
the two reservoirs are at the same temperature. On the one hand, the 
greater emissive power of the black face of A is compensated by the 
smaller absorptive power of the white face of C ; while, on the other 
hand, the feebler radiating power of the white face cf A is compensated 
by the greater absorbing power of the black face of B. 

The experiment may be varied by replacing the two white faces by 
discs of paper, glass, porcelain, etc. 

366. Causes which modify the reflecting 1 , absorbing*, and 
radiating powers.— As the radiating and absorbing powers are equal, 
any cause which affects the one affects the other also. And as the 
reflecting power varies in an inverse manner, whatever increases it 
diminishes the radiating and absorbing powers, and vice versa. 

It has been already stated that these different powers vary with 
different bodies, and that metals have the greatest reflecting power, and 
lampblack the feeblest. In the same body these powers are modified by 
the degree of polish, the density, the thickness of the radiating substance, 
the obliquity of the incident or emitted rays, and, lastly, by the nature 
of the source of heat. 

It has been assumed usually that the reflecting power increases with 
the polish of the surface, and that the other powers diminish therewith. 
But Melloni showed that by scratching a polished metallic surface its 
reflecting power was sometimes diminished and sometimes increased. 
This phenomenon he attributed to the greater or less density of the re¬ 
flecting surface. If the plate had been originally hammered, its homo¬ 
geneity would be destroyed by this process, the molecules would be 
closer together on the surface than in the interior, and the reflecting 
power would be increased. But if the surface is scratched the internal 
and less dense mass becomes exposed, and the reflecting power dimi¬ 
nished. On the contrary, in a plate which has not been hammered and 
which is homogeneous, the reflecting power is increased when the plate is 
scratched, because the density at the surface is increased by the scratches. 

The experiments of Leslie, Rumford, and Melloni further prove, that 
the thickness of the radiating substance also modifies its emissive 
power. The latter philosopher found that when the faces of a cube 
filled with water at a constant temperature were varnished, the emis¬ 
sive power increased with the number of layers up to 16 layers, and 
that above that point it remained constant, whatever the number. He 
calculated that the thickness of the 16 layers was 0*04 of a millimeter. 


RADIANT HEAT. 


323 


- 368 ] 

With reference to metals, gold leaves of 0-008, 0 004, and 0-002 of a 
millimeter in thickness, having been successively applied on the sides of 
a cube of glass, the diminution of radiant heat was the same in each case. 
It appears therefore that between certain limits, the thickness of the 
radiating layer of metal is without influence. 

The absorbing power varies with the inclination of the incident 
rays. It is greatest at the normal incidence, that is, at right angles; 
and it diminishes in proportion as the incident rays deviate from the 
normal. This is one of the reasons why the sun is hotter in summer 
than in winter, because, in the former case, the solar rays are less oblique. 

The radiating power of gaseous bodies in a state of combustion is 
very weak, as is seen by bringing the bulb of a thermometer near a 
hydrogen flame, the temperature of which is very high. But if a 
platinum spiral be placed in this flame, it assumes the temperature of 
the flame, and radiates a considerable quantity of heat, as is indicated 
by the thermometer. It is for an analogous reason, that the flames of 
oil and of gas lamps radiate more than a hydrogen flame, in consequence 
of the excess of carbon which they contain, and which, not being entirely 
burned, becomes incandescent in the flame. 

367. RXelloni’s researches on radiant heat. —For our knowledge 
of the phenomena of the reflection, emission, and absorption of heat 
which have up to now been described, science is indebted mainly to 
Leslie. But since his time the discovery of other and far more delicate 
modes of detecting and measuring heat has not only extended and 
corrected our previous knowledge, but has led to the discovery of other 
phenomena of radiant heat, which without such improved means must 
have remained unknown. 

This advance in science is due to an Italian philosopher, Melloni, who 
first applied an instrument called the thermo-electric pile, invented by 
Nobili, to the measurement of very small differences of temperature. 
Fully to understand the action of the apparatus a knowledge of thermo¬ 
electricity is necessary; but for the present purpose it is sufficient to 
know that a very slight difference in temperature between the two ends 
of the thermo-electric pile is sufficient to produce an electric current, and 
thus to cause a deflection of the magnetic needle of a delicate galvano¬ 
meter, and that, within certain limits, this deflection is proportional to 
the temperature. The sensibility of the instrument is such, that the 
warmth of the hand at a distance of a yard is sufficient to develope in the 
instrument a current capable of deflecting the needle of the galvanometer. 
On account of the delicacy and accuracy of its indications the thermo¬ 
pile is now invariably employed for researches in radiant heat. 

368. Dynamical theory of heat.— Before describing the results ar¬ 
rived at by Melloni and others, it will be convenient to state here the view 


324 


ON HEAT. 


[368- 

now generally taken of the nature of heat and of the mode in which it is 
propagated. For additional information the chapter on the Mechanical 
Theory of Heat and the book on Light should he read. According to 
what is called the mechanical or dynamical theory of heat , a hot body is 
nothing more than one whose particles are in a state of vibration. The 
higher the temperature of the body the more rapid are these vibrations, and 
a diminution in temperature is but a diminished rapidity of vibration of 
the particles. The propagation of heat through a bar is due to a gradual 
communication of this vibratory motion from the heated part to the rest 
of the bar. A good conductor is one which readily takes up and trans¬ 
mits the vibratory motion from particle to particle, while a bad conductor 
is one which takes up and transmits the motion with difficulty. But 
even through a bad conductor the propagation of this motion is compara¬ 
tively slow; how then are we to explain the instantaneous perception of 
heat experienced when a screen is removed from a fire or when a cloud 
is drifted from the face of the sun ? In this case, the heat passes from one 
body to another without affecting the temperature of the medium which 
transmits it. In order to explain these phenomena it is imagined that all 
space, the interplanetary spaces as well as the interstices in the hardest 
crystal or the heaviest metal, in short, matter of any kind, is permeated 
by a medium having the properties of a fluid of infinite tenuity called the 
ether. The particles of a heated body being in a state of intensely rapid- 
vibration, communicate their motion to the ether around them, throwing 
it into a system of waves which travel through space and pass from one 
body to another with the velocity of light. When the undulations of 
the ether reach a given body, the motion is again delivered up to the 
particles of that body, which in turn begin to vibrate, that is, the body 
becomes heated. This passage of motion through the hypothetical ether 
is termed radiation, and a so-called ray of heat is merely the direction 
of the motion of one series of waves. 

It will facilitate the understanding of this to consider the analogous 
mode in which sound is produced and propagated. A sounding body is 
one whose entire mass is in a state of vibration; the more rapid 
the rate of vibration, the more acute the sound; the slower the rate 
of vibration, the deeper the sound. This vibratory motion is communi¬ 
cated to the surrounding air, by means of which the vibrations reach 
the auditory nerve and there produce the sensation of sound. If a metal 
ball be heated, say to the temperature of boiling water, we can ascertain 
that it radiates heat, although we cannot see any luminosity, and if its 
temperature be gradually raised we see it become successively of a dull 
red, bright red, and dazzling white. Here it is assumed that at each 
particular temperature the heated body emits waves of a definite length, 
in other words, its particles vibrate in a certain period. As its tempera- 


DYNAMICAL THEORY OF HEAT. 


325 


- 369 ] 

ture rises it sends out other and more rapid undulations, which coexist 
however with all those which it had previously emitted. Thus the motion 
at each successive temperature is compounded of all preceding ones. 

It has been seen that vibrations of the air below and above a certain 
rate do not affect the auditory nerve; it can only take up and transmit to 
the brain vibrations of a certain periodicity. So too with the vibrations 
which produce heat. The optic nerve is insensible to a large number of 
wave lengths. It can apprehend only those waves that form the visible 
spectrum. If the rate of undulation be slower than the red or faster 
than the violet, though intense motion may pass through the humours 
of the eye and fall upon the retina, yet we shall be utterly unconscious 
of the fact, for the optic nerve cannot take up and respond to the rate of 
vibrations which exist beyond the visible spectrum in both directions. 
Hence these are termed invisible or obscure rays. A vast quantity of 
these obscure rays are emitted by flames which, though intensely hot, 



are yet almost non-luminous, such as the oxy-hydrogen flame or that of 
a Bunsen’s burner ; for the vibrations which these emit, though capable 
in part of penetrating the media of the eye, are incapable of exciting in 
the optic nerve the sensation of light. 

369. Thermal analysis of solar light.— When a solar ray (fig. 257) 
admitted through an aperture in a dark room, is concentrated on a prism 
of rock salt by means of a lens of the same material, and then after 
emerging from the prism is received on a screen, it will be found to 
present a band of colours in the following order: red, orange, yellow, 
green, blue, and violet. This is called the spectrum. 

If now a narrow and delicate thermo-pile be placed successively on the 
space occupied by each of the colours, it will scarcely be affected on the 
violet, but in passing over the other colours it will indicate a gradual 
rise of temperature, which is greatest at the red. Painters thus, guided 





326 


ON HEAT. 


[370- 

by a correct but unconscious feeling, always speak of blue and green 
colours as cold, and of red and orange as warm tones. If tbe pile be now 
moved in tbe same direction beyond tbe limits of the luminous spectrum, 
tbe temperature will gradually rise up to OP, at which it attains its 
maximum. From this point tbe pile indicates a decrease of temperature 
until it reaches a point 0, where it ceases to be affected. This point is 
about as distant from R, as the latter is from V; that is, there is a region 
in which thermal effects are produced extending as far beyond the red 
end of the spectrum in one direction as the entire length of the visible 
spectrum is in the other. In accordance with what we have stated the 
sun’s light consists of rays of different rates of vibration; by their pas¬ 
sage through the prism they are unequally broken or refracted; those of 
greatest wave length or slowest vibrating period are least bent aside, or 
are said to be the least refrangible, while those with shorter wave lengths 
are the most refrangible. 

These non-luminous rays outside the red are called the extra or ultra- 
red rays, or sometimes the Herschelian rays, from Sir W. Herschel, who 
first discovered their existence. 

If in the above case prisms of other materials than rock salt be used, 
the position of maximum heat will be found to vary with the nature of 
the prism, a fact first noticed by Seebeck. Thus with a prism of 
water it is in the yellow; with one of crown glass, in the middle of the 
red, and so on. These changes are due, as Mellon! subsequently found, to 
the circumstances that prisms of different materials absorb rays of different 
refrangibility to unequal extents. But rock salt practically allows heats 
of all kinds to pass with equal facility, and thus gives a normal spectrum. 

370. Tyndall’s researches.— Prof. Tyndall has recently investigated 
the spectrum produced by the electric light, and has arrived at some 
highly important results. His mode of experimenting was as follows :— 
The electric light was produced between charcoal points by a Grove’s 
battery of fifty cells. The beam, rendered parallel by a double rock salt 
lens, was caused to pass through a narrow slit, and then through a second 
lens of rock salt; the slices of white light thus obtained being decomposed 
by a prism of the same material. To investigate the thermal conditions 
of the spectrum, a linear thermo-electric pile was used ; that is, one con¬ 
sisting of a number of elements arranged in a line, and in front of which 
was a slit that could be narrowed to any extent. The instrument was 
mounted on a moveable bar connected with a fine screw, so that by 
turning a handle the pile could be pushed forward through the smallest 
space. On placing this apparatus, originally devised by Melloni for his 
researches on the solar spectrum, successively in each part of the spectrum 
of the electric light, the heating effected at various points near each 
other was determined by the indications of a very delicate galvanometer. 


RADIANT HEAT. 


327 


- 370 ] 

As in the case of the solar spectrum, the heating effect gradually in¬ 
creased from the violet end towards the red, and was greatest in the dark 
space beyond the red. The position of the greatest heat was about as 
far from the limit of the visible red as the latter was from the green, and 
the total extent of their visible spectrum was found to be twice that of 
the visible. 



Fig. 258. 


The increase of temperature in the dark space is very considerable. 
If thermal intensities are represented by perpendicular lines of propor¬ 
tionate length erected at those parts of the spectrum to which they 



Fig. 259. 


correspond, on passing beyond the red end these lines increase rapidly 
and greatly in length, reach a maximum, and then fall somewhat more 
suddenly. If these lines are connected they form a curve (fig. 258), 
which beyond the red represents a massive peak, which quite dwarfs by 
its magnitude that of the visible spectrum. In fig. 259 the dark parts at 























328 


ON HEAT. 


[ 371 - 

the end represent the obscure radiation. The curve is based in the manner 
above stated, on the results obtained by Prof. Tyndall with the electric 
light. The upper curve, in fig. 259, represents the spectrum of solar 
light from the experiments of Muller with a rock salt prism, while the 
lower curve represents the results obtained with the use of a flint glass 
prism, which is thus seen to absorb some of the ultra red radiation. 

Prof. Tyndall found that by interposing various substances, more espe¬ 
cially water, in certain thicknesses, in the path of the electric light, the 
ultra-red radiation was greatly diminished, the peak was not so lofty. 
Now aqueous vapour would, like water, absorb the obscure rays. And 
most probably the reason why the obscure part of the spectrum of the 
solar light is not so intense as in the case of the electric light, is that the 
obscure rays have been partially absorbed by the aqueous vapour of the 
atmosphere. If a solar spectrum could be produced outside the atmo¬ 
sphere, it doubtless would give a spectrum more like that of the electric 
light, which is uninfluenced by the atmospheric absorption. 

This has been remarkably confirmed in other ways. Melloni observed 
that the position of the maximum in the solar spectrum differs on differ¬ 
ent days; which is probably due to the varying absorption of the atmo¬ 
sphere, in consequence of its varying hygrometric state. Recently, 
Secchi, in Rome, has found the same shifting of the maximum to occur 
in the different seasons of the year; for in winter, when there is least 
moisture in the atmosphere, the maximum is farther from the red than 
in summer, when the aqueous vapour in the air is most abundant. An 
important observation on the luminous rays has also been made by Cooke, 
in America, who found that the faint black lines in the solar spectrum 
attributed to the absorption of light by our atmosphere (see book on 
Optics) are chiefly caused by the presence of aqueous vapour. 

371. Luminous and obscure radiation.— It has been stated that 
the radiation from a luminous object, a gas flame for example, is of 
a composite character; a portion consists of what we term light, but 
a far greater part consists of heat rays, which are insensible to our 
eyes, being unable to affect the optic nerve. When this mixed radiation 
falls upon the blackened face of a thermo-electric pile, the whole of it 
is taken to be absorbed, the light by this act being converted into heat, 
and affecting the instrument proportionally with the purely calorific rays. 
The total radiation of a luminous source, expressed in units of heat or 
force, can thus be measured. By introducing into the path of the rays 
a body capable of stopping either the luminous or the obscure radiation, 
we can ascertain by the comparative action on the pile the relative 
quantities of heat and light radiated from the source. Melloni sought 
to do this by passing a luminous beam through a layer of water con¬ 
taining alum in solution) a liquid which he found in previous experi- 


RADIANT HEAT. 


329 


-372] 

merits absorbed all the radiation from bodies heated under incandescence. 
Comparing the transmission through this liquid—which allowed the 
luminous part of the beam to pass, but quenched the obscure portion— 
with the transmission through a plate of rock salt—which affected 
neither the luminous nor the obscure radiation, but gave the loss due to 
reflection—Melloni revealed the astonishing fact that 90 per cent, of the 
radiation from an oil flame and 99 per cent, of the radiation from an 
alcohol flame consist of invisible calorific rays. This proportion has been 
still further increased by the recent experiments of Prof. Tyndall, who 
employed a liquid free from the objections which have caused a slight 
error in Melloni’s method. Prof. Tyndall discovered that iodine, whilst 
opaque to light, is transparent to the obscure heat rays. Dissolving this 
substance in bisulphide of carbon a solution was obtained which was 
impervious to the most intense light, but wonderfully pervious to radiant 
heat; only a slight absorption being effected by the bisulphide. By 
successively comparing the transmission through the transparent liquid, 
and the transmission through the same liquid rendered opaque by iodine, 
the value of the luminous radiation from various sources was found to be 
as follows:— 


Source. 

Luminous. 

Obscure. 

Bed-hot spiral . 

0 

100 

Hydrogen flame . 

0 

100 

Oil flame . 

3 

97 

Gas flame . 

4 

96 

White-hot spiral. 

4-6 

95-4 

Electric light 

. 10 

90 


Here by direct experiment the ratio of luminous to obscure rays in 
the electric light is found to be 10 per cent of the total radiation. By 
prismatic analysis, the curve shown in fig. 258 was obtained, graphically 
representing the proportion of luminous to obscure rays in the electric 
light; by calculating the areas of the two spaces in the diagram 
the obscure portion is found to be nearly 10 times as large as the 
luminous. 

372. Transmutation of obscure rays. —We shall find in speaking 
of the luminous spectrum that beyond the violet there are rays which 
are invisible to the eye, but which are distinguished by their chemical 
action, and are spoken of as the actinic or chemical rays ; they are also 
known as the Bitteric rays, from the philosopher who first discovered 
their existence. 

As we shall also see in the book on Optics, Prof. Stokes has succeeded 
in converting these rays into rays of lower refrangibility, which then 
became visible; so Prof. Tyndall has recently effected the corresponding 







ON HEAT. 


330 


[373- 


but inverse change, and has increased the refrangibilitv of the Hers- 
chelian or extra red rays, and thus rendered them visible. 

Prof. Tyndall worked with the electric light. The charcoal points were 
placed in front of a concave silvered glass mirror in such a manner that 
the rays from the points after reflection were concentrated to a focus 
about 6 inches distant. On the path of the beam was interposed a cell 
full of a solution of iodine in bisulphide of carbon, which, as we have 
seen, has the power of completely stopping all luminous radiation, but 
gives free passage to the non-luminous rays. On now placing in the 
focus of the beam thus sifted a piece of platinum, this was raised to 
incandescence by the impact of perfectly invisible rays. In like manner 
a piece of charcoal in vacuo was heated to redness. 

By a proper arrangement of the charcoal points a metal may be raised 
to whiteness, and the light now emitted by the metal yields on prismatic 
analysis a brilliant luminous spectrum, which is thus entirely derived 
from the invisible rays beyond the red. 

To the new phenomenon here described, this transmutation of non- 
luminous into luminous heat, Prof. Tyndall has applied the term calo- 
rescence. 

When the eye was cautiously placed in the focus, guarded by a small 
hole being pierced in a metal screen, so that the converged rays should 
only enter the pupil and not affect the surrounding part of the eye, no 
impression of light was produced, and there was scarcely any sensation of 
heat. A considerable portion was absorbed by the humours of the eye, 
but yet a powerful beam undoubtedly reached the retina; for, as Prof. 
Tyndall showed by a separate experiment, about 18 per cent, of the 
obscure radiation from the electric light passed through the humours 
of an ox’s eye. 

373. Transmutation of thermal rays. —Melloni was the first who 
examined extensively and accurately the absorption of heat by solids 
and liquids. The apparatus he employed has already been referred to. 
A figure of it is given in the annexed figure, 260, where AB is the 
thermo-electric pile, consisting of a series of slender bars of antimony 
and bismuth alternately soldered together. The terminal bars of anti¬ 
mony A, and of bismuth B, are connected with a galvanometer D, by 
means of wires. 

The other parts of the apparatus are readily intelligible. There is a 
graduated brass support about a yard long, on which are placed the 
various pieces of apparatus, and which slide, and can be fixed at 
measured distances ; a is a support for the source of heat, in this case a 
Locatelli’s lamp; F and E are screens, and C is a support for the body 
experimented upon; while m is the pile, and D the galvanometer. 

Melloni used in his experiments five different sources of heat: 1st, 


RADIANT HEAT. 


331 


- 373 ] 

a Locatelli’s lamp—that is, an ordinary oil lamp with a reflector, but 
without a chimney; 2nd, an Argand lamp, which had a double cur¬ 
rent of air, and a chimney j 3rd, a spiral of platinum wire heated to 
redness in the flame of a spirit lamp ; 4th, a small copper canister 
tilled with water at 100° j and 5th, a plate of copper kept at a tempera¬ 
ture of about 400°. 

To express the power which bodies have of transmitting heat, Melloni 
used the term diathermancy ; diathermancy bears the same relation to 
radiant heat that transparency does to light; and in like manner the 
power of stopping radiant heat is called athermancy, which thus corre¬ 
sponds to opacity for light. In experimenting on the diathermancy of 
liquids, Melloni used glass troughs with parallel sides, the thickness of 
the liquid layer being 0-36 in. The radiant heat of an Argand lamp with 
a glass chimney was first allowed to fall directly on the face of the pile, 
and the deflection produced in the galvanometer taken as the total radia¬ 
tion ; the substance under examination was then interposed, and the 
deflection noted. This corresponded to the quantity of heat transmitted 
by the substance. If t indicate this latter number, and t' the total 
radiation, then 

t ': t :: 100 : x 

which is the percentage of rays transmitted. Thus, calling the total 
radiation 100, Melloni found that 


Bisulphide of carbon transmitted . 

63 

Olive oil 

r> 

30 

Ether 


21 

Sulphuric acid 

if 

17 

Alcohol 

ff 

15 

Solution of alum 

or sugar „ 

12 

Distilled water 


11 


In experimenting with solids the substances were cut into plates 0T 
inch in thickness, and it was found that of every 100 rays there was 
transmitted by 


Rock salt ....... 

92 

Iceland spar and plate glass .... 

62 

Smoky quartz. 

57 

Transparent carbonate of lead 

52 

Selenite ....... 

20 

Alum. 

12 

Sulphate of copper. 

0 


The transmission of heat through liquids has been re-examined by 
Prof. Tyndall by a more perfect mode of experiment than that employed 













332 ON HEAT. 1 . 373 - 

by Melloni. The experiments were made in the following way:—Instead 
of employing a glass vessel to hold the liquids under examination, he 
made use of a little cell whose ends were stopped by parallel plates of rock 
salt. The plates were separated by a ring of brass, with an aperture on 
the top through which the liquid could be poured. As this plate could 
be changed at will, liquid layers of various thicknesses were easily ob¬ 
tainable, the apparatus being merely screwed together and made liquid 
tight by paper washers. The instrument was mounted on a support 
before an opening in a brass screen placed in front of the pile. The 
source of heat employed was a spiral of platinum wire raised to incan¬ 


descence by an electric current; the spiral being enclosed in a small glass 
globe with an aperture in front through which the radiation passed un¬ 
changed in its character, a point of essential importance overlooked by 
Melloni. The following table contains the results of experiments made 
with liquids in the various thicknesses indicated, the numbers expressing 
the absorption per cent, of the total radiation. The transmission per cent, 
can be found in each case by subtracting the absorption from 100. Thus 
a layer of water 0-2 inch thick absorbs 80-7 and transmits 193 per cent, 
of the radiation from a red-hot spiral:— 


Fig. 260 . 



















-373] 


RADIANT HEAT. 


333 


Absorption of heat by liquids. 


Liquid. 

Thickness of liquid in parts of an inch. 


002 

0-04 

0-07 

0-14 

0-27 

Bisulphide of carbon 

5‘5 

8-4 

12*5 

15-2 

17*3 

Chloroform . 

16-6 

250 

350 

400 

44-8 

Iodide of methyl . 

36T 

46-5 

53-2 

65-2 

68-6 

Iodide of ethyl 

38-2 

50-7 

590 

690 

71-5 

Benzole 

43-4 

557 

62-5 

71-5 

73-6 

1 Amylene 

58-3 

65-2 

73-6 

77-7 

82-3 

| Ether .... 

633 

735 

761 

78-6 

85-2 

Acetic ether. 

— 

740 

78-0 

82 0 

86-1 

j Formic ether 

65-2 

76-3 

79-0 

840 

87-0 

Alcohol 

67*3 

7843 

83-6 

85*3 

89 T 

Water . 

80-7 

86-1 

88-8 

910 

91-0 


It appears from these tables, that there is no connection between dia¬ 
thermancy and transparency. The liquids, except olive oil, are all 
colourless and transparent, and yet vary as much as 75 per cent, in the 
amount of heat transmitted. Among the solids, smoky quartz, which is 
nearly opaque to light, transmits heat very well; while alum, which is 
perfectly transparent, cuts off 88 per cent, of heat rays. As there are dif¬ 
ferent degrees of transparency, so there are different degrees of diather¬ 
mancy ; and the one cannot he predicated from the other. 

By studying the transmission of heat from different parts of the spec¬ 
trum separately the connection between light and heat becomes manifest. 
"With this view Masson and Jamin received the spectrum of the solar 
light given by a prism of rock salt, on a moveable screen provided with 
an aperture, so that by raising or lowering the screen the action of any 
given part of the spectrum on different plates could be investigated. They 
thus found— 

That glass, rock, crystal, ice, and generally substances transparent for 
light, are also diathermanous for all kinds of luminous heat j 

That a coloured glass, red for instance, which only transmits the red 
rays of the spectrum and extinguishes the others, also extinguishes every 
kind of luminous heat, excepting that of the red rays; 

That glass and rock crystal, which are diathermanous for luminous 
heat, also transmit the obscure heat near the red, that is, the most re¬ 
frangible, but extinguish the extreme obscure rays, or those which are 
the least deflected by the prism. 
























334 on heat. [ 374 - 

Alum extinguishes a still greater proportion of the obscure spectrum, 
and ice stops it altogether. 

374. Influence of the nature of the heat. —The diathermanous 
power differs greatly with the heat from different sources, as Melloni made 
evident from the following table, in which the numbers express what 
proportion of every 100 rays from the different sources of heat incident on 
the plates is transmitted. 


Rock salt 

Loeatelli’s 

lamp. 

. 92 

Incandescent 

platinum 

wire. 

92 

Copper 
at 400°. 

92 

Copper 
at 100°. 

92 

Fluorspar 

. 78 

69 

42 

33 

Plate glass . 

. 39 

24 

6 

0 

Black glass . 

. 26 

25 

12 

0 

Selenite 

. 14 

5 

0 

0 

Alum . 

. 9 

2 

0 

0 

Ice 

. 6 

05 

0 

0 


These different sources of heat correspond to light from different sources. 
Rock salt is here stated to transmit all kinds of heat with equal facility, 
and to be the only substance which does so. It is analogous to white 
glass, which is transparent for light from all sources. Fluor spar transmits 
78 per cent, of the rays from a lamp, but only 33 of those from a black¬ 
ened surface at 100°. A piece of plate glass only one-tenth of an inch 
thick and perfectly transparent to light, is opaque to all the radiation from 
a source at 100°, transmits only 6 per cent, of the heat from a source at 
400°, and but 39 of the radiation from the lamp. Black glass, on the 
contrary, though it cuts off all heat from a source at 100°, allows 12 per 
cent, of the heat at 400° to pass, and is equally transparent to the heat 
from the spiral, but on account of its blackness is more opaque to the heat 
from the lamp. AS we have already seen, every luminous ray is a heat 
ray ; now as several of the substances in this table are pervious to all the 
luminous rays, and yet, as in the case of ice, transmit but 6 per cent, of 
luminous heat, we have an apparent anomaly; which, however, is only a 
confirmation of the remarkably small proportion which the luminous rays 
of a lamp bear to the obscure. 

From these experiments Melloni concluded that as the temperature of 
the source rose more heat was transmitted. This may be taken as a general 
law, which has been recently confirmed by some refined experiments 
of Prof. Tyndall. The platinum lamp, previously described, was used 
as the source, the temperature of which Prof. Tyndall was enabled 
to vary from a dark to a brilliant white heat, without disturbing in any 
way the position of the apparatus; the gradations of temperature being 
obtained by a gradual augmentation of the strength of the electric current 
which heated the platinum spiral. Instead of liquids, vapours were 





RADIANT HEAT. 


335 


-374] 

chosen as the subject of experiment, and examined in a manner to be 
described subsequently; the measurements are given in the following 
table : 


Absorption of heat by vapours. 


Name of Vapour. 

Source, platinum spiral. 

Barely 

visible. 

Bright 

red. 

White 

hot. 

Near 

fusion. 

| 

Bisulphide of carbon . 

6*5 

4-7 

2-9 

2-5 

Chloroform 

91 

6-3 

5-6 

3-9 ; 

Iodide of methyle 

12*5 

9-6 

7-8 


Iodide of ethyle . 

21-3 

17-7 

12-8 


Benzole .... 

26-4 

20-6 

16-5 


Amylene .... 

35-8 

27*5 

22-7 


Ether. 

43-4 

31-4 

25-9 

23-7 

Formic ether 

45-2 

31-9 

25-1 

21-3 

Acetic ether 

49-6 

34-6 

27-2 

i 


The percentage of rays absorbed is here seen to diminish in each case 
as the temperature of the source rises. Mere elevation of temperature 
does not, however, invariably produce a high penetrative power in the rays 
emitted; for Prof. Tyndall has shown that the rays from sources of far 
higher temperature than any of the foregoing are more largely absorbed 
by certain substances than are the rays emitted from any one of the 
sources as yet mentioned. Thus it was found that the radiation from a 
hydrogen flame was completely intercepted by a layer of water only 0-27 
of an inch thick, the same layer transmitting 9 per cent, of the radiation 
from the red-hot spiral, a source of much lower temperature. The ex¬ 
planation of this is, that those rays which heated water emits (and water, 
the product of combustion, is the main radiant in a hydrogen flame), are 
the very ones which this substance most largely absorbs. This statement, 
which will become clearer after reading the analogous phenomena in the 
case of light, was strikingly exemplified by the powerful absorption of 
the heat from a carbonic oxide flame by carbonic acid gas. It will be 
seen directly (377) that of the rays from a heated plate of copper olefiant 
gas absorbs 10 times the quantity intercepted by carbonic acid, whilst of 
the rays from a carbonic oxide flame Tyndall found carbonic acid absorbed 
twice as much as olefiant gas. A tenth of an atmosphere of carbonic acid 
enclosed in a tube 4 feet long, absorbs 60 per cent, of the radiation from 
a carbonic oxide flame. Radiant heat of this character can thus be used 
as a delicate test for the presence of carbonic acid, the amount of which 


















336 


ON HEAT. 


[ 375 - 

can even be accurately measured by the same means. This has been done 
by Mr. Barrett, who, in this way, has made a physical analysis of the 
human breath. In one experiment the quantity of carbonic acid con¬ 
tained in breath physically analysed was found to be 4-56 per cent., whilst 
the same breath chemically analysed gave 4-66, a difference of only one- 
tenth per cent. 

375. Influence of the thickness and nature of screens. —It will 

be seen from the table (374) that of every 100 rays rock salt transmits 
92. The other 8 may either have been absorbed or reflected from the 
surface of the plate. According to Melloni, the latter is the case; for if, 
instead of on one plate, heat be allowed to fall on two or more plates 
whose total thickness does not exceed that of the one, the quantity of 
heat arrested will be proportional to the number of reflecting surfaces. 
He therefore concluded rock salt to be quite diathermanous. 

The experiments of MM. Provostaye and Desains, of Mr. Balfour 
Stewart, and those of Prof. Tyndall, show that this conclusion is not 
strictly correct; rock salt does absorb a very small proportion of obscure 
rays. 

The quantity of heat transmitted through rock salt is practically the 
same, whether the plate be 1, 2, or 4 millimeters thick. But with 
other bodies, absorption increases with the thickness, although by no 
means in direct proportion. This is seen to be the case in the table of 
absorption by liquids at different thicknesses. The following table tells 
what proportion of 1,000 rays from a Locatelli’s lamp pass through a 
glass plate of the given thickness : 

Thickness in millimeters . 0*5 12345678 

Bays transmitted . . . .775 733 682 653 634 620 609 600 592 

The absorption takes place in the first layers; the ravs which have 
passed these possess the property of passing through other layers in a 
higher degree, so that beyond the first layers the heat transmitted ap¬ 
proaches a certain constant value. If a thin glass plate be placed behind 
another glass plate a centimeter thick, the former diminishes the 
transmission by little more than the reflection from its surface. But if 
a plate of alum were placed behind the glass plate, the result would be 
different, for the latter is opaque for much of the heat transmitted by 
glass. 

Heat, therefore, which has traversed a glass plate traverses another 
plate of the same material with very slight loss, but is very greatly 
diminished by a plate of alum. Of 100 rays which had passed through 
green glass or tourmaline, only 5 and 7 were respectively transmitted by 
the same plate of alum. A plate of blackened rock salt only transmits 
obscure rays, while alum extinguishes them. Consequently, when these 


9 


- 376 ] RADIANT HEAT. 337 

two substances are superposed, a system impervious to light and heat is 
obtained. 

These phenomena find their exact analogies in the case of light. The 
different sources of heat correspond to flames of different colours, and the 
various screens to glasses of different colours. A red flame looked at 
through a red glass appears quite bright, but through a green glass it 
appears dim or is scarcely visible. So in like manner heat which has 
traversed a red glass passes through another red glass with little 
diminution, but is almost completely stopped by a green glass. 

Different luminous rays being distinguished by their colours , to these 
different obscure calorific rays Melloni gave the name of thermocrosis or 
heat coloration. The invisible portion of the spectrum is accordingly 
mapped out into a series of spaces, each possessing its own peculiar 
feature, corresponding to the coloured spaces which are seen in that 
portion of the spectrum visible to our eyes. 

Besides thickness and colour, the polish of a substance influences the 
transmission. Glass plates of the same kind and thickness transmit 
more heat as their surface is more polished. Bodies which transmit heat 
of any kind very readily are not heated. Thus a window pane is 
not much heated by the strongest sun’s heat; but a glass screen held 
before a common fire stops most of the heat, and is itself heated thereby. 
The reason of this is that by far the greater part of the heat from a fire 
is obscure, and to this kind of heat glass is opaque. 

376. Diffusion of beat. —When a ray of light falls upon an 
unpolished surface in a definite direction, it is decomposed into a va¬ 
riety of rays which are reflected from the surface in all directions. 
This irregular reflection is called diffusion , and it is in virtue of it that 
bodies are visible when light falls upon them. A further peculiarity is, 
that all solar rays are not equally diffused from the surface of bodies. 
Certain bodies diffuse certain rays and absorb others, and accordingly 
appear coloured. The red colour of a geranium is caused by its absorbing 
all the rays, excepting the red, which are irregularly reflected. Just 
as is the case with transmitted light in transparent bodies, so with 
diffused light in opaque ones, for if a red body is illuminated by red 
light it appears of a bright red colour, but if green light fall upon it 
it is almost black. We shall now see that here again analogous phe¬ 
nomena prevail with heat. 

Various substances diffuse different thermal rays to a different extent; 
each possesses a peculiar thermocrose or heat tint. Melloni placed a number 
of strips of brass foil between the source of heat and the thermo-pile. 
They were coated on the side opposite to the pile with lampblack, and 
on the other side with the substances to be investigated. Representing 

Q 


ON HEAT. 


338 


[377- 


the quantity of heat absorbed by the lampblack at 100, the absorption 
of the other bodies was as follows : 


Incandescent Copper Copper 

platinum. at 400°. at 100°. 


Lampblack 

. 100 

100 

100 

White lead 

56 

89 

100 

Isinglass 

54 

64 

91 

Indian ink 

. 95 

87 

85 

Shellac 

47 

70 

72 

Polished metal . 

13-5 

13 

13 


Hence, white lead absorbs far less of the heat radiated from incan¬ 
descent platinum than lampblack, but it absorbs the obscure rays from 
copper at 100° as completely as lampblack. Indian ink is the reverse of 
this; it absorbs obscure* rays less completely than luminous rays. Lamp¬ 
black absorbed the heat from all sources in equal quantities, and very 
nearly completely. In consequence of this property, all thermoscopes 
which are used for investigating radiant heat are covered with lamp¬ 
black, as it is the best known absorbent of heat. The behaviour of 
metals is the reverse of that of lampblack. They reflect the heat of 
different sources in the same degree. They are to heat what white bodies 
are to light. 

As coloured light is altered by diffusion from several bodies, so 
Knoblauch has shown that the different kinds of heat are altered by re¬ 
flection from different surfaces. The heat of an Argand lamp diffused 
from white paper passes more easily through calcspar than when it has 
been diffused from black paper. 

The rays of heat, like the rays of light, are susceptible of polarisation 
and double refraction. These properties will be better understood after 
treating of light. 

377. Relation of gases and vapours to radiant heat.— For a long 
time it was believed that gaseous bodies were as permeable to heat as a 
vacuum; and though subsequently this was disproved, yet down to a 
recent period it was thought that whatever absorption such bodies 
might exercise was slight and similar in degree. The whole subject 
has, however, been investigated by Prof. Tyndall in a series of laborious 
experiments, which, with regard to the absorption of heat by gases, are of 
equal importance to those of Leslie, and afterwards of Melloni, in refe¬ 
rence to solids and liquids. 

The apparatus used in these experiments is represented, in its essential 
features, in the adjacent figure: the arrangement being looked upon from 

above. 

A is a cylinder about 4 feet in length and 2| inches in diameter, 




RADIANT HEAT. 


339 


-377] 

placed horizontally, the ends of which can he closed with rock salt plates; 
by means of a lateral tube at r it can be connected with an air pump and 
exhausted ; while at t is another tube which serves for the introduction 
of gases and vapours. T is a sensitive thermo-pile connected with an 
extremely delicate galvanometer M. 

The deflections of this galvanometer were proportional to the degrees 
of heat up to about 30°; beyond this point the proportionality no longer 
held good, and accordingly for the higher degrees a table was empirically 
constructed, in which the value of the higher deflections was expressed 
in units ; the unit being the amount of heat necessary to move the needle 
through one of the lower degrees. 

C is a source of heat, which usually was either a Leslie’s tube filled 
with boiling water, or else a sheet of blackened copper heated by gas. 
Now when the source of heat was permitted to radiate through the ex¬ 
hausted cube, it caused the needle to assume a very high deflection; and 


j§l 

iH 


Fig. 261. 

in this position a very considerable degree of absorption would have been 
needed to produce an alteration of 1° of the galvanometer. And if to lessen 
this deflection a lower source of heat had been used, the fractionabsorbed 
would be correspondingly less, and might well have been insensible. Hence 
Prof. Tyndall adopted the following device, by which he was enabled to 
use a powerful flux of heat, and at the same time discover small variations 
in the quantity falling on the pile. 

The source of heat at C was allowed to radiate through the tube at the 
end of which the pile was placed; a deflection was produced of, say 70°; a 
second source of heat, D, was then placed near the other face of the pile ? 
the amount of heat falling on the pile from this compensating cube being 
regulated by means of a moveable screen S. When both faces of the pile 
are warmed, two currents are produced, which are in opposite directions, 
and tending therefore to neutralise each other: when the heat on both 
faces is precisely equal the neutralisation is perfect, and no current at all 
is produced, however high may be the temperature on both sides. In the 
arrangement just described, by means of the screen S, the radiation from 
the compensating cube was caused to neutralise exactly the radiation from 
the source C; the needle consequently was brought down from 70° to 

q 2 


















340 


ON HEAT. 


[ 378 - 


zero, and remained there so long as both sources were equal. If now a gas 
or vapour be admitted into the exhausted tube, any power of absorption 
it may possess will be indicated by the destruction of this equilibrium, 
and preponderance of the radiation from the compensating cube, by an 
amount corresponding to the heat cut off by the gas. Examined in this 
way, air, hydrogen, and nitrogen, when dried by passing through sulphuric 
acid, were found to exert an almost inappreciable effect j their presence as 
regards radiant heat being but little different to a vacuum. But with 
olefiant and other complex gases the case was entirely different. Repre¬ 
senting by the number 1 the quantity of radiant heat absorbed by air, 
olefiant gas absorbs 970 times, and ammoniacal gas 1195 times this 
amount. In the following table is given the absorption of obscure heat 
by various gases, referred to air as unity : 


Name of gas. 

Air . 

Oxygen . 
Nitrogen . 
Hydrogen 
Chlorine . 
Hydrochloric acid 
Carbonic acid . 
Nitrous oxide . 
Marsh gas 
Sulphurous acid 
Olefiant gas 
Ammonia 


Absorption under 
30 inches pressure. 

1 

1 

1 

1 

. 39 

62 
. 90 

. 35 5 
. 403 
. 710 
. 970 
. 1195 


If instead of comparing the gases at a common pressure of one atmo¬ 
sphere, they are compared at a common pressure of an inch, their differ¬ 
ences in absorption are still more strikingly seen. Thus assuming the 
absorption by 1 inch of dry air to be 1, the absorption by 1 inch of olefi¬ 
ant gas is 7950, and by the same amount of sulphurous acid 8800. 

378. Influence of pressure and thickness on the absorption 
of heat by gases.— The absorption of heat by gases varies with 
the pressure; this variation cannot be seen in the case of air, as the 
total absorption is so small, but in the case of those gases which have 
considerable absorptive power it is easily shown. Taking the total ab¬ 
sorption by atmospheric air under ordinary pressure at unity, the num¬ 
bers of olefiant gas under a pressure of 1, 3, 5, 7, and 10 inches of 
mercury are respectively 90, 142, 168, 182, and 193. Thus one-thirtieth 
of an atmosphere of olefiant gas exerts 90 times the absorption of an 
entire atmosphere of air. And the absorption, it is seen, increases with 









RADIANT HEAT. 


341 


-379] 

the density, though not in a direct ratio. Prof. Tyndall showed, how¬ 
ever, by special experiments, that for very low pressures the absorption 
does increase with the density. Employing as a unit volume of the gas 
a quantity which measured only ^ of a cubic inch, and admitting 
successive measures of olefiant gas into the experimental tube, it was 
found that up to 15 measures the absorption was directly proportionate 
to the density in each case. 

In these experiments the length of the experimental tube remained 
the same whilst the pressure of the gas within it was caused to vary: in 
other subsequent experiments the pressure of the gas was kept constant, 
whilst the length of the tube was, by suitable means, varied from 0 01 of 
an inch up to 50 inches. The source was a heated plate of copper; of 
the total radiation from this nearly 2 per cent, were absorbed by a film 
of olefiant gas - 01 of an inch thick, upwards of 9 per cent, by a layer of 
the same gas 0T of an inch thick, 33 per cent, by a layer 2 inches thick, 
68 per cent, by a column 20 inches long, and 77 per cent, by a column 
rather more than 4 feet long. 

379. Absorptive power of vapours.— Great as is the absorptive 
power of olefiant gas, it is exceeded, as Prof. Tyndall found, by that of 
several vapours. The mode of experimenting was analogous to that with 
the gases. The liquid from which the vapours were to be derived was 
enclosed in a small flask which could be attached with a stopcock to the 
exhausted experimental tube. The absorption was then determined 
after admitting the vapours into the tube in quantities measured by the 
pressure of the barometer gauge attached to the air pump. 

The following table shows the absorption of vapours under pressures 
varying from 0T to 10 inch of mercury: 


Name of vapours. 

Absorption under pressures 
in inches of mercury. 


01 

0-5 

10 

Bisulphide of carbon 

. 15 

47 

62 

Benzole .... 

. 66 

182 

267 

Chloroform .... 

. 85 

182 

136 

Ether. 

. 300 

710 

870 

Alcohol .... 

. 325 

622 


Acetic ether.... 

. 590 

980 

1195 


These numbers refer to the absorption of a whole atmosphere of dry 
air as their unit, and it is thus seen that a quantity of bisulphide of car¬ 
bon vapour, the feeblest absorbent yet examined, which only exerts a 
pressure of A of an inch of mercury, or the ^ of an atmosphere, gave 
15 times the absorption of an entire atmosphere of air; and ~ of an inch 
of acetic ether 590 times as much. Comparing air at a pressure of 01 



ON HEAT. 


342 


[379- 


with acetic ether of the same pressure, the absorption of the latter would 
he more than 17,500 times as great as that of the former. 

The absorption by the infinitesimally small quantity of matter consti¬ 
tuting a perfume can even be measured; for Prof. Tyndall found that 
the odours from the essential oil exercised a marked influence on radiant 
heat. Perfectly dry air was allowed to pass through a tube containing 
dried paper impregnated with various essential oils, and then admitted 
into the experimental tube. Taking the absorption of dry air as unity, 
the following were the numbers respectively obtained for air scented 
with various oils:—Patchouli 31, otto of roses 37, lavender 60, thyme 
68, rosemary 74, cassia 109, aniseed 372. Thus the perfume of a flower¬ 
bed absorbs a large percentage of the heat of low refrangibility emitted 
from it. 

Ozone prepared by electrolysing water was also found to have a 
remarkable absorptive effect. The small quantity of ozone present in 
electrolytic oxygen was found in one experiment to exercise 136 times 
the absorption of the entire mass of the oxygen itself. 

But the most remarkable, perhaps, and certainly the most important 
results which Prof. Tyndall has obtained are those which follow from 
his very numerous experiments on the behaviour of aqueous vapour to 
radiant heat. The experimental tube was filled with air, dried as per¬ 
fectly as possible, and the absorption it exercised was found to be one 
unit. Exhausting the tube, and admitting the ordinary undried, but not 
specially moist, air from the laboratory, the absorption now rose to 72 
units. This difference between dried and undried air can only be 
ascribed to the aqueous vapour the latter contains. Thus on a day of 
average humidity the absorptive effect due to the transparent aqueous 
vapoui' present in the atmosphere is 72 times as great as that of the air 
itself, though in quantity the latter is about 200 times greater than the 
former. Analogous results were obtained on different days, and with 
specimens of air taken from various localities. When air which had 
been specially purified was allowed to pass through a tube filled with 
fragments of moistened glass and examined, it was found to exert an 
absorption 90 times that of pure air. 

In some other experiments Prof. Tyndall suppressed the use of rock 
salt plates in his experimental tube, and even the tube itself, and yet in 
every case the results were such as to show the great power which 
aqueous vapour possesses as an absorbent of radiant heat. 

The absorptive action which the aqueous vapour in the atmosphere 
exerts on the sun’s heat has been established by a series of actinometrical 
observations made by Soret at Geneva and on the summit of Mont 
Blanc; he finds that the intensity of the solar heat on the top of Mont 
Blanc is § of that at Geneva ; in other words, that of the heat which is 


RADIANT HEAT. 


343 


- 381 ] 

radiated at the height of Mont Blanc, about | is absorbed in passing* 
through a vertical layer of the atmosphere 14,436 feet in thickness. The 
same observer has found that with virtually equal solar heights there is 
the smallest radiation on those days on which the tension of aqueous va¬ 
pour is greatest, that is, when there is most moisture in the atmosphere. 

380. Radiating- power of gases.— Prof. Tyndall also examined the 
radiating power of gases. A red-hot copper ball was placed so that the 
current of heated air which rose from it acted on one face of a thermo¬ 
pile; this action was compensated by a cube of hot water placed in front 
of the opposite face. On then allowing a current of dry olefiant gas 
from a gasholder to stream through a ring burner over the heated ball 
and thus supplant the ascending current of hot air, it was found that 
the gas radiated energetically. By comparing in this manner the action 
of many gases it was discovered that, as is the case with solids, those gases 
which are the best absorbers are also those which radiate most freely. 

381. Dynamic radiation and absorption.— To another class of 
phenomena which Prof. Tyndall discovered he gives the name, dynamic 
radiation and absorption. 

A gas when permitted to enter an exhausted tube is heated in conse¬ 
quence of the collision of its particles against the sides of the vessel; it 
thus becomes a source of heat, which is perfectly capable of being mea¬ 
sured. Prof. Tyndall calls this dynamic heating. In like manner, when 
a tube full of gas or vapour is rapidly exhausted, a chilling takes place 
owing to the loss of heat in the production of motion. This Prof. 
Tyndall calls dynamic chilling or absorption. 

He could thus determine the radiation or absorption of a gas without 
any source of heat external to the gas itself. An experimental tube 
was taken, one end of which was closed with a polished metal plate, 
and the other with a plate of rock salt; in front of the latter was the 
face of the pile. The needle being at zero, aud the tube exhausted, a 
gas was allowed quickly to enter until the tube was full, the effect on 
the galvanometer being noted. This being only a transitory effect the 
needle soon returned to zero; the tube was then rapidly pumped out, by 
which a sudden chilling was produced, and the needle exhibited a 
deflection in the opposite direction. 

Comparing in this way the dynamic heating and chilling of various 
gases, it was found that those gases which are the best absorbers are in 
like manner the best radiators. 

Metallic surfaces when polished are, as we have seen (364), bad 
radiators, but radiate freely when covered with varnish. Now Prof. 
Tyndall made the curious experiment of varnishing a metallic surface by 
a film of gas. A Leslie’s tube was placed with its polished metal side 
in front of the pile, and its effect neutralised by a second cube placed 


ON HEAT. 


'344 


[382- 


before the other face of the pile. On allowing, by a special arrangement, 
a stream of olefiant or coal gas to flow from a gasholder over the metallic 
face of the first cube, a copious radiation from that side was produced as 
long as the flow of gas continued. Acting on the principle indicated in 
the foregoing experiment, Prof. Tyndall determined the dynamic radiation 
and absorption of vapours. The experimental tube containing a vapour 
under a small known pressure, air was allowed to enter until the pres¬ 
sure inside the tube was the same as that of the atmosphere. In this 
way the entering air by its impact against the tube became heated; and 
its particles mixing with those of the minute quantity of vapour present, 
each of them became, so to speak, coated with a layer of the vapour. 
The entering air was in this case the source of heat, just as in the above 
experiments the Leslie cube was; here, however, one gas varnished 
another; the radiation and subsequently the absorption of various 
vapours could thus be determined. 

It was found that vapours differed very materially in their power of 
radiating under these circumstances: of those which were tried bisul¬ 
phide of carbon vapour was the worst, and boracic ether the best radiant. 
And in all cases those which were the best absorbents were also the best 
radiators. By this method Prof. Tyndall was able to observe a definite 
radiative power with the more powerful vapours when the quantity 
present was immeasurably small. 

•°>82. Relation of absorption to molecular state.— Up to a recent 
period it was considered that the absorption of heat was mainly dependent 
upon the physical condition of the body examined. This led to the 
belief that it was impossible for substances of such tenuity as gases and 
vapours to absorb any sensible amount of heat; and that the absorption 
by bodies when in a liquid state would be unlike the same bodies when 
solid; moreover, that if all solid bodies were reduced to an equally fine 
state of division, the present differences in their absorbent and radiative 
powers would disappear. A few experiments made by Melloni on 
atmospheric air supported the first idea, and a series of experiments by 
Masson and Courtepee established the belief in the last. But we have 
seen that Prof. Tyndall’s researches have revealed the powerful absorption 
of heat by various gases and vapours, and we shall now briefly show that 
the researches of the same philosopher have overthrown the last two 
conclusions, giving us an insight into the cause of the absorption of heat, 
which before was unattainable. 

After the examination of the absorption of heat by vapours, Prof. 
Tyndall tried the same substances in a liquid form. The conditions of 
the experiments were in both cases the same; the source of-heat was 
always a spiral of platinum, heated to redness by an electric current of 
known strength ; and plates of rock salt were, invariably employed to 


RADIANT HEAT. 


345 


-382] 


contain both vapours and liquids. Finally, the absorption by the vapours 
was remeasured; in this case introducing into the experimental tube, not 
as before equal quantities of vapour, but amounts proportional to the 
density of the liquid. When this last condition had been attained, it 
was found that the order of absorption by a series of liquids, and by the 
same series when turned into vapour, was precisely the same. Thus the 
substances tried stood in the following order as liquid and as vapour, begin¬ 
ning with the feeblest absorbent, and ending with the most powerful. 


Liquids. 

Bisulphide of carbon 
Chloroform . 

Iodide of methyl . 
Iodide of ethyl 
Benzole 
Amylene 

Sulphuric ether . 
Acetic ether 
Formic ether 
Alcohol 
Water. 


Vapours. 

Bisulphide of carbon. 
Chloroform. 

Iodide of methyl. 
Iodide of ethyl. 
Benzole. 

Amylene. 

Sulphuric ether. 
Acetic ether. 

Formic ether. 
Alcohol. 


A direct determination of the proportional amount of the vapour of 
water could not be made, on account of the lowness of its tension, and 
the hygroscopic nature of the plates of the rock salt. But the remark¬ 
able and undeviating regularity of the absorption by all the other sub¬ 
stances in the list, when as liquid and vapour, establishes the fact, which 
is corroborated by the experiments we have already mentioned, that 
aqueous vapour is one of the most energetic absorbents of heat. 

In this table it will be noticed that those substances which have the 
simplest chemical constitution stand first in the list, with one anomalous 
exception, namely, that of water. In the absorption of heat by gases, Prof. 
Tyndall found that the elementary gases were the feeblest absorbents, 
while the gases of most complex constitution were the most powerful 
absorbers. These facts, which were found in a general way to be true for 
solids, liquids, and gases, have led Prof. Tyndall to infer that absorption 
is mainly dependent on chemical constitution; that is to say, that ab¬ 
sorption and radiation are molecular acts independent of the physical con¬ 
dition of the body. 

But this conclusion appeared to be contradicted by the experiments of 
Masson and Courtepee on powders. Prof. Tyndall has therefore repeated 
these experiments, and found them to be entirely incorrect. Avoiding 
the source of error into which the French experimenters had fallen, 
Tyndall has discovered that the radiation of powders is similar to that of 

q 3 







346 


ON HEAT. 


[383- 

the solids from which they were derived, and therefore differs greatly 
inter se. The absorbent power of powders was also found to correspond 
with their radiative power—as we have shown to be the case with solids, 
and gases, and though as yet we have no experiments on the subject, is 
doubtless also true for liquids. The powders were attached to the tin 
surfaces of a Leslie’s cube, in such a manner that radiation took place 
from the surface of the powder alone. The following table gives the 
radiation in units from some of the powders examined by Tyndall; the 
metal surface of the cube giving a deflection of 15 units. 

Radiation from powders. 


Rock salt.35-3 Sulphate of calcium . . . 77*7 

Biniodide of mercury . . 39*7 Red oxide of iron .... 78’4 

Sulphur.40 6 Hydrated oxide of zinc . . 80-4 

Chloride of lead .... 55*4 Black oxide of iron . . . 81-3 

Carbonate of calcium . . 70‘2 Sulphide of iron .... 81*7 

Red oxide of lead . . . 74 2 Lampblack.84 0 


It will be noticed that these substances are of various colours. Some 
are white, such as rock salt, chloride of lead, carbonate and sulphate of 
calcium, and hydrated oxide of zinc; some are red, such as biniodide of 
mercury and oxide of lead; whilst others are black, as sulphide of iron 
and lampblack: we have besides other colours. The colours therefore 
have no influence on the radiating power: for example, rock salt is the 
feeblest radiator, and hydrated oxide of zinc one of the most powerful 
radiators. The views of Prof. Tyndall therefore, instead of being over¬ 
thrown, were confirmed by these his latest experiments. 

Nearly a century ago Franklin made experiments on coloured pieces 
of cloth, and found their absorption, indicated by their sinking into snow 
on which they were placed, to increase with the darkness of the colour. 
But all the cloths were equally powerful absorbents of obscure heat, and 
the effects noticed were only produced by their relative absorptions of 
light. In fact, the conclusion to be drawn from Franklin's experiment 
only holds good for luminous heat, especially sunlight, such as he employed. 

383. Applications.— The property which bodies possess of absorb¬ 
ing, emitting, and reflecting heat, meets with numerous applications in 
domestic economy and in the arts. Leslie stated in a general manner 
that white bodies reflect heat very well, and absorb very little, and that 
the contrary is the case with black substances. As we have seen, this 
principle is not generally true, as Leslie supposed; for example, for 
non-luminous rays white lead has as great an absorbing power as 
lampblack (376). Leslie’s principle applies to powerful absorbents like 
cloth, cotton, wool, and other organic substances when exposed to 








RADIANT HEAT. 


347 


- 383 ] 

luminous heat. Accordingly, the most suitable coloured clothing for 
summer is just that which experience has taught us to use, namely 
white, for it absorbs less of the sun’s rays than black clothing, and hence 
feels cooler. 

The polished fire-irons before a fire are cold, whilst the black fender 
is often unbearably hot. If, on the contrary, a liquid is to be kept hot 
as long as possible, it must be placed in a brightly polished metallic 
vessel, for then, the emissive power being less, the cooling is slower. It 
is for this reason advantageous that the steam pipes, etc., of locomotives 
should be kept bright. 

In the Alps, the mountaineers accelerate the fusion of the snow by 
covering it with earth, which increases the absorbing power. 

In our dwellings, the outsides of the stoves and of hot-water apparatus 
ought to be black, and the insides of fireplaces ought to be lined with 
fire-clay, in order to increase the radiating power towards the apartment. 

It is in consequence of the great diathermaneity of dry atmospheric 
air that the higher regions of the atmosphere are so cold, notwith¬ 
standing the great heat which traverses them: whilst the intense heat 
of the sun’s direct rays on high mountains is probably due to the com¬ 
parative absence of aqueous vapour at those high elevations. 

As nearly all the luminous rays of the sun pass through water, and 
the sun’s radiation as we receive it on the surface of the earth consisting 
of a large proportion of luminous rays, accidents have often arisen from 
the convergence of these luminous rays by bottles of water which act as 
lenses. In this way gunpowder could be fired by the heat of the sun’s 
rays concentrated by a water lens ; and the drops of water on leaves in 
greenhouses have, it is said, been found to act as lenses, and burn the 
leaves on which they rest. 

Certain bodies can be used (371) to separate the heat and light radiated 
from the same source. Rock salt covered with lampblack, or still better 
with iodine, transmits heat, but completely stops light. On the other 
hand, alum, either as a plate or in solution, or a thin layer of water, is 
permeable to light, but stops all the heat from obscure sources. This 
property is made use of in apparatus which are illuminated by the sun’s 
rays, in order to sift the rays of their heating power, and a vessel full of 
water or a solution of alum is used with the electric light when it is 
desirable to avoid too intense a heat. 

In gardens, the use of shades to protect plants depends partly on the 
diathermancy of glass for heat from luminous rays and its athermancy 
for obscure rays. The heat which radiates from the sun is largely of 
the former quality, but by contact with the earth it is changed into 
obscure heat, which as such cannot retraverse the glass. This explains 
the manner in which greenhouses accumulate their warmth, and also the 


348 


ON HEAT. 


[ 384 - 

great heat experienced in summer in rooms having glass roofs, for the 
glass in both cases effectually entraps the solar rays. On the same 
principle plates of glass are frequently used as screens to protect us from 
the heat of a fire : the glass allows us to see the cheerful light of the 
fire, but intercepts the larger part of the heat radiated from the fire. 
Though the screens thus become warm by the heat they have absorbed, 
yet as they radiate this heat in all directions, towards the fire as well as 
towards us, we finally receive less heat when they are interposed. 


CHAPTER IX. 

CALORIMETRY. 

384. Calorimetry. Thermal unit.— The object of calorimetry is to 
measure the quantity of lieat which a body parts with or absorbs when its 
temperature sinks or rises through a certain number of degrees, or when 
it changes its condition. 

Quantities of heat may be expressed by any of its directly measurable 
effects, but the most convenient is the alteration of temperature, and 
quantities of heat are usually defined by stating the extent to which tliev 
are capable of raising a known weight of a known substance, such as 
water. 

The unit chosen for comparison, and called the thermal unit, is not 
everywhere the same. In France it is the quantity of heat necessary to 
raise the temperature of one kilogramme of water through one degree 
Centigrade ; this is called a calorie. In this book we shall adopt, as a 
thermal unit, the quantity of heat necessary to raise one pound of water 
through one degree Centigrade : 1 calot'ie = 2‘2 thermal units, and 1 ther¬ 
mal unit = 0-45 calorie. 

385. Specific heat.— When equal weights of two different substances 
at the same temperature placed in similar vessels are subjected for the 
same length of time to the heat of .the same lamp, or are placed at the 
same distance in front of the same fire, it is found that their temperatures 
will vary considerablyj the mercury will be much hotter than the water. 
But as from the conditions of the experiment, they have each been re¬ 
ceiving the same amount of heat, it is clear that the quantity of heat 
which is sufficient to raise the temperature of mercury through a certain 
number of degrees will only raise the temperature of the same quantity 
of water through a less number of degrees ; in other words, that it re¬ 
quires more heat to raise the temperature of water through one degree 




SPECIFIC HEAT. 


349 


- 386 ] 

than it does to raise the temperature of mercury by the same extent. 
Conversely, if the same quantities of water and of mercury at 100° C. be 
allowed to cool down to the temperature of the atmosphere, the water will 
require a much longer time for the purpose than the mercury: hence in 
cooling through the same number of degrees, water gives out more heat 
than does mercury. 

It is readily seen that all bodies have not the same specific heat. If a 
pound of mercury at 100° is mixed with a pound of water at zero, the 
temperature of the mixture will only be about 3°. That is to say, that 
while the mercury has cooled through 97°, the temperature of the water 
has only been raised 3°. Consequently, the same weight of water requires 
about 32 times as much heat as mercury does to produce the same eleva¬ 
tion of temperature. 

If similar experiments are made with other substances it will be found 
that the quantity of heat required to effect a certain change of tempera¬ 
ture is different for almost every substance, and we speak of the specific 
heat or calorific capacity of a body as the quantity of heat which it absorbs 
when its temperature rises through a given range of temperature, from 
zero to 1° for example, compared with the quantity of heat which would 
be absorbed under the same circumstances, by the same weight of water. 
In other words, water is taken as the standard for the comparison of 
specific heats. Thus, to say that the specific heat of lead is 0’0314, 
means that the quantity of heat which would raise the temperature of 
any’given quantity of lead through 1° C. would only raise the temperature 
of the same quantity of water through 0*0314. 

Three methods have been employed for determining the specific heats 
of bodies : (i.) the method of the melting of ice, (ii.) the method of 
mixtures, and (iii.) that of cooling. In the latter, the specific heat of a 
body is determined by the time which it takes to cool through a certain 
temperature. Previous to describing these methods it will be convenient 
to explain the expression for the quantity of heat absorbed or given out 
by a body of known weight and specific heat, when its temperature rises 
or falls through a certain number of degrees. 

386. Measure of the sensible heat absorbed by a body.— Let rn 
be the weight of a body in pounds, c its specific heat, and t its tempera¬ 
ture. The quantity of heat necessary to raise a pound of water through 
one degree being taken as unity, m of these units would be required to 
raise m pounds of water through one degree, and to raise it through t 
degrees, t times as much, or mt. As this is the quantity of heat neces¬ 
sary to raise through t degrees m pounds of water whose specific heat is 
unity, a body of the same weight, but of different specific heat, would 
require mtc. Consequently, when a body is heated through t degrees, 
the quantity of heat which it absorbs is the product of its weight into its 


ON HEAT. 


350 


[ 387 - 


temperature into its specific heat. This principle is the basis of all the 
formulae for calculating specific heats. 

If a body is heated or cooled from t' to t degrees, the heat absorbed or 
disengaged will be represented by the formula 

m ([f — t ) c, or m ( t — t f ) c. 

A thorough comprehension of these formulae will prevent any difficulty 
in the solution of problems on specific heat. 

387. XVlethod of the fusion of ice. —This method of determining 
specific heats is based on the fact that to melt a pound of ice 80 thermal 
units are necessary, or more exactly 79'25. Black’s calorimeter (fig. 
262) consists of a block of ice in which a cavity is made, and which is 
provided with a cover of ice. The substance whose specific heat is to be 
determined is heated to a certain temperature, and then placed in the 

cavity, which is covered. After some 
time the body becomes cooled to zero. 
It is then opened, and both the sub¬ 
stance and the cavity wdped dry with a 
cloth which has been previously weighed. 
The increase of weight of this cloth 
obviously represents the ice which has 
been converted into water. 

Now, since one pound of ice at 0° in 
melting to water at 0° absorbs 80 ther¬ 
mal units, P pounds absorbs 80 P units. 
On the other hand, this quantity of heat is equal to the heat given out 
by the body in cooling from t° to zero, which is mtc, for it may be taken 
for granted that in cooling from t° to zero a body gives out as much heat 
as it absorbs in being heated from zero to t°. Consequently, from 

mtc = 80 P we have c = —^ 
mt 

It is difficult to obtain blocks of ice as large and pure as those used by 
Black in his experiments, and Lavoisier and Laplace have replaced the 
block of ice by a more complicated apparatus, which is called the ice 
calorimeter. Fig. 263 gives a perspective view of it, and fig. 264 repre¬ 
sents a section. It consists of three concentric tin vessels; in the central 
one is placed the body M, whose specific heat is to be determined, while 
the two others are filled with pounded ice. The ice in the compartment 
A is melted by the heated body, while the ice in the compartment B cuts 
off the heating influence of the surrounding atmosphere. The two stop¬ 
cocks E and D give issue to the water which arises from the liquefaction 
of the ice. 



Fig. 262 . 


SPECIFIC HEAT. 


-388] 


351 


In order to find the specific heat of a body by this apparatus, its 
weight, m, is first determined ; it is then raised to a given temperature, 
t , by keeping it for some time in an oil or water bath, or in a current of 
steam. Having been quickly brought into the central compartment, the 
lids are replaced and covered with ice, as represented in the figure. The 
water which flows out by the stopcock D, is collected. Its weight, P, is 
manifestly that of the melted ice. The calculation is then made as in the 
preceding case. 

There are many objections to the use of this apparatus. From its size 
it requires some quantity of ice, and a body, M, of large mass; while the 
experiment lasts a considerable time. A certain weight of the melted 
water remains adhering to the ice, so that the water which flows out from 
D does not exactly represent the weight of the melted ice. 



Fig. 263. 


Fig. 264. 


388. Method of mixtures. —In determining the specific heat of a 
solid body by this method, it is weighed and raised to a known tempera¬ 
ture, by keeping it, for instance, for some time in a closed space heated by 
steam ; it is then immersed in a mass of cold water, the weight and tem¬ 
perature of which are known. From the temperature of the water after 
mixture the specific heat of the body is determined. 

Let M be the weight of the body, T its temperature, c its specific 
heat; and let m be the weight of the cold water, and t its temperature. 

As soon as the heated body is plunged into the water, the temperature 
of the latter rises until both are at the same temperature. Let this tem¬ 
perature be e. The heated body has been cooled by T — 0 ; it has, there¬ 
fore, lost a quantity of heat, M (T — 0) c. The cooling water has, on the 















352 


ON HEAT. 


[ 389 - 


contrary, absorbed a quantity of beat equal to m (0 — t), for the specific 
heat of water is unity. Now the quantity of heat given up by the body 
is manifestly equal to the quantity of heat absorbed by the water; that is, 
M (T — 0) c = m (0 — t), from which 

m (0 — t) 

c ~ M (T— ej’ 

An example will illustrate the application of this formula. A piece of 
iron weighing 60 ounces, and at a temperature of 100° C., is immersed in 
180 ounces of water whose temperature is 19° C. After the temperatures 
have become uniform, that of the cooling water is found to be 22° C. 
What is the specific heat of the iron P 

Here the weight of the heated body, M, is 60, the temperature T is 
100°, c is to be determined ; the temperature of mixture, 0, is 22°, the 
weight of the cooling water is 180, and its temperature 19°. Therefore 
e= 180 (22 - 19) = 0 = 0 , U53 . 

60 (100 - 22) Vrf 

389. Corrections.— The vessel containing the cooling water is usually 
a small cylinder of silver or brass, with thin polished sides, and is sup¬ 
ported by some badly conducting arrangement. It is obvious that this 
vessel, which is originally at the temperature of the cooling water, shares 
its increase of temperature, and in accurate experiments this must be al¬ 
lowed for. The decrease of temperature of the heated body is equal to 
the increase of temperature of the cooling water, and of the vessel in which 
it is contained. If the weight of this latter be m', and its specific heat c', 
its temperature, like that of the water, is t : consequently the previous 
equation becomes 

Me (T — 0) — m (0 — t ) + m' c' (0 — t ), 
from which, by obvious.transformations, 


_ (m m' c(0 — t) 

M (T — e) 

Generally speaking, the value, m' c', is put = ju; that is to say, is 
the weight of water which would absorb the same quantity of heat as the 
vessel. This is said to be the reduced value in water of the vessel, or the 
water equivalent. The expression accordingly becomes 

( m + M ) ( e — t ) 

M (T — 0) * 

In accurate experiments, it is necessary also to allow for the heat ab¬ 
sorbed by the glass and mercury of the thermometer, by introducing into 
the equation their values reduced on this principle. 

In order to allow for the loss of heat due to radiation, a preliminary ex- 





SPECIFIC HEAT. 


353 


-390] 

periment is made with the body whose specific heat is sought, the only 
object of which is to ascertain approximately the increase of temperature 
of the cooling; water. If this increase be 10°, for example, the tempera¬ 
ture of the water is reduced by half this number—that is to say, 5° below 
the temperature of the atmosphere, and the experiment is then carried out 
in the ordinary manner. 

By this method of compensation, first introduced by Rumford, the water 
receives as much heat from the atmosphere during the first part of the 
experiment as it loses by radiation during the second part. 



Fig. 265. 


390. Re&nault’s apparatus for determining- specific heats..— 

Fig. 265 represents one of the forms of apparatus used by M. Regnault in 
determining specific heats by the method of mixtures. 

The principal part is a water-bath, AA, of which fig. 266 represents 
a section. It consists of three Concentric compartments ; in the central 
one there is a small basket of brass wire, c, containing fragments of the 










































354 


ON HEAT. 


[ 391 - 

substance to be determined, in the middle of which is placed a thermo¬ 
meter, T. The second compartment is heated by a current of steam 
coming through the tube, e, from a boiler, B, and passing into a worm, a, 
where it is condensed. The third compartment, ii, is an air chamber to 
hinder the loss of heat. The water bath, AA, rests on a chamber, K, 
with double sides, EE, forming a jacket, which is kept full of cold 
water in order to exclude the heat from AA, and from the boiler B. The 
central compartment of the water bath is closed by a damper, r , which 
can be opened at pleasure, so that the basket, c, can be lowered into the 
chamber K. 

On the left of the figure is represented a small and very thin brass ves¬ 
sel, D, suspended by silk threads on a small carriage, which can be moved 
out of, or into, the chamber K. This vessel, which serves as a calorimeter, 
contains water, in which is immersed a thermometer, t. Another ther¬ 
mometer at the side, t gives the temperature of the air. 

When the thermometer T shows that the temperature of the substance 
in the bath is stationary, the screen h is raised, and the vessel D moved to 
just below the central compartment of the water bath. The damper r is 
then withdrawn, and the basket c and its contents are lowered into the 
water of the vessel D, the thermometer T remaining fixed in the cork. 
The carriage and the vessel D are then moved out, and the water agitated 
until the thermometer t becomes stationary. The temperature which it 
indicates is d. This temperature known, the rest of the calculation is 
made in the manner described in art. 389, care being taken to make all the 
necessary corrections. 

In determining the specific heat of substances—phosphorus, for instance 
—which could not be heated without causing them to melt, or undergo 
some change which would interfere with the accuracy of the result, 
Regnault adopted an inverse process: he cooled them down to a tempe¬ 
rature considerably below that of the water in the calorimeter, and then 
observed the diminution in the temperature of the latter, which resulted 
from immersing the cooled substance in it. 

To ascertain the specific heat of bodies, such as potassium, where the 
use of water is quite inapplicable, the determination is made in another 
liquid, such as turpentine or benzole, the specific heat of which is known. 

391. Method of cooling-.— Equal weights of different bodies whose 
specific heats are different, will occupy different times in cooling through 
the same number of degrees. Dulong and Petit have applied this princi¬ 
ple in determining the specific heats of bodies in the following manner: A 
small polished silver vessel is filled with the substance in a state of fine 
powder, and a thermometer placed in the powder, which is pressed down. 
This vessel is heated to a certain temperature, and is then introduced into 
a copper vessel, in which it fits hermetically. This copper vessel is ex- 


SPECIFIC HEAT. 


355 


- 393 ] 

hausted, and maintained at the constant temperature of melting ice, and 
the time noted which the substance takes in falling through a given range 
of temperature, from 15° to 5° for example. The times which equal 
weights of different bodies require for cooling through the same rauge of 
temperature are directly as their specific heats. 

Regnault has proved that with solids this method does not give trust¬ 
worthy results ; it assumes, which is not quite the case, that the cooling 
in all parts is equal, and that all substances part with their heat to the 
silver case with equal facility. The method may, however, be employed 
with success in the determination of the specific heat of liquids. 

392. Specific heat of liquids.— The specific heat of liquids may be 
determined either by the method of cooling, by that of mixtures, or by 
that of the ice calorimeter. In the latter case they are contained in a 
small metal vessel, or a glass tube, which is placed in the compartment 
M (fig. 264), and the experiment then made in the usual manner. 

It will be seen from the following table that water and oil of turpentine 
have a much greater specific heat than that of other substances, and more 
especially than the metals. It is from its great specific heat that water 
requires a long time in being heated or cooled, and that for the same 
weight and temperature it absorbs or gives out far more heat than other 
substances. This double property is applied in the hot water apparatus, 
of which we shall presently speak, and it plays a most important part in 
the economy of nature. 

393. Mean specific heats of solids and liquids between 0° and 

100°.—By means of the method of mixture and of that of cooling, M. 
Regnault has determined the specific heats of a number of bodies. The 
following table contains the numbers obtained for the bodies usually met 
with in the arts: 


Substances. 

Specific 

heats. 

Substances. 

Specific 

heats. 

Water. 

1-00000 

Nickel. 

. 0-10863 

Turpentine. 

0-42590 

Cobalt. 

0-10696 

Calcined animal charcoal 

0-26085 

Zinc. 

. 0-09555 

Wood charcoal . . 

0-24111 

Copper. 

. 009515 

Sulphur. 

0-20259 

Brass. 

. 0-09391 

Graphite. 

0-20187 

Silver. 

. 0-05701 

Thermometer glass . . 

0-19768 

Tin. 

. 005623 

Phosphorus .... 

018949 

Antimony .... 

. 005077 

Diamond. 

0-14687 

Mercury. 

. 003332 

Grey iron ..... 

0-12983 

Gold . 

. 003244 

Steel. 

0-11750 

Platinum .... 

. 0 03244 

Iron ... . * . . . . 

0-11379 

Bismuth ...» 

. 0-03084 









356 


ON HEAT. 


[393- 

These numbers represent the mean specific heats between 0° and 100°. 
Dulong and Petit’s investigations have, however, shown that the specific 
heats increase with the temperature. Those of the metals, for instance, 
are greater between 100° and 200° than between zero and 100°, and are 
still greater between 200° and 300°. That is to say, a greater amount of 
heat is required to raise a body from 200° to 250°, than from 100° to 150°, 
qnd still more than from zero to 50°. For silver, the mean specific heat 
between 0° and 100° is 0-0557, while between 0° and 200° it is 0 0611. 
The specific heat of platinum for any temperature may be expressed by 
the formula 0-0328 + 0-0000042 t, where t is the temperature : and that 
of water by the formula 1 + 0-00004 t + 0-0000009 t 2 . 

The increase of specific heat with the temperature is greater as bodies 
are nearer their fusing point. Any action which increases the density 
and molecular aggregation of a body, diminishes its specific heat. The 
specific heat of copper is diminished by its being hammered, but it regains 
its original value after the metal has been again heated. 

The specific heat of a liquid increases with the temperature much more 
rapidly than that of a solid. Water is, however, an exception ; its specific 
heat increases less rapidly than does that of solids. 

A substance in the liquid state has a greater specific heat than when 
it is solid; thus, melted tin has the specific heat 0-0637, while that of 
solid tin is only 0-05623. The specific heat of liquid bromine is 0-111, 
that of solid bromine being 0-081. The difference in the case of water is 
greater. Its specific heat is 1, that of ice, according to Person, being 
0-504. In the gaseous state a body has a higher specific heat than in the 
liquid state. 

Pouillet used the specific heat of platinum for measuring high degrees 
of heat. Supposing 200 ounces of platinum had been heated in a furnace 
and had then been placed in 1,000 ounces of water, the temperature of 
which it had raised from 13° to 20°. From the formula we have M=200, 
m — 1000 ; 6 is 20, and t is 13. The specific heat of platinum is 0*033, 
and we have, therefore, from the equation, 

Me (T — e) = m (0 — t ), 

T _ m(0 — t) -f Mc0 7000 + 132 7132 1AQAO 
1 -Mo-=- =W= 1080 • 


It is found, however, that the specific heat of platinum at temperatures 
of about 1000° is 0-0373 ; if this value, therefore, be substituted for c in 
the above equation, 


T _ 7159-2 
7-46 


=958° 0. 


By this method, which requires great skill in the experimenter, 




SPECIFIC HEAT. 


357 


- 394 ] 

Pouillet determined a series of high temperatures. He found, for ex¬ 
ample, the temperature of melting iron to be 1500° to 1600° C. 

394. Dulong and Petit’s law. —A knowledge of the specific heat of 
bodies has become of great importance, in consequence of Dulong and 
Petit’s discovery of the remarkable law, that the product of the specific 
heat of any element into its atomic weight is a constant number, a law 
which may also he enunciated by saying that the specific heats of simple 
bodies are inversely as their atomic weights. Thus, taking the atomic weight 
of iron at 28, its specific heat 0T1379, and the product 3-186 ; the atomic 
weight of nickel is 29*5, its specific heat 0*10863, product 3 204; the 
atomic weight of hydrogen is 1, its specific heat 3-2, and the product is 3*2. 

Regnault, who determined the specific heats of a large number of 
elements with great care, confirmed Dulong and Petit’s law, hut he found 
that the number, instead of being constant, as Dulong and Petit had sup¬ 
posed, varies between 2 95 and 3*41. These variations may depend partly on 
the difficulty of obtaining the elements quite pure, and partly on the errors 
incidental to the determinations of the specific heats, and of the equi¬ 
valents. But the specific heats of bodies vary with the state of aggrega¬ 
tion, and also with the limits of the temperature at which they are 
determined. Some, such as potassium, have been determined at tempe¬ 
ratures very near their fusing points; others, like platinum, at great 
distances from these points. And, doubtless, the principal reason of the 
discrepancies is the fact that the determinations have not been made 
under identical physical conditions, and at temperatures equally distant 
from the fusing point. 

The equivalents of the elements represent the relative weights of equal 
numbers of »atoms of these bodies, and the product, pc, of the specific 
heat, c, into the equivalent, p, is the atomic specific heat, or the quantity 
of heat necessary to raise the temperature of the same number of atoms 
by one degree ; and Dulong and Petit’s law may be thus expressed; the 
same quantity of heat is needed to heat an atom of all simple bodies to the 
same eoctent. 

The atomic heat of a body, when divided by its specific heat, gives the 
equivalent of a body. Regnault has even proposed to use this relation 
as a means of determining the equivalent, and it certainly is of great 
service in deciding on the equivalent of a body in cases where the 
chemical relations permit a choice between two or more numbers. 

In compound bodies the law also prevails; the product of the specific 
heat into the equivalent is an almost constant number, which varies, 
however, with the different classes of bodies. Thus, for the class of 
oxides of the general formula RO, it is 1130, for the sesquioxides, R 2 0 3 , 
it is 27*15; for the sulphides, RS, it is 18-88; and for the carbonates, 
RCO 3 , it is 21-54. 



358 


ON HEAT. 


[395- 

The law may be expressed in the following general manner: With 
compounds of the same formula, and of a similar chemical constitution , the 
product of the atomic weight into the specific heat is a constant quantity. 
This includes Dulong and Petit’s law as a particular case. 

395. Specific heat of compound bodies. —In order to deduce the 
specific heat of a compound from that of its elements, M. Woestyn has 
made the following hypothesis : he assumes that an element in entering 
into combination with others to form a compound body, retains its own 
specific heat, so that if p, p', p", .... represent the atomic weights of 
the elements, and P that of the compound ; c, c', c", .... C, the cor¬ 
responding specific heats, while n, n', n", .... are the numbers of atoms 
of these simple bodies which make up the molecule of the compound, 
the relation obtains: 

PC — npc + n'p'c’ -f- n' r p"c'' -f . . . . 

M. Woestyn has found that the results obtained by calculating, on 
this hypothesis, the specific heats of the sulphides, iodides and bromides, 
agree with experimental results. 

396. Specific beat of gases. —The specific heat of a gas may be 
referred either to that of water or to that of air. In the former case, it 
represents the quantity of heat necessary to raise a given weight of the 
gas through one degree, as compared with the heat necessary to raise the 
same weight of water one degree. In the latter case it represents the 
quantity of heat necessary to raise a given volume of the gas through one 
degree, compared with the quantity necessary for the same volume of air 
treated in the same manner. 

De la Roche and Berard determined the specific heats of gases in refer¬ 
ence to water by causing known volumes of a given gas under constant 
pressure, and at a given temperature, to pass through a spiral glass tube 
placed in water. From the increase in temperature of this water, and 
from the other data, the specific heat was determined by a calculation 
analogous to that given under the method of mixtures. The same 
physicists also determined the specific heats of different gases relatively 
to that of air, by comparing the quantities of heat which equal volumes 
of a given gas, and of air at the same pressure and temperature, im¬ 
parted to equal weights of water. Subsequently to these researches, 
De la Rive and Marcet have applied the method of cooling to the same 
determination; and still more recently Regnault has made a series of 
investigations on the calorific capacities of gases and vapours, in which he 
has adopted, but with material improvements, the method of De la Roche 
and Berard. He has thus obtained the following results for the specific 
heats of the various gases and vapours, compared first with an equal 


SPECIFIC HEAT. 


359 


- 396 ] 

weight of water taken as unity; secondly, with that of an equal volume 
of air, referred, as before, to its own weight of water taken as unity. 

Specific heats. 



Air .... 

Equal 

weights. 

. 0*2374 

Equal 

volumes. 

0-2374 


Oxygen 

. 0-2175 

0-2405 

Simple 

Nitrogen 

. 0-2438 

0-2370 

gases 

Hydrogen 

. 3-4090 

0-2359 


- Chlorine 

. 0-1210 

0-2962 


r Binoxide of nitrogen 

. 0-2315 

0-2406 


Carbonic oxide 

. 0-2450 

0-2370 

Compound 

Carbonic acid 

. 0-2163 

0-3307 

gases 

Hydrochloric acid 

. 0-1845 

0-2333 


Ammonia 

. 0-5083 

0-2966 

. 

- Olefiant gas . 

. 0-4040 

0-4106 


r Water .... 

. 0-4805 

0-2984 


Ether .... 

. 0-4810 

1-2296 


Alcohol 

. 0-4534 

0-7171 

Vapours 

Turpentine . 

. 0-5061 

2-3776 


Bisulphide of carbon 

. 0-1570 

0-4140 


' Benzole 

. 0-3754 

1-0114 


In making these determinations the gases were under a constant pres¬ 
sure, hut variable volume; that is, the gas as it was heated could expand, 
and this is called the specific heat under constant pressure. But if the gas 
when being heated is kept at a constant volume, its pressure or elastic force 
then necessarily increasing, it has a different capacity for heat • this latter 
is spoken of as the specific heat under constant volume. That this latter is 
less than the former is evident from the following considerations. 

Suppose a given quantity of gas to have had its temperature raised t°, 
while the pressure remained constant, this increase of temperature will 
have been accompanied by a certain increase in volume. Supposing 
now, that the gas is so compressed as to restore it to its original volume, 
the result of this compression will be to raise its temperature again to a 
certain extent, say t'°. The gas will now be in the same condition as 
if it had been heated, and not been allowed to expand. Hence, the same 
quantity of heat which is required to raise the temperature of a given 
weight of gas, t °, while the pressure remains constant and the volume 
alters, will raise the temperature t -f t' degrees if it is kept at a constant 
volume but variable pressure. The specific heat, therefore, of a gas at 
constant pressure, <\, is greater than the specific heat under constan 

volume c, and they are to each other as t -j- t': t y that is -' = —. 










360 


ON HEAT. 


[ 397 - 

It is not possible to determine by direct means tbe specific beat of gases 
under constant volume with even an approach to accuracy ; and it has 
always been determined by some indirect method, of which the most ac¬ 
curate is based on the theory of the propagation of sound (200). The 
latest determination made on this basis gives the number 1*414 for the 

value of — 
c 

397. latent heat of fusion. —Black was the first to observe that dur¬ 
ing the passage of a body from the solid to the liquid state, a quantity of 
heat disappears, as far as thermometric effects are concerned, and which is 
accordingly said to become latent. 

In one experiment he suspended in a room at the temperature 8°*5, two 
thin glass flasks, one containing water atO°, and the other the same weight 
of ice at 0°. At the end of half an hour the temperature of the water had 
risen 4°, that the ice being unchanged, and it was 10£ hours before the ice 
had melted and attained the same temperature. Now the temperature of 
the room remained constant, and it must be concluded that both vessels 
received the same amount of heat in the same time. Hence 21 times as 
much heat was required to melt the ice and raise it to 4°, as was sufficient 
to raise the same weight of water through 4°. So that the total quantity 
of heat imparted to the ice was 21x4 = 84, and as of this only 4 was 
used in raising the temperature, the remainder, 80, was used in simply 
melting the ice. 

He also determined this latent heat by immersing 119 parts of ice at 
0° in 135 parts of water at 87-7° C. He thus obtained 254 parts of water 
at 11*6° O. Taking into account the heat received by the vessel in which 
the liquid was placed, he obtained the number 79*44 as the latent heat of 
liquidity of ice. 

We may thus say : 

Water at 0° = Ice at 0° -f latent heat of liquefaction. 

The method which Black adopted is essentially that which is now used 
for the determination of latent heats of liquids j it consists in placing the 
substance under examination at a known temperature in the water (or 
other liquid) of a calorimeter, the temperature of which is sufficient to 
melt the substance if it is solid, and to solidify it if liquid, and when 
uniformity of temperature is established in the calorimeter this tempera¬ 
ture is determined. Thus, to take a simple case, suppose it is required 
to determine the latent heat of liquidity cf ice. Let M be a certain 
weight of ice at zero, and m a weight of water at t° sufficient to melt the 
ice. The ice is immersed in the water, and as soon as it has melted the 
final temperature, 0°, is noted. The water, in cooling from t° to 0°, has 
parted with a quantity of heat, m(t —0). If x be the latent heat of the 
ice, it absorbs, in liquefying, a quantity of heat, M.r; but, besides this, 
the water which it forms has risen to the temperature 6°, and to do so 


LATENT HEAT OF FUSION. 


361 


- 397 ] 

has required a quantity of heat represented by M 0 . We thus get the 
equation 

M.r -f M 0 = m(t— 0 ), 
from which the value of x is deduced. 

By this method, and avoiding all sources of error, MM. Desains and De 
la Provostaye found that the latent heat of the liquefaction of ice is 79-25 ; 
that is, a pound of ice, in liquefying, absorbs the quantity of heat which 
would be necessary to raise 79-25 pounds of water, 1°, or, what is the same 
thing, one pound of water from zero to 79-25°. 

This method is thus essentially that of the method of mixtures; the 
same apparatus may be used, and the same precautions are required in the 
two cases. In determining the latent heat of liquidity of most solids, the 
different specific heats of the substance require to be taken into account. 
In such a case, let m be the weight of the water in the calorimeter (the 
water equivalents of the calorimeter and thermometer supposed to be in¬ 
cluded) ; M the weight of the substance operated on ; t the original and 
0 the final temperature of the calorimeter; T the original temperature of 
the substance; % its melting (or freezing) point; C the specific heat of 
the substance in the solid state between the temperatures C and 0 ; c its 
specific heat in the liquid state between the temperatures T and C ; and 
let L be the latent heat sought. 

If the experiment is made on a melted substance which gives out heat 
to the calorimeter and solidifies it (it is taken for granted that a body 
gives out as much heat in solidifying as it absorbs in liquefying), it is 
plain that the quantity of heat absorbed by the calorimeter, m(6 — t ), is 
made up of three parts: first, the heat lost by the substance in cooling 
from its original temperature T to the solidifying point % ; secondly, the 
heat given out in solidification L ; and thirdly, the heat it loses in sink¬ 
ing from its solidifying point C to the temperature of the water of the 
calorimeter. That is: 

m( 0 —0=M (T—£)c+L x (&— 0 )C] 
whence, . 7 . 

L = (T— ®) c— <rc— e)C. 


M. Person, who has made several researches on this subject, ha& 
obtained the following numbers for the latent heats of fusion of several 
bodies: 


Water. 

. . 79-25 

Bismuth. 

. 12-64 

Nitrate of sodium . 

. . 62-97 

Sulphur. 

. 9-37 

Zinc. 

. 28-13 

Lead. 

. 5-37 

Silver. 

. . 21-07 

Phosphorus .... 

. 5-03 

Tin. 

. . 14-25 

D’Arcet’s alloy . . . 

. 4-50 

Cadmium. 

, . 13-66 

Mercury. 

. 2-83 


B 













362 


ON HEAT. 


[ 398 - 

These numbers represent the number of degrees through which a 
pound of water would be raised by a pound of the body in question in 
passing from the liquid to the solid state; or, what is the same thing, the 
number of pounds of water that would be raised 1° C. by one of the bodies 
in solidifying. 

398. Determination of the latent heat of vapours. —Liquids, as 

we have seen, in passing into the state of vapour, absorb a very conside¬ 
rable quantity of heat, which is termed latent heat of vaporisation. In 
determining the heat absorbed in liquids, it is assumed that a vapour, in 
liquefying, gives out as much heat as it had absorbed in becoming con¬ 
verted into vapour. 

The method employed is essentially the same as that for determining 
the specific heat of gases. Fig. 267 represents the apparatus used by 
M. Despretz. The vapour is produced in a retort, C, where its tempera¬ 
ture is indicated by a thermometer. It passes into a worm immersed in 
cold water, where it condenses, imparting its latent heat to the condens¬ 
ing water in the vessel B. The 
condensed vapour is collected in 
a vessel, A, and its weight repre¬ 
sents the quantity of vapour which 
has passed through the worm. 
The thermometers in B give the 
change of temperature. 

Let M be the weight of the 
condensed vapour, T° its tempe¬ 
rature on entering the worm, 
which is that of its boiling point, 
and x the latent heat of vaporisa¬ 
tion. Similarly let m be the 
weight of the condensing water 
(comprising the weight of the 
vessel B and of the worm SS 
reduced in water), let t° be the temperature of the water at the beginning 
and 0° its temperature at the end of the experiment. 

It is to be observed that, at the commencement of the experiment, 
the condensed vapour passes out at the temperature t°, while at the 
conclusion its temperature is 6°; we may, however, assume that its 

mean temperature during the experiment is The vapour M 

after its condensation has therefor^ parted with a quantity of heat 
M ^T — c ’ h ea t disengaged in liquefaction is repre¬ 

sented by Mx The quantity of heat absorbed by the cold water, the 













363 



Fig. 268 . 

398rt. Pavre and Silbermann’s calorimeter. The apparatus (fig. 
268) furnishes a very delicate means of determining the calorific capacity 
of liquids, latent heats of evaporation, and the heat disengaged in chemi¬ 
cal actions. 

The principal part is a spherical iron reservoir, A, full of mercury, of 

r 2 


-398 «] FAVRE AND SILBERMANN’S CALORIMETER. 

worm, and the vessel is m(0—t). Therefore, 

Ma:+M (T —<? = m(e— 0; 

from which x is obtained. M. Despretz found that the latent heat of 
aqueous vapour at 100° is 540 ; that is, a pound of water at 100° absorbs 
in vaporising as much heat as would raise 540 pounds of water through 
1°. M. Regnault found the number 537, and MM. Favre and Silbermann 
535-8. 

As in the case of the latent heat of water we may say, 

Steam at 100° = Water at 100° + latent heat of gaseification. 


























364 


ON HEAT. 



which it holds about 50 pounds, and represents, therefore, a volume of 
more than half a gallon. On the left there are two tubulures, B, in 
which are fitted two sheet iron tubes or muffles , projecting into the interior 
of the bulb. Each can be fitted with a glass tube for containing the sub¬ 
stance experimented upon. In most cases one muffle and one glass tube are 
enough; the two are used when it is desired to compare the quantities of 
heat produced in two different operations. In a third vertical tubulure, C, 
there is also a muffle, which can be used for determining calorific capacities 
by Regnault’s method (390), in which case it is placed beneath the r of 
fig. 264. 

The tubulure d contains a steel piston; a rod, turned by a 
handle m , and which is provided with a screw thread, transmits a verti- 


n 



Fig. 269, 


cal motion to the piston ; but by a peculiar mechanism, gives it no rota¬ 
tory motion. In the last tubulure is a glass bulb, a, in which is a lono- 
capillary glass tube, bo , divided into parts of equal capacity. 

It will be seen from this description that the mercury calorimeter is 
nothing more than a thermometer with a very large bulb and a very 
capillary stem : it is therefore very delicate. It differs, however, from a 
thermometer in the fact that the divisions do not indicate the temperature 
of the mercury in the bulb, but the number of thermal imits imparted to 
it by the substances placed in muffle. 

This gradation is effected as follows:—By working the piston the 
mercury can be made to stop at any point of the tube, bo, at which it is 
desired the graduation should commence. Having then placed in the 
iron tube a small quantity of mercury which is not afterwards changed, a 
thin glass tube, e, is inserted, which is kept fixed against the buoyancy 




RADIATION OF IIEAT. 


365 


- 399 ] 

of the mercury by a small wedge not represented in the figure. The 
tube being thus adjusted, the point of a bulb tube (see fig. 269) is intro¬ 
duced containing water, which is raised to the boiling point: turning 
the position of the pipette, then, as represented on n', a quantity of the 
liquid flows into the test tube. 

The heat which is thus imparted to the mercury makes it expand, the 
column of mercury in bo is lengthened by a number of divisions, which 
we shall call n. If the water poured into the test glass be weighed, and 
if its temperature be taken when the column, bo, is stationary, the pro¬ 
duct of the weight of the water into the number of degrees through 
which it has fallen indicates the number of thermal units which the 
water gives up to the entire apparatus (386). Dividing by n this 
number of thermal units, the quotient gives the number, a, of thermal 
units corresponding to a single division of the tube bo. 

In determining the specific heat of liquids, a given weight, M, of the 
liquid in question is raised to the temperature T, and is poured in the 
tube C. Calling the specific heat of the liquid C, its final temperature 
6, and n the number of divisions by which the mercurial column bo has 
advanced, we have, 

Mc(T—0) = na from which = ——- 
v ' M(T—0) 

The boards represented round the apparatus are hinged so as to form a 
box which is lined with eider down or wadding to prevent any loss of 
heat. It is closed at the top by a board which is provided with a 
suitable case also lined, which fit over the tubulures, d and a. A small 
magnifying glass which slides along the latter enables the divisions on 
scale to be read off. 

399. Examples. —I. What weight of ice at zero must be mixed with 
9 pounds of water at 20° in order to cool it to 5° ? 

Let M be the weight of ice necessaiy; in passing from the state of ice 
to that of water at zero, it will absorb SOM thermal units; and in order 
to raise it from zero to 5°, 5M thermal units will be needed. Hence the 
total heat which it absorbs is 80M+5M=85M. On the other hand, the 
heat given up by the water in cooling from 20° to 5°, is 9 X (20—5)=135. 
Consequently, 

85M = 135 ; from which, M = 1*588 pounds, 

II. What weight of steam at 100° is necessary to raise the temperature 
of 208 pounds of water from 14° to 32° P 

Let p be the weight of the steam. The latent heat of steam is 540°, 
and consequently p pounds of steam in condensing into water give up a 
quantity of heat, 540 p, and form p pounds of water at 100°. But the tem¬ 
perature of the mixture is 32°, and therefore p gives up a further quantity 


3GG 


ON HEAT. 


[ 400 - 

of heat ;?(100 —32)=68p, for in this case c is unity. The 208 pounds of 
water in being heated from 14° to 32° absorb 208(32 14) = *j 744 units. 

Therefore 

540/9 -f- 68/; = 3744 ; from which p = 6T58 pounds. 


CHAPTER X. 

STEAM ENGINES. 

400. Steam engines. —Steam engines are machines in which the elastic 
force of aqueous vapour is used as motive force. In the ordinary engines 
the alternate expansion and condensation of steam imparts to a piston an 
alternating rectilinear motion, which is changed into a circular motion by 
means of various mechanical arrangements. 

Every steam engine consists essentially of two distinct parts : the ap¬ 
paratus in which the vapour is produced, and the engine proper. AN e 
shall first describe the former. 

401. steam boiler.— The boiler is the apparatus in which steam is 
generated. Fig. 270 represents a cylindrical boiler, such as is com- 



Fig. 270. 


monlv used in France, and which, in this country, is known as the French 
boiler. Boilers of this kind are used for a fixed engine ; those of locomo¬ 
tives and of steam vessels are very different. 

It is a long wrought iron cylinder, with hemispherical ends, beneath 
which there are two smaller cylinders of the same material, and commu¬ 
nicating with the boiler by two tubes. Only one of these cylinders is 































STEAM ENGINES. 


- 402 ] 


3G7 


represented in the figure. They are called heaters, and are quite full of 
water, while the boiler is only about half full. 

Below these heaters is the fire. The smoke and heated air, after hav¬ 
ing circulated about the heaters and the boiler, escape into the atmosphere 
by means of a high chimney. 


Explanation of figure 270. 

A. Tube which conducts the steam to the tube, c, of the valve chest 
(fig. 272, page 371). 

B. Tube by which the steam passes to a manometer or pressure gauge, 
which indicates the pressure of vapour in the boiler. 

C. Feed pipe of the boiler. 

D. Safety whistle , so called because it gives a whistle when there is 
not enough water in the boiler, a circumstance which might produce an 
accident. As long as the level of the water is not too low in the boiler, 
the vapour does not pass into the whistle, but if the level sinks below a 
certain point, a small float, which is not represented in the figure, and 
which closes the bottom of the whistle, sinks, and the steam escapes; in 
so doing it grazes against the edge of a metallic plate, which it sets in 
vibration, and produces the sharp sound. This steam whistle is the 
sound heard frequently on railways; it is u-ed as a signal in locomotives. 

F. Float, to indicate the level of the water in the boiler. It consists 
of a rectangular piece of stone, partially immersed in water, as seen 
through the space represented as left open. This stone, which is sus¬ 
pended at one end of a lever, is kept poised by the loss of weight which 
it sustains by immersion in water, and by a weight, p, at the other end 
of the lever. As long as the water is at the desired height, the lever 
which sustains the float remains horizontal, but it sinks when there is 
too little water, and rises in the contrary direction when there is too 
much. Guided by these indications, the stoker can regulate the supply 
of water. 

G. Cylindrical wrought iron boiler. 

H. Heaters , opposite each other. 

O. Chimney. 

P. Weight which loads the safety valve. 

p. Counterpoise of the float. 

R. Fire door. 

S. Safety valve, described under Papin's digester (318). 

T. Man-hole, an aperture by which the boiler can be repaired and 
cleaned. 

402. Double action, or Watt’s engine. —In the double acting steam 
engine the steam acts alternately above and below the piston. It is also 
known as Watt's engine , from its illustrious inventor. 


3G8 


ON HEAT. 


[ 402 - 

We shall first give a general idea of this engine, and shall then describe 
each part separately. On the left of the fig. 271, is the cylinder which 
receives the steam from the boiler. A part of its side is represented 
as being left open, and a piston, P, can be seen which is moved alter¬ 
nately up and down by the pressure of the steam above or below the 
piston. By the piston rod, A, this motion is transmitted to a huge iron 
lever, L, called the beam, which is supported by four iron columns. 



Pig. 271. 


The beam transmits its motion to a connecting rod, I, working on a crank, 
K, to which it imparts a continuous rotatory motion. The crank is 
fixed to a horizontal shaft, which turns with it, and by means of wheels 
or endless bands, this shaft sets in motion various machines, such as 
spinning frames, saw mills, lathes, &c. 

On the left of the cylinder is a valve chest, where, by a mechanism, 
which will presently be described, the steam passes alternately above 

































































STEAM ENGINES. 


369 


- 402 ] 

and below the piston. Now, after its action on either face of the piston 
it must disappear, for otherwise a pressure would be exerted in two 
opposite directions, and the piston would remain at rest. To effect this, 
the steam, after it has acted on one side of the piston, passes into a vessel, 
0, called the condenser, into which cold water is injected. It is almost 
completely condensed there, and consequently, the pressure ceases in 
that part of the cylinder which is in communication with the condenser, 
and as there is now pressure on only one face of the piston, it either 
rises or sinks. 

The use of the condenser depends upon Watt’s law of vapours (309), 
that when two vessels communicating with each other, and containing 
saturated vapour, are at different temperatures, the tension is the same 
in both vessels, and is that corresponding to the temperature of the 
colder vessel. 

The injected water is rapidly heated by the condensation of the steam, 
and must be constantly renewed. This is effected by means of two 
pumps ; one, M, is called the air pump, and pumps, from the condenser, 
the heated water which it contains, and also the air which was dis¬ 
solved in the water of the boiler, and which passes with the steam into 
the cylinder and condenser; the other, R, is called the cold water 
pump, and forces cold water from a well, or from a river, into the con¬ 
denser. 

A third pump, Q, which is called the feed pump, utilises the heated 
water by forcing it from the condenser into the boiler. 

Double action steam engine. 

A. Piston rod connected with a parallel motion, and serving to trans¬ 
mit to the beam the upward and downward motion of the piston. 

B. Rod fixed to the cylinder, or elsewhere, and supporting the guiding 
arm or radius rod, C. 

C. Double guiding arm directing the parallel motion. 

DDDE. Rods forming at the end of the beam a parallel motion, to 
which is fixed the piston rod, and the object of which is to guide the 
motion of this rod in a straight line. 

F. Rod of the air pump, which removes from the condenser the air 
and heated water which it contains. 

G. Rod of the feed pump which forces into the boiler through the 
tube, S, the heated water pumped from the condenser. 

H. Rod of the cold water pump, which supplies the cold water neces¬ 
sary for condensation. 

I. Connecting rod, which transmits the motion of the beam to the crank. 

K. Crank, which imparts the motion of the rod to the horizontal shaft. 

r 3 


370 * ON HEAT. [ 403 - 

L. Beam, which moves on an axle in its middle, and transmits the 
motion of the piston to the connecting rod V. 

M. Cylinder of the air pump, in connection with the condenser 0. 

N. Reservoir for the heated water pumped by the air pump from the 
condenser. 

O. Condenser into which cold water is injected, to condense the steam 
after it has acted on the piston. 

P. Metallic piston, moving in a cast-iron cylinder; this piston receives 
the direct pressure of the steam, and transmits the motion to all parts of 
the machine. 

Q. Feeding force pump, which sends the water into the boiler. 

R. Cold water pump. 

S. Pipe by which the hot water from the feed-pump passes into the 
boiler. 

T. Pipe by which cold water from the reservoir of the pump, R, passes 
into the condenser. 

U. Pipe by which the steam from the cylinder passes into the condenser 
after acting on the piston. 

V. Large iron wheel, called the fly ivheel, which, by its inertia, serves 
to regulate the motion, especially when the piston is at the top or bottom 
of its course, and the crank, K, at its dead points. 

Y. Bent lever which imparts the motion of the eccentric, e, to the 
slide valve, b. 

Z. Eccentric rod. 

a. Aperture which communicates both with the upper and lower part 
of the cylinder, according to the position of the slide valve, and by which 
steam passes into the condenser through the tube U. 

b. Rod transmitting motion to the slide valve, by which steam is alter¬ 
nately admitted above and below the piston. This will be described in 
greater detail in the next article. 

c. Aperture by which steam reaches the valve chest. 

d. Stuffing box , in which the piston rod works without giving exit to 
the steam. 

e. Eccentric, fixed to the horizontal shaft, and rotating in a collar to 
which the rod Z is attached. 

m. Rod which connects the rod of the slide valve b to the bent lever 
Y, and to the eccentric. 

The lower part of the figure does not exactly represent the usual 
arrangement of the pumps. The drawing has been modified in order 
more clearly to show how these parts work, and their connection with 
each other. 

403. Distribution of the steam. Eccentric.— Figure 272 repre¬ 
sents the details of the valve chest or arrangement for the distribution of 


STEAM ENGINES. 


371 



Fig. 272. 

But the vapour which is above the piston passes through u and through 
a into the hole r, from which it enters the condenser. The piston is then 
onlv pressed upwards, and therefore ascends. 

When the slide is at the bottom of its course, the steam enters the 
cylinder by the aperture u, and passes from the lower part of the cylinder 
into the condenser by n and a. The piston consequently descends, and 
this motion goes on for each displacement of the slide. 

The upward and downward motion of the slide is effected by means of 
the eccentric. This is a circular piece, E, fixed to the horizontal shaft. 


- 403 ] 

steam. The steam from the boiler passes by a pipe, c, into a cast iron 
box on the side of the cylinder. In the sides of the cylinder there are 
three openings or ports, u , n , and a , of which u communicates by an 
internal conduit with the upper part of the cylinder, and n with the 
lower part. A slide, t, works over these three orifices. It is fixed to a 
vertical rod, b, which is jointed at m, to a larger rod, d , and receives an 
upward and downward motion from the bent lever, yoS, attached to the 
eccentric rod. When the slide is at the top of its course, as shown in 
the figure, the steam passes through n into the lower part of the cylinder, 
while the steam cannot pass through the orifice u , for it is covered by 
the slide. 
























372 


ON HEAT. 


[ 404 - 

A, but in such a manner that its centre does not coincide with the axis 
of this shaft. The eccentric works with gentle friction in a collar, C, to 
which the rod, ZZ, is fixed. The collar, without rotating, follows the 
motion of the eccentric, and receives an alternating motion in a horizontal 
direction, which it communicates to the lever Soy, and from thence to 
the slide. 

404. Single acting engine. —In a single acting engine the steam only 
acts on the upper face of the piston; a counterpoise fixed to the other 
end of the beam makes the piston rise. These engines were first con¬ 
structed by Watt for pumping water from mines, and are still used for 



Fig. 273. 


this purpose in Cornwall, and also for the supply of water to towns. 
They are preferred for these purposes from their simplicity, but for other 
uses they have been superseded by the double action engine. 

Fig. 273 represents a section. The beam, BB, is of wood, with 
wooden segments at each end, to which chains are attached. One of 
those chains is connected with the piston, and the other with the pump. 





































LOCOMOTIVE ENGINES. 


373 


- 405 ] 

On the right of the cylinder, A, is a valve chest, C, into which steam 
passes from the boiler by the tube T. There are three valves m, n, and 
o, on a vertical rod. The valves m and o open upwards, the valve n 
downwards. 

When m and o are open, as shown in the drawing, the steam passes 
through the tube, T, over the piston, while the steam, which is below, is 
forced into the condenser through the tube M. The piston therefore 
descends. The rod, on which are the valves m, n, and o, is connected 
with a bent lever, dck, moving on a joint c. This bent lever closes and 
opens the valves. For this purpose there are two catches, b and a, on a 
rod, F, connected with the beam, by means of which the rod works 
against the end of the bent lever. From the arrangement of the valves, 
as represented in the drawing, the piston sinks and carries with it the 
rod F, and, consequently, the catch strikes against the lever, and makes 
it sink at the same time as the rod dmo, the valves m and o then close, 
while n opens. 

The communication with the boiler as well as with the condenser is 
now cut off, and the steam which has made the piston sink passes below 
by the pipe C. As it presses equally on both faces, the piston would 
remain at rest, but it rises in consequence of the traction of the weight 
Q ; very little force is necessary for this; for the pump, the rod of which 
is fixed to the weight Q, only requires power when its piston rises. When 
the piston P is at the top of its course, the catch a strikes in turn against 
the lever k, raises the rod dmo , the steam again passes to the top of the 
piston, which again descends, and so on. 

405. Iiocomotives. — Locomotive engines , or simply locomotives , are 
steam engines which, mounted on a carriage, propel themselves by 
transmitting their motion to wheels. 

The parallel motion, the beam, and the fly wheel form no part of a 
locomotive. The principal parts are the framework , the fire box , the 
casing of the boiler, the smoke box , the steam cylinders with their valves, 
the driving wheels , and the feedpump. 

The framework is of oak, and rests on the axles of the wheels. Fig. 
274 represents the driver of the locomotive in the act of opening the 
regulator valve, I, placed in the upper part of the steam dome. In the 
lower part of this is the fire box, from whence the flame and the pro¬ 
ducts of combustion pass into the smoke box, Y, and then into the 
chimney, Q, after having previously traversed 125 brass Jvre tubes which 
pass through the boiler. The boiler, which connects the fire box with 
the smoke box, is made of iron, and is cylindrical. It is cased with 
staves of mahogany, which, being a bad conductor, prevents its cooling 
too rapidly. The steam passes from the boiler into two cylinders placed 
on either side of the smoke box. There, by means of a steam chest 


374 


ON HEAT. 


[ 405 - 

similar to tliat already described, it acts alternately on the two faces of 
the piston, the motion of which is transmitted to the axle of the large 
driving wheels. This arrangement of the slide valve is not seen in the 
drawing, because it is placed under the frame between the two 
cylinders. After having acted on the pistons the steam is forced 
through the blast pipe, E, into the chimney, thus increasing the 
draught. 

The motion of the pistons is transmitted to the two large driving 
wheels by two connecting rods, which, by means of cranks, connect the 
piston rods with the axles of the wheels. The alternating motion of 
the slide valve is effected by means of eccentrics placed on the axles of 
the large wheels. 

The feeding or supply of water to the boiler is obtained by means 
of two pumps placed under the frame, and moved by eccentrics. These 
pumps suck the water from a reservoir placed on the tender , which is 
a carriage attached to the locomotive for carrying the necessary water 
and coal. 


Explanation of figure 274. 

A. Copper tube, into which steam passes by the extremity I, and 
which, dividing at the other end into two branches, conveys the steam 
to the two cylinders which contain the pistons. 

B. Handle of the lever, by which the motion is reversed. It imparts 
motion to a rod, C, which communicates with the steam chest. 

C. Rod by which the motion is reversed. 

D. Lower part of the fire box and ash pan. 

E. Escape pipe for the steam after acting on the pistons. 

F. Iron cylinder containing a piston, P. There is one of these on each 
side of the engine, and the one in front is represented as being left open 
in order that the piston may be seen. 

G. Rod which opens the regulator valve I, in order to allow the steam 
to pass into the tube A. In the drawing the driver holds in his hand 
the lever which moves this rod. 

H. Cock for blowing off water from the boiler. 

I. Regulator valve, which is opened and closed by hand, so as to 
regulate the quantity of steam passing into the cylinders. 

K. Large rod connecting the head of the piston rod with the crank M 
of the driving wheel. 

L. Lamp for use by night. 

M. Crank, which transmits the motion of the piston to the axle of 
the large wheel. 

N. Coupling iron, by which the tender is attached. 

O. Fire door, by which coke is introduced. 


LOCOMOTIVE ENGINES. 


375 


- 405 ] 

P. Metallic piston, the rod of which is connected with the rod K. 

Q. Chimney, by which both steam and smoke escape. 



R, R. Feed pipes, through which the water in the tender passes to 
two force pumps, which are not shown in the drawing. 








































376 


ON HEAT. 


[ 406 - 


S. Guard for removing obstructions on the rails. 

T, T. Springs on which the engine rests. 

U, U. Iron rails fixed in chairs on wooden sleepers. 

V. Frame of the stuffing box of the cylinder. 

X, X. Cylindrical boiler, covered with mahogany staves, which, from 
the bad conductivity, hinder the loss of heat. The level of the water 
is just below the tube A. In the water are the tubes aa, through which 
the smoke and flame pass into the smoke box. 

Y, Smoke box, in which the fire tubes, a , terminate. 

Z, Z. Fire box, covered by a dome, into which the steam passes. 

a. Brass tubes, of w r hich there are 125, open at both ends, and ter¬ 
minating at one end in the fire box, and at the other in the smoke box. 
These tubes transmit to the water the heat of the fire. 

bb. Toothed segment, placed on the side of the fire box, and in which 
the arm of the lever B works. When the handle is pushed forward or 
pulled back as far as it can go, the engine is in full forward or backward 
gear respectively; the intermediate teeth give various rates of expansion 
in backward and forward motion, the middle tooth being a dead point. 
e. Cases containing springs by which the safety valves i are regulated. 
g. Signal whistle, 
t. Safety valves. 

, m, m. Steps. 

n. Glass tube, showing the height of water in the boiler. 
r, r. Guiding rods, for keeping the motion of the piston in a straight line. 
tj t. Blowing-off taps, for use when the pistons are in motion. 
v. Rod by which motion is transmitted to these taps. 

406. Reaction machines. Eolipyle. —In reaction machines steam 
acts by a reactive force like water in the hydraulic tourniquet (193). 
The idea of these machines is by no means new; Hero of Alexandria, 
who invented the fountain which bears his name, described the following 
apparatus, which is known as the reaction machine. 

It consists of a hollow metallic sphere which rotates on two pivots 
(fig. 275). At the ends of a diameter are two tubulures, pierced later¬ 
ally in opposite directions by orifices through which vapour escapes. 
Water is introduced into this apparatus by heating it, and then allowing 
it to cool in cold water. If the apparatus be then heated to boiling, the 
vapour disengaged imparts to it a rotatory motion, which is due to the 
pressure of the vapour on the side opposite to that from which it 
escapes. 

Numerous attempts have been made to use this reactive force of the 
vapour on a large scale as a motive force, and endeavours have also been 
made to cause steam to act by impulse by directing a jet of steam on 
the float board of a paddle wheel; but in both cases the steam exerts 


i 


VARIOUS KINDS OF STEAM ENGINES. 


- 408 ] 


377 


by no means so great an effect as is obtained when it acts by expansion 
on a piston. 

407. Various kinds of steam engines. —A low pressure engine is 
one in which the tension of the vapour does not much exceed an atmo¬ 
sphere : and a high pressure engine is one in which the pressure of the 
steam usually exceeds this amount considerably. Low pressure engines 
are mostly condensing engines ; in other words, they generally have a 
condenser where the steam becomes condensed after having acted on the 
piston: on the other hand, high pressure engines are frequently without a 
condenser; the locomotive is an example. 

If the communication between the cylinder and boiler remains open 



big. 2 75. 


during the whole motion of the piston, the steam retains essentially the 
same elastic force, and is said to act without expansion : but if, by a 
suitable arrangement of the slide valve, the steam ceases to pass into 
the cylinder when the piston is at § or f of its course, then the vapour 
expands ; that is to say, in virtue of its elastic force, which is due to 
the high temperature, it still acts on the piston and causes it to finish 
its course. Hence a distinction is made between expanding and non¬ 
expanding engines. 

408. Work of an engine. Horse-power.— The work of an engine 
is measured hy the mean pressure on the piston X area of the piston 
X length of the stroke. In England the unit of work is the foot-pound ; 
that is, the work performed in raising a weight of one pound through a 










378 


ON HEAT. 


[ 409 - 

height of a foot. Thus, to raise a weight of 14 pounds through a height 
of 20 feet would require 280 foot-pounds. In France the kilogrammeter 
is used; that is, the work performed in raising a kilogramme through a 
metre. This unit corresponds to 7'233 foot-pounds. 

The rate of work in machines is the amount of work performed in a 
given time; a second or an hour, for example. In England the rates 
of work are compared by means of horse-power, which is a conventional 
unit, and represents 550 foot-pounds in a second/ In France a similar 
unit is used, called the cheval-vapeur , which represents the work per¬ 
formed in raising 75 kilogrammes through one metre in a second. It is 
equal to about 542 foot-pounds per second. 


CHAPTER XI. 

SOURCES OE HEAT AND COLD. 

409. Different sources of heat.— The following different sources of 
heat may be distinguished : i. the mechanical sources, comprising fric¬ 
tion, percussion, and pressure ; ii. the physical sources —that is, solar 
radiation, terrestrial heat, the molecular actions, the changes of condition, 
and electricity ; iii. the chemical sources , or molecular combinations, and 
more especially combustion. 

MECHANICAL SOURCES. 

410. Heat due to friction. —The friction of two bodies, one against 
the other, produces heat, which is greater the greater the pressure and 
the more rapid the motion. For example, the axles of carriage wheels 
by their friction against the boxes often become so strongly heated as to 
take fire. By rubbing together two pieces of ice in a vacuum below 
zero, Sir H. Davy partially melted them. In boring a brass cannon 
Rumford found that the heat developed in the course of 24 hours was 
sufficient to raise 26£ pounds of water from zero to 100°, which repre¬ 
sents 2650 thermal units (384). At the Paris Exhibition, in 1855, 
MM. Beaumont and Mayer exhibited an apparatus, which consisted of 
a wooden cone covered with hemp, and moving with a velocity of 400 
revolutions in a minute, in a hollow copper cone, which was fixed and 
immersed in the water of an hermetically closed boiler. The surfaces 
were kept covered with oil. By means of this apparatus 88 gallons of 
water were raised from 10 to 130 degrees in the course of a few hours. 

In the flint and steel, the friction of the flint against the steel raises 




MECHANICAL SOURCES OF HEAT. 


- 411 ] 


379 


the temperature of the metallic particles, which fly off heated to such 
an extent that they take Are in the air. 

Dr. Tyndall has devised an experiment by which the great heat 
developed by friction is illustrated in a striking manner. A brass tube 
(fig. 276) about 4 inches in length and f of an inch in diameter, is fixed 
on a small wheel. By means of a cord passing round a much larger one, 
this tube can be rotated with any desired velocity. The tube is three 
parts full of water, and is closed by a cork. In making the experiment 
the tube is pressed between a wooden clamp, while the wheel is rotated 
with some rapidity. The water rapidly becomes heated by the friction, 
and its temperature soon exceeding the boiling point the cork is projected 
to a height of several yards by the elastic force of the steam. 


Fig. 276. 



411. Heat due to pressure and percussion. —If a body be so 
compressed that its density is increased, its temperature rises according 
as the volume diminishes. Joule has verified this in the case of water 
and of oil, which were exposed to pressures of 15 to 25 atmospheres. 
In the case of water at 1*2° C., increase of pressure caused lowering of 
temperature, a result which agrees with the fact that water contracts by 
heat at this temperature. Similarly when weights are laid on metallic 
pillars, heat is evolved, and absorbed when they are removed. So in 
like manner the stretching of a metallic wire is attended with a diminu¬ 
tion of temperature. 

The production of heat by the compression of gases is easily shown 
by means of the ‘pneumatic syringe (fig. 277). This consists of a glass 
tube with thick sides, closed hermetically by a leather piston. At the 
bottom of this, there is a cavity in which a small piece of tinder is 




380 


ON HEAT. 


[ 412 - 

placed. The tube being full of air the piston is suddenly plunged 
downwards, the air thus compressed disengages so much heat as to 
ignite the tinder, which is seen to burn when the pisttfn is rapidly 
withdrawn. The inflammation of the tinder in this experiment in¬ 
dicates a temperature of at least 300°. At the moment of compression 
a bright flash is observed, which was originally attributed to the high 
temperature of the air; but it is simply due to the combustion of the 
oil which greases the piston. Instead of the tinder, cotton very slightly 
moistened with ether or bisulphide of carbon may be used. 



The elevation of temperature produced by the pressure in the above 
experiment is sufficient to effect the combination, and therefore the 
detonation, of a mixture of hydrogen and oxygen. 

Percussion is also a source of heat. In firing shot at an iron target, a 
sheet of flame is frequently seen at the moment of impact; and Mr. 
Whitworth has used iron shells which are exploded by the concussion 
on striking an iron target. A small piece of iron hammered on the 
anvil becomes very hot. The heat is not simply due to an approximation 
of the molecules, that is, to an increase in density, but arises from a 
vibratory motion imparted to them; for lead, which does not increase in 
density by percussion, nevertheless becomes heated. 

PHYSICAL SOURCES. ~ 

412. Solar radiation.— The most intense of all sources of heat is 
the sun. The cause of its heat is unknown; some have considered it to 
be an ignited mass experiencing immense eruptions, while others have 
regarded it as composed of layers acting chemically on each other like 
the couples of a voltaic battery, and giving rise to electrical currents, 
which produce light and solar heat. On both hypotheses the incandes¬ 
cence of the sun would have a limit. 

Different attempts have been made to determine the quantity of heat 
annually emitted by the sun. M. Pouillet, by means of an apparatus 





PHYSICAL SOURCES OF HEAT. 


381 


- 414 ] 

which, he calls a pyrheliometer, has calculated that if the total quantity 
of heat which the earth receives from the sun in the course of a year 
were employed to melt ice, it would he capable of melting a layer 
of ice all round the earth of 35 yards in thickness. But from the 
surface which the earth exposes to the solar radiation, and from the 
distance which separates the earth from the sun, the quantity of heat 
which the earth receives can only be a.asi.ooo.ooo of tlie heat emit ted 
by the sun. 

Faraday has calculated that the average amount of heat radiated in a 
day on each acre of ground in the latitude of London is equal to that 
which would be produced by the combustion of sixty sacks of coal. 

413. Terrestrial heat. —Our globe possesses a heat peculiar to it, 
which is called the terrestrial heat. The temperature of the earth gra¬ 
dually sinks from the surface to a certain depth, at which it remains 
constant in all seasons. It is hence concluded that the solar heat does 
not penetrate below a certain internal layer, which is called the layer of 
constant temperature : its depth below the earth’s external surface varies, 
of course, in different parts of the globe j at Paris it is about 30 yards, 
and the temperature is constant at 11-8° C. 

Below the layer of constant temperature, the temperature is observed 
to increase, on the average 1° C. for every 90 feet. This increase has 
been verified in mines and artesian wells. According to this, at a 
depth of 3,000 yards, the temperature of a corresponding layer would 
be 100°, and at a depth of 20 to 30 miles there would be a temperature 
sufficient to melt all substances which exist on the surface. Hot springs 
and volcanoes confirm the existence of this central heat. 

Various hypotheses have been proposed to account for the existence of 
this central heat. That most usually admitted by physicists is that the 
earth was originally in a liquid state in consequence of the high tem¬ 
perature, and that by radiation the surface has gradually solidified, so as 
to form a solid crust. The thickness of this crust is not believed to be 
more than 40 to 50 miles, and the interior is probably still in a liquid 
state. The cooling must be very slow, in consequence of the imperfect 
conductivity of the crust. For the same reason the central heat does 
not appear to raise the temperature of the surface more than ~ of a 
degree. 

414. Heat produced by absorption and imbibition.— Molecular 
phenomena, such as imbibition, absorption, capillary actions, are usually 
accompanied by disengagement of heat. Pouillet found that whenever 
a liquid is poured on a finely divided solid, an increase of temperature 
is produced which varies with the nature of the substances. With 
inorganic substances, such as metals, the oxides, the earths, the increase 



ON HEAT. 


382 


[ 414 - 


is ~ of a degree; but with organic substances, such as sponge, flour, starch, 
roots, dried membranes, the increase varies from 1 to 10 degrees. 

The absorption of gases by solid bodies presents the same phenomena. 
Dobereiner found that when platinum, in the fine state of division known 
as platinum black, is placed in oxygen, it absorbs many hundred times 
its volume, and that the gas is then in such a state of density, and 
the temperature so high, as to give rise to intense combustions. Spongy 
platinum produces the same effect. A jet of hydrogen directed on it 
takes fire. 

The apparatus knowm as Dobereiner's Lamp depends on this property 
of finely divided platinum. It consists of two glass vessels (fig. 278). 

The first, A, fits in the lower vessel by 
means of a tubulure which closes it her¬ 
metically. At the extremity of the tubu¬ 
lure there is a mass of zinc, Z, immersed 
in dilute sulphuric acid. By the chemical 
action of the zinc on the dilute acid hy¬ 
drogen gas is generated, which, finding no 
issue, forces the liquid out of the vessel B 
into the vessel A, so that the zinc is not in 
contact with the liquid. The stopper of 
the upper vessel is raised to give exit to the 
air in proportion as the water rises. On a 
copper tube, H, fixed in the side of the 
vessel B, there is a small cone, E, perfo¬ 
rated by an orifice; above this there is some 
spongy platinum in the capsule D. 

As soon now as the cock, which closes the 
tube H, is opened, the hydrogen escapes, 
and coming in contact with the spongy pla¬ 
tinum, is ignited. 

M. Favre, who has recently examined the question of the heat disen¬ 
gaged when a gas is absorbed by charcoal, has found that the amount 
of heat produced by the absorption of a given weight of sulphurous 
acid, or of protoxide of nitrogen, greatly exceeds that which is disen¬ 
gaged in the liquefaction of the same weight of gas; for carbonic acid, 
the heat produced by absorption exceeds even the heat which would be 
disengaged by the solidification of the gas. The heat produced by the 
absorption of these gases cannot, therefore, be explained by assuming 
that the gas is liquefied, or even solidified in the pores of the charcoal. 
It is probable that it is due to that produced by the liquefaction of the 
gas, and the heat due to the imbibition of the liquid so produced in the 
charcoal. 





CHEMICAL SOURCES OF HEAT. 


383 


- 416 ] 

The heat produced by the changes of condition has been already treated 
of in the articles solidification and liquefaction ; the heat produced by elec¬ 
trical action will be discussed under the head of Electricity. 

CHEMICAL SOURCES. 

415. Chemical combinations. Combustion. — Chemical combi¬ 
nations are usually accompanied by a certain elevation of temperature. 
When these combinations take place slowly, as when iron oxidises in the 
air, the heat produced is imperceptible ; but if they take place rapidly, 
the disengagement of heat is very intense. The same quantity of heat 
is produced in both cases, but when evolved slowly it is dissipated as 
fast as formed. 

Combustion is chemical combination attended with the evolution of 
light and heat. In the ordinary combustion in lamps, fires, candles, the 
carbon and hydrogen of the coal or of the oil, etc., combine with the 
oxygen of the air. But combustion does not necessarily involve the pre¬ 
sence of oxygen. If either powdered antimony or a fragment of phos¬ 
phorus be placed in a vessel of chlorine, it unites with chlorine, producing 
thereby heat and flame. 

Many combustibles burn with flame. A flame is a gas or vapour 
raised to a high temperature by combustion. Its illuminating power 
varies with the nature of the product formed. The presence of a solid 
body in the flame increases the illuminating power. The flames of hy¬ 
drogen, carbonic oxide, and alcohol are pale, because they only contain 
gaseous products of combustion. But the flames of candles, lamps, coal 
gas, have a high illuminating power. They owe this to the fact that the 
high temperature produced decomposes certain of the gases with the pro¬ 
duction of carbon, which, not being perfectly burned, becomes incandes¬ 
cent in the flame. Coal gas, when burnt in an arrangement by which it 
obtains an adequate supply of air, is almost entirely devoid of luminosity. 
A non-luminous flame may be made luminous by placing it in platinum 
wire, or asbestos. The temperature of a flame does not depend on its 
illuminating power; A hydrogen flame, which is the palest of all flames, 
gives the greatest heat. 

416. Heat disengaged during combustion.— Many physicists, more 
especially Lavoisier, Bumford, Dulong, Despretz, Hess, Favre and Silber- 
mann, and Andrews, have investigated the quantity of heat disengaged 
by various bodies in chemical combinations. 

In these experiments Lavoisier used the ice calorimeter already de¬ 
scribed. Bumford used a calorimeter known by his name, which con¬ 
sists of a rectangular copper canister filled with water. In this canister 
there is a worm which passes through the bottom of the box, and 
terminates below in an inverted funnel. Under this funnel is burnt the 


384 


ON HEAT. 


[ 417 - 

substance experimented upon. The products of combustion, in passing 
through the worm, heat the water of the canister, and from the increase 
of its temperature the quantity of heat evolved is calculated. MM. 
Despretz and Dulong have successively modified Fumford’s calorimeter 
by allowing the combustion to take place, not outside the canister, but 
in a chamber of combustion placed in the liquid itself; the oxygen ne¬ 
cessary for the combustion entered by a tube in the lower part of the 
chamber, and the products of combustion escaped by another tube 
placed at the upper part and twisted in a serpentine form in the mass of 
the liquid to be heated. MM. Favre and Silbermann have improved 
this calorimeter very greatly, not only by avoiding or taking account of 
all possible sources of error, but by arranging it for the determination 
of the heat evolved in other chemical actions than those of ordinary 
combustion. 

The experiments of MM. Favre and Silbermann are the most trust¬ 
worthy, as having been executed with the greatest care. They agree 
very closely with those of Dulong. Taking as thermal unit the heat 
necessary to raise the temperature of a pound of water through one degree 
Centigrade, the following table gives the thermal units in round numbers 
disengaged by a pound of each of the substances in burning in oxygen. 


Hydrogen. 34500 Sulphur . 2200 

Marsh gas. 13000 Anthracite. 8460 

Olefiant gas. 12000 Charcoal. 8080 

Oil of turpentine . . . 10080 Coal. 8000 

Olive oil. 9860 Tallow. 8000 

Ether. 9030 Diamond. 7700 

Coke. 7000 Absolute alcohol .... 7180 

Wood, dry. 4025 Phosphorus. 5900 

Wood, moist .... 3100 Iron ..1582 

Carbonic oxide .... 2400 


The experiments of Dulong, of Despretz, and of Hess, prove that a 
body in burning always produces the same quantity of heat in reaching 
the same degree of oxidation, whether it attains this at once or only 
reaches it after passing through intermediate stages. Thus a given 
weight of carbon gives out the same amount of heat in burning directly 
to carbonic acid, as if it were first changed into carbonic oxide, and then 
this burnt into carbonic acid. 


HEATING. 

417. Different kinds of Heating Heating is the art of utilising for 
domestic and industrial purposes the sources of heat which nature offers 
to us. 














DIFFERENT KINDS OF HEATING. 


- 419 ] 


385 


Our principal source of artificial heat is the combustion of coal, coke, 
turf, wood, and charcoal. 

We may distinguish five kinds of heating, according to the apparatus 
used: 1st, heating with an open fire ; 2nd, heating with an enclosed fire, 
as with a stove; 3rd, heating by hot air; 4th, heating by steam; 5th, 
heating by the circulation of hot water. 

418. Fire-places.— Fire-places are open hearths built against a wall 
under a chimney, through which the products of combustion escape. 

However much they may be improved, fire-places will always remain 
the most imperfect and costly mode of heating, for they only render 
available 13 per cent, of the total heat yielded by coal or coke, and 6 per 
cent, of that by wood. This enormous loss of temperature arises from 
the fact, that the current of air necessary for combustion always carries 
with it a large quantity of the heat produced, which is lost in the atmo¬ 
sphere. Hence it was that Franklin said fire-places should be adopted 
in cases where the smallest quantity of heat was to be obtained from 
a given quantity of combustible. Notwithstanding their want of 
economy, however, they will always be preferred as the healthiest and 
pleasantest mode of heating, on account of the cheerful light which 
they emit, and the ventilation which they ensure. 

419. Draught of fire-places.— The draught of a fire is the upward 
current in the chimney caused by the as¬ 
cent of the products of combustion; when 
the current is rapid and continuous the 
chimney is said to draw well. 

The draught is caused by the diffe¬ 
rence between the temperature of the 
inside and that on the outside of the 
chimney; for in consequence of this 
difference the gaseous substances which 
fill the chimney are lighter than the air 
of the room, and consequently equili¬ 
brium is impossible. The weight of 
the column of gas, CD, fig. 279, in the 
chimney being less than that of the ex¬ 
ternal column of air, AB, of the same 
height, there is a pressure from the 
outside to the inside which causes the 
products of combustion to ascend the 
more rapidly in proportion as the difference in weight of the two gaseous 
masses is greater. 

The currents caused by the difference in temperature of two communi¬ 
cating gaseous masses may be demonstrated by placing a candle near the 

s 



Fig. 279. 













386 


ON HEAT. 


* [ 420 - 

top and near the bottom of the partially opened door of a warm room. 
At the top, the flame will he turned from the room towards the outside, 
while the contrary effect will he produced when the candle is placed on 
the ground. These two effects are caused by the current of heated air 
which issues by the top of the door, while the cold air which replaces it 
enters at the bottom. 

In order to have a good draught a chimney ought to satisfy the follow¬ 
ing conditions: 

i. The section of the chimney ought not to be larger than is necessary 
to allow an exit for the products of combustion, otherwise ascending and 
descending currents are produced in the chimney, which cause it to smoke. 
It is advantageous to place on the top of the chimney a conical pot 
narrower than the chimney, so that the smoke may escape with suflicient 
velocity to resist the action of the wind. 

ii. The chimney ought to be sufficiently high, for as the draught is 
caused by the excess of the external over the internal pressure, this ex¬ 
cess is greater in proportion as the column of heated air is longer. 

iii. The external air ought to pass into the chamber with sufficient 
rapidity to supply the wants of the fire. In a hermetically closed room 
the combustibles would not bum, or descending currents would be 
formed which would drive the smoke into the room. Usually air enters 
in sufficient quantity by the' crevices of the doors and windows. 

iv. Two chimneys should not communicate, for if one draws better than 
the other a descending current of air is produced in the latter, which car¬ 
ries smoke with it. 

420. Stoves.— Stoves are apparatus for heating with a detached fire, 
placed in the room to be heated, so that the heat radiates in all directions 
round the stove. At the lower part is the draught hole by which the 
air necessary for combustion enters. The products of combustion escape 
by means of iron chimney pipes. This mode of heating is one of the most 
economical, but it is by no means so healthy as that by open fire-places, 
for the ventilation is very bad, more especially where, as in Sweden, the 
stoves are fed from the outside of the room. These stoves also emit a 
bad smell, probably arising from the decomposition of organic sub¬ 
stances in the air .by their contact with the heated sides of the chimney 
pipes; or possibly, as Deville and Troost’s recent researches seem to 
show, from the diffusion of gases through the heated sides of the stove. 

The heating is very rapid with blackened metal stoves, but they also cool 
very rapidly. Stoves constructed of polished earthenware, which are 
common on the Continent, heat more slowly but more pleasantly, and they 
retain the heat longer. 

421. Heating by steam. —Steam, in condensing, gives up its latent 
heat of vaporisation, and this property has been used in heating baths, 


HEATING. 


387 


- 423 ] 

workshops, public buildings, hothouses, &c. For this purpose steam is 
generated in boilers similar to those used for steam engines, and is then 
made to circulate in pipes placed in the room to be heated. The vapour 
condenses, and in doing so imparts to the pipes the latent heat which 
becomes free, and thus heats the surrounding air. 

422. Heating 1 by hot air.— Heating by hot air consists in heating 
the air in the lower part of a building, from whence it rises to the higher 
parts in virtue of its lessened density. The apparatus is arranged as re¬ 
presented in figure 280. 

A series of bent tubes, AB, only one of which is shown in the figure, 
is placed in a furnace, F, in the cellar. The air passes into the tubes 



through the lower end, A, where it becomes heated, and rising in the 
direction of the arrows reaches the room, M, by the higher aperture, 
B. The various rooms to be heated are provided with one or more of 
those apertures, which are placed as low in the room as possible. The 
conduit, 0, is an ordinary chimney. 

These apparatus are more economical than open fire-places, but they 
are less healthy owing to the want of ventilation. 

423. Heating- by bot water.— This consists of a continuous circulation 
of water, which having been heated in a boiler, rises through a series of 
tubes, and then, after becoming cool, passes into the boiler again by a 
similar series. 

Figure 281 represents an apparatus for heating a building of several 

s 2 


























388 


ON HEAT. 


[423- 

stories. The heating apparatus, which is in the cellar, consists of a hell- 
shaped boiler, oo, with an internal flue, F. A long pipe, M, fits in the 
upper part of the boiler, and also in the reservoir, Q, placed in the upper 
part of the building to be heated. At the top of this reservoir there is 
a safety valve, s, by which the pressure of the vapour in the interior can 
be regulated. 

The boiler, the pipe M, and a portion of the reservoir Q, being filled 
with water, as it becomes heated in the boiler an ascending current of 



hot water rises to the reservoir Q, while at the same time descending 
currents of colder and denser water pass from the lower part of the re¬ 
servoir Q into receivers b, d,f, filled with water. The water from these 
passes again through pipes into other receivers, a, c, e, and ultimately 
reaches the lower part of the boiler. 

During this circulation the hot water heats the pipes and the receivers, 
which thus become true water stoves. The number and the dimensions 
of these parts are readily determined from the experimental fact that a 
cubic foot of water is sufficient to communicate the necessary heat to 
3200 cubic feet of air. In the interior of the receivers, a, b, c, d, e. f, 



























































SOURCES OF COLD. 


389 


- 426 ] 

there are cast-iron tubes which communicate with the outside by pipes, 
P, placed underneath the flooring. The air becomes heated in these 
tubes, and emerges at the upper part of the receivers. 

The principal advantage of this mode of heating is that of giving a 
temperature which is constant for a long time; for the mass of water 
only cools slowly. It is much used in hothouses, baths, artificial incuba¬ 
tion, drying rooms, and generally wherever a uniform temperature is 
desired. 


SOURCES OF COLD. 

424. Various sources of cold. —Besides the cold caused by the pas¬ 
sage of a body from the solid to the liquid state, of which we have already 
spoken, cold is produced by the expansion of gases, by radiation in general, 
and more especially by nocturnal radiation. 

425. Cold produced by the expansion of gases. —We have seen, 
that when a gas is compressed, the temperature rises. The reverse of 
this is also the case: when a gas is rarefied a reduction of temperature 
ensues, because a quantity of sensible heat disappears when the gas be¬ 
comes increased to a larger volume. This may be shown by placing a 
delicate Breguet’s thermometer under the receiver of an ,air pump, and 
exhausting; at each stroke of the piston the needle moves in the direc¬ 
tion of zero, and regains its original temperature when air is admitted. 
Kirk has invented a machine for the manufacture of ice which depends 
on this property. The heat developed by the compression of air is re¬ 
moved by a current of cold water ; the vessel containing the compressed 
air being placed in brine, the air is allowed to expand ; in so doing it 
cools the brine so considerably as to freeze water contained in vessels 
placed in the brine. It is stated that by this means a ton of coals (used 
in working a steam engine by which the compression is effected). can 
produce a ton of ice. 

426. Cold produced by nocturnal radiation. —During the day, 
the ground receives from the sun more heat than radiates into space, 
and the temperature rises. The reverse is the case during night. The 
heat which the earth loses by radiation is no longer compensated for, and 
consequently a fall of temperature takes place, which is greater according 
as the sky is clearer, for clouds send towards the earth rays of greater 
intensity than those which come from the celestial spaces. In some 
winters it has been found that rivers have not frozen, the sky having been 
cloudy, although the thermometer has been for several days below —4° ; 
while in other less severe winters the rivers freeze when the sky is clear. 
The emissive power exercises a great influence on the cold produced by 
radiation •, the greater it is the greater is the cold. 


390 


ON HEAT. 


[ 427 - 

In Bengal, tlie nocturnal cooling is used in manufacturing ice. Large 
flat vessels containing water are placed on non-conducting substances, 
such as straw or dry leaves. In consequence of the radiation the water 
freezes, even when the temperature of the air is 10° 0. The same 
method can "be applied in all cases with a clear sky. 

It is said that the Peruvians, in order to preserve the shoots of young 
plants from freezing, light great fires in their neighbourhood, the smoke 
of which, producing an artificial cloud, hinders the cooling produced by 
radiation. 

427. Absolute zero of temperature.— As a gas is increased ~ of 
its volume for each degree Centigrade, it follows that at a temperature of 
273° C. the volume of any gas measured at zero is doubled. In like 
manner if the temperature of a given volume at zero were lowered 
through —273° the contraction would be equal to the volume; that is, 
the volume would not exist. 

At this temperature the motion of the molecules of the gas would 
completely cease, and the pressure thereby occasioned. In all pro¬ 
bability, before reaching this temperature, gases would undergo some 
change. 

This point on the Centigrade scale is called the absolute zero of tem¬ 
perature ; the temperatures reckoned from this point are called absolute 
temperatures. They are clearly obtained by adding 273 to the tempera¬ 
ture on the Centigrade scale. 


CHAPTER XII. 

MECHANICAL EQUIVALENT OF HEAT. 

428. Mechanical equivalent of heat.— If the various instances of 
the production of heat by motion be examined, it will be found that in 
all cases mechanical force is consumed. Thus, in rubbing two bodies 
against each other, motion is apparently destroyed by friction ; it is not, 
however, lost, but appears in the form of a motion of the particles of the 
body; the motion of the mass is transformed into a motion of the 
molecules. 

Again, if a body be allowed to fall from a height, it strikes against the 
ground with a certain velocity. According to older views its motion is 
destroyed, vis viva is lost. This, however, is not the case ; the vis viva of 
the body appears as vis viva of its molecules. 

In the case, too, of chemical action, the most productive artificial 
source of heat, it is not difficult to conceive that there is in the act of 




MECHANICAL EQUIVALENT OF HEAT. 


391 


- 428 ] 

combining an impact of tbe dissimilar molecules against each other; an 
effect analogous to the production of heat by the impact of masses of 
matter against each other. 

In like manner, heat may be made to produce motion, as in the case of 
the steam engine, the propulsion of shot from a gun. 

Traces of a view that there is a connection between heat and motion 
are to be met with in the older writers, Bacon for example; and Locke 
says—‘ Heat is a very brisk agitation of the insensible parts of the object, 
which produces in us that sensation from whence we denominate the object 
hot; so that what in our sensation is heat, -in the object is nothing but 
motion.’ Rumford, in explaining his great experiment of the production 
of heat by friction, was unable ta assign any other cause for the heat 
produced than motion ; and Davy, in the explanation of his experiment 
of melting ice by friction in vacuo, expressed similar views. Carnot, in a 
work on the steam engine, published in 1824, also indicated a connection 
between heat and work. 

The views, however, which had been stated by isolated writers, had 
little or no influence on the progress of scientific investigation, and it is 
in the year 1842 that the modern theories may be said to have had their 
origin. In that year Dr. Mayer, a physician in Heilbronn, formally 
stated that there exists a connection between heat and work ; and he it 
was who first introduced into science the expression 1 mechanical equi¬ 
valent of heat? Mayer also gave a method by which this equivalent 
could be calculated; the particular results, however, are of no value, as 
the method, though correct in principle, is founded on incorrect data. 

In the same year, too, Colding of Copenhagen published experiments 
on the production of heat by friction, from 'which he concluded that the 
evolution of heat was proportional to the mechanical energy expended. 

About the same time as Mayer, but quite independently of him, Joule 
commenced a series of experimental investigations on the relation between 
heat and work. These first drew the attention of scientific men to the 
subject, and were admitted as a proof that the transformation of heat 
into mechanical energy, or of mechanical energy into heat, always takes 
place in a definite numerical ratio. 

Subsequently to Mayer and Joule, several physicists by their theoretical 
and experimental investigations have contributed to establish the mecha¬ 
nical theory of heat, namely, in this country, Sir W. Thomson and Ran- 
kine ; in Germany, Helmholtz, Clausius, and Holtzmann ; and in France, 
Clapeyron and Regnault. 

The following are some of the most important and satisfactory of 
Joule’s experiments. 

A copper vessel, B (fig. 281), was provided with a brass paddle-wheel 
(indicated by the dotted lines), which could be made to rotate about a 


392 


ON HEAT. 


[ 428 - 

vertical axis. Two weights, E and F, were attached to cords which 
passed over the pulleys, C and D, and were connected with the axis, A. 
These weights in falling caused the wheel to rotate. The height of the 
fall, which in Joule’s experiments was about 63 feet, was indicated on 
the scales, G and H. The roller, A, was so constructed that by de¬ 
taching a pin the weights could be raised without moving the wheel. 
The vessel B was filled with water and placed on a stand, and the weights 
allowed to sink. When they had reached the ground, the roller was 


Fig. 282 . 



detached from the axis and the weights again raised, the same operations 
being repeated 20 times. The heat produced was measured by ordinary 
calorimetric methods. 

The work expended is measured by the product of the weight into the 
height through which it falls, or wh, less the labour lost by the friction 
of the apparatus. This is diminished as far as possible by the use of 
friction wheels, and its amount is determined by connecting C and D 
without causing them to pass over A, and then determining the weight 
necessary to communicate to them a uniform motion. 

In this way it has been found that a thermal unit—that is, the 
quantity of heat by which a pound of water is raised through 1° C.—is 
generated by the expenditure of the same amount of work as would be 
required to raise 1392 pounds through 1 foot, or 1 pound through 1392 
feet. This is expressed by saying that the mechanical equivalent of the 
thermal unit is 1392 foot-pounds. 

The friction of an iron paddle-wheel in mercury gave 1397 foot-pounds, 
and that of the friction of two iron plates gave 1395 foot-pounds, as the 
mechanical equivalent of one thermal unit. 







MECHANICAL EQUIVALENT OF HEAT. 


393 


- 428 ] 


In another series of experiments, the air in a receiver was compressed 
by means of a force pump, both being immersed in a known weight of 
water at a known temperature. After 300 strokes of the piston, the heat, 
C, was measured which the water had gained. This heat was due to 
the compression of the air and to the friction of the piston. To eliminate 
the latter influence, the experiment was made under the same conditions, 
but leaving the receiver open. The air was not compressed, and 300 
strokes of the piston developed C' thermal units. Hence C—C' is the 
heat produced by the compression of the gas. Representing the foot 


pounds expended in producing this heat 


by W, we have 


W 

C—O' 


for the 


value of the mechanical equivalent, E. By this method Joule obtained 
the number 1442. 

The mean number which Joule adopted for the mechanical equivalent 
of one thermal unit on the Centigrade scale is 1390 foot-pounds; on the 
Fahrenheit scale it is 772 foot-pounds. This number is called Joule's 
equivalent. 

The following is the method which Mayer employed in calculating the 
mechanical equivalent of heat. It is taken with slight moditications from 
Prof. Tyndall’s work on Heat, who, while strictly following Mayer’s reason¬ 
ing, has corrected the data. 

Let us suppose that a rectangular vessel with a section of a square 
foot contains at 0° a cubic foot of air under the ordinary atmospheric 
pressure; and let us suppose that it is enclosed by a piston without 
weight. 

Suppose now that the cubic foot of air is heated until its volume is 
doubled : from the coefficient of expansion of air we know that this is 
the case at 273° C. The gas in doubling its volume will have raised 
the piston through a foot in height; it will have lifted the atmospheric 
pressure through this distance. But the atmospheric pressure on a square 
foot is in round numbers 15 x 144 — 2160 pounds. Hence a cubic foot 
of air in doubling its volume has lifted a weight of 2160 pounds through 
a height of a foot. 

Now a cubic foot of air at zero weighs 1*29 ounces, and the specific 
heat of air under constant pressure, that is, when it can expand freely, as 
compared with that of an equal weight of water, is 0-24; so that the 
quantity of heat which will raise 1-29 ounces of air through 273° will 
only raise 0-24 x 1'29 = 0-31 oz. of water through the same temperature; 
but 0*31 oz. of water raised through 273° is equal to 5*29 pounds of water 
raised through 1° 0. 

That is, the quantity of heat which will double the volume of a cubic 
foot of air, and in so doing will lift 2240 pounds through a height of a foot, 
is 5'29 thermal units. 


s 3 



394 


ON HEAT. 


[ 428 - 


Now in the above case the gas has been heated under constant pres¬ 
sure, that .is, when it could expand freely. If, however, it had been 
heated under constant volume, its specific heat would have been less in 
the ratio 1 : 1-414 (396), so that the quantity of heat required under 
these circumstances to raise the temperature of a cubic foot of air would 

be 5 29 X —- = 3-74. Deducting this from 5-29, the difference 1-55 
1*41 

represents the weight of water which would have been raised 1° C. by 
the- excess, of heat imparted to the air when it could expand freely. But 
this excess has been consumed in the work of raising 2160 pounds through 
a foot. Dividing this by 1-55 we have 1393. Hence the heat which will 
raise a pound of water through 1° C. will raise a weight of 1393 through 
a height of a foot; a numerical value of the mechanical equivalent of 
heat agreeing as closely as can be expected with that which Joule adopted 
as the most certain of his experimental results. 

The law of the relation of heat to mechanical energy may thus be stated. 
Heat and mechanical enei'gy are mutually convertible ; and heat requires for 
its production , and produces by its disappearance , mechanical enei'gy m the 
ratio of 1390 foot-pounds for every thermal unit. 

A variety of experiments may in like manner be adduced to show that 
whenever heat disappears work is produced. For example, if in a reser¬ 
voir immersed in water the air be compressed to the extent of 10 atmo¬ 
spheres: supposing that now, when the compressed air has acquired the 
temperature of the water, it be allowed to act upon a piston loaded by a 
weight, the weight is raised. At the same time the water becomes cooler, 
showing that a certain quantity of heat had disappeared in producing the 
mechanical effort of raising the weight. 

Joule placed in a calorimeter two equal copper reservoirs, which could 
be connected by a tube. One of these contained air at 22 atmospheres, 
the other was exhausted. When they were connected, they came into 
equilibrium under a pressure of 11 atmospheres; but as the gas in expand¬ 
ing had done no work, there was no alteration in temperature. When, 
however, the second reservoir was full of water, the air in entering was 
obliged to expel it and thus perform work, and the temperature sank 
owing to an absorption of heat. 

For further information the student of this subject is strongly recom¬ 
mended to read Professor Tyndall’s Heat as a Mode of Motion , in which 
the phenomena of heat are throughout explained in accordance with 
modern views. A condensed, though complete and systematic, account 
of the dynamical theory of heat is met with in Professor Foster’s articles 
on ‘Heat,’ in Watts’ Dictionary of Chemistry. 


- 429 ] 


ON LIGHT. 


395 


BOOK VII. 

ON LIGHT. 


CHAPTER I. 

TRANSMISSION, VELOCITY, AND INTENSITY OF LIGHT. 

429. Theories of light. —Light is the agent which, by its action on 
the retina, excites in us the sensation of vision. That part of physics 
which deals with the properties of light is known as optics. 

In order to explain the origin of light, various hypotheses have been 
made, the most important of which are the emission or corpuscular theory, 
and the undulatory theory. 

On the emission theory it is assumed that luminous bodies emit, in all 
directions, an imponderable substance, which consists of molecules of an 
extreme degree of tenuity: these are propagated in right lines with an 
almost infinite velocity. Penetrating into the eye they act on the retina, 
and determine the sensation which constitutes vision. 

On the undulatory theoiy, all bodies, as well as the celestial spaces, 
are filled by an extremely subtle elastic medium, which is called the 
luminiferous ether. The luminosity of a body is due to an infinitely 
rapid vibratory motion of its molecules, which, when communicated to 
the ether, is propagated in all directions in the form of spherical waves, 
and this vibratory motion, being thus transmitted to the retina, calls 
forth the sensation of vision. The vibrations of the ether take place not 
in the direction of the wave, but in a plane at right angles to it. The 
latter are called the transversal vibrations. An idea of these may be 
formed by shaking a rope at one end. The vibrations, or to and fro 
movements, of the particles of the rope, are at right angles to the length 
of the rope, but the onward motion of the wave’s form is in the direction 
of the length of the rope. 

On the emission theory the propagation of light is effected by a motion 
of translation of particles of light thrown out from the luminous body, as 
a bullet is discharged from a gun ; on the undulatory theory there is no 
progressive motion of the particles themselves, but only of the state of 
disturbance which was communicated by the luminous body ; it is a 



396 ON LIGHT. [ 430 - 

motion of oscillation, and, like the propagation of waves in water, takes 
place by a series of vibrations. 

The luminiferous ether penetrates all bodies, but on account of its 
extreme tenuity it is uninfluenced by gravitation ; it occupies space, and 
although it presents no appreciable resistance to the motion of the denser 
bodies, it is possible that it hinders the motion of the smaller comets. 
It has been found, for example, that Encke’s comet, whose period of revo¬ 
lution is about 3^ years, has its period diminished by about 0*11 of a day 
at each successive rotation, and this diminution is ascribed by some to the 
resistance of the ether. 

The fundamental principles of the undulatory theory were enunciated by 
Huyghens, and subsequently by Euler. The emission theory, principally 
owing to Newton’s powerful support, was for long the prevalent scientific 
creed. The undulatory theory was adopted and advocated by Young, who 
showed how a large number of optical phenomena, particularly those of 
diffraction, were to be explained by that theory. Subsequently to, though 
independently of, Young, Fresnel showed that the phenomena of dif¬ 
fraction, and also those of polarisation, are explicable on the same theory, 
which, since his time, has been generally accepted. 

The undulatory theory not only explains the phenomena of light, but 
it reveals an intimate connection between these phenomena and those of 
heat; it shows, also, how completely analogous the phenomena of light 
are to those of sound, regard being had to the differences of the media in 
which these two classes of phenomena take place. 

430. Luminous, transparent, translucent, and opaque bodies.— 
Luminous bodies are those which emit light, such as the sun, and ignited 
bodies. Transparent or diaphanous bodies are those which readily transmit 
light, and through which objects can be distinguished; water, gases, 
polished glass, are of this kind. Translucent bodies transmit light, but 
objects cannot be distinguished through them ; ground glass, oiled paper, 
etc., belong to this class. Opaque bodies do not transmit light; for ex¬ 
ample, wood, metals, etc. No bodies are quite opaque ; they are all more 
or less translucent when cut in sufficiently thin leaves. 

Foucault has recently shown that when the object glass of a telescope 
is thinly silvered, the layer is so transparent, that the sun can be viewed 
through it without danger to the eyes, since the metallic surface reflects 
the greater part of the heat and light. 

431. Luminous ray and pencil. —A luminous ray is the line in 
which light is propagated ; a luminous pencil is a collection of rays from 
the same source ; it is said to be parallel when it is composed of parallel 
rays, divergent when the rays separate from each other, and convergent 
when they tend towards the same point. Every luminous body emits 
divergent rectilinear rays from all its points, and in all directions. 



397 


- 433 ] TRANSMISSION, VELOCITY, AND INTENSITY OF LIGHT. 

432. Propagation of light in a homogeneous medium. —A me¬ 
dium is any space or substance which light can traverse, such as a vacuum, 
air, water, glass, etc. A medium is said to be homogeneous when its 
chemical composition and density are the same in all parts. 

In every homogeneous medium light is propagated in a right line. For, 
if an opaque body is placed in the right line which joins the eye 
and the luminous body, the light is intercepted. The light which 
passes into a dark room by a small aperture, leaves a luminous trace, 
which is visible from the light falling on the particles suspended in 
the atmosphere. 

Light changes its direction on meeting an object which it cannot 
penetrate, or when it passes from one medium to another. These pheno¬ 
mena will be desciibed under the heads reflection and refraction. 

433. Shadow, penumbra. —When light falls upon an opaque body, 
it cannot penetrate into the space immediately behind it, and this space 
is called the shadoio. 

In determining the extent and the shape of shadow projected by a body, 
two cases are to be distinguished: that in which the luminous source is a 
single point, and that in which it is a body of any given extent. 

In the first case, let S (fig. 283) be the luminous point, and M a spherical 



Fig. 283. 


body, which causes the shadow. If an infinitely long straight line, SG, 
move round the sphere M tangentially, always passing through the point 
S, this line will produce a conical surface, which, beyond the sphere, 
separates that portion of space which is in shadow from that which is 
illuminated. In the present case, on placing behind the opaque body a 
screen, PQ, the limit of the shadow, HG, will be sharply defined. This 
is not, however, usually the case, for luminous bodies have always a cer¬ 
tain magnitude, and are not merely luminous points. 

Suppose that the luminous and illuminated bodies are two spheres, SL 
and MN (fig. 284). If an infinite straight line, AG, moves tangentially 
to both spheres, always cutting the line of the centres in the point A, it 
will produce a conical surface with this point for a summit, and which 
traces behind the sphere MN a perfectly dark space, MGHN. If a second 










398 


ON LIGHT. 


[ 434 - 

right line, LD, which cuts the line of centre in B, moves tangentially 
to the two spheres, so as to produce a new conical surface, BDC, it will 
he seen that all the space outside this surface is illuminated, hut that the 
part between the two conical surfaces is neither quite dark nor quite light. 
So that if a screen, PQ, is placed behind the opaque body, the portion cG^H 
of the screen is quite in the shadow, while the space ab receives light from 
certain parts of the luminous body, and not from others. It is brighter 



Fig. 284. 


than the true shadow, and not so bright as the rest ot the screen, and it 
is accordingly called the 'penumbra. 

Shadows such as these are geometrical shadows ^physical shadows , or 
those which are really seen, are by no means so sharply defined. A cer¬ 
tain quantity of light passes into the shadow, even when the source of 
light is a mere point, and conversely the shadow influences the illumin¬ 
ated part. This phenomenon, which will be afterwards described, is 
known by the name of diffraction. 

434. Images produced by small apertures.— When luminous 
rays, which pass into a dark chamber through a small aperture , are received 



Fig. 285. 


upon a screen, they form images of external objects. These images are 
inverted; their shape is always that of the external objects, and is in¬ 
dependent of the shape of the aperture. 

The inversion of the images arises from the fact that the luminous 
rays proceeding from external objects, and penetrating into the 










VELOCITY OF LIGHT. 


399 


-435] 

chamber, cross one another in passing the aperture, as shown in fig. 
285. Continuing in a straight line, the rays from the higher parts 
meet the screen at the lower parts, and inversely, those which come 
from the lower parts meet the higher parts of the screen. Hence the in¬ 
version of the image. In the article camera obscut'a, it will be seen how 
the brightness and precision of the images are increased by means of lenses. 

In order to show that the shape of the image is independent of that 
of the aperture, when the latter is sufficiently small, and the screen 
at an adequate distance, imagine a triangular aperture, 0 (fig. 286), 
made in the door of a dark chamber, and let ab be a screen on which 
is received the image of a flame, AB. A divergent pencil from each 
point of the flame penetrates through the aperture, and forms on the 
screen a triangular image resembling the aperture. But the union of 
all these partial images produces a total image of the same form as 
the luminous object. For if we conceive that an infinite straight 



Fig. 286. 

line moves round the aperture, with the condition that it is always 
tangential to the luminous object, AB, and that the aperture is very 
small, the straight line describes two cones, the apex of which is the 
aperture, while one of the bases is the luminous object, and the other 
the luminous object on the screen—that is, the image. Hence, if the 
screen is perpendicular to the right line joining the centre of the 
aperture and the centre of the luminous body, the image is similar to 
the body, but if the screen is oblique the image is elongated in the 
direction of its obliquity. This is what is seen in the shadow pro¬ 
duced by foliage; the luminous rays passing through the leaves 
produce images of the sun, which are either round or elliptical, 
according as the ground is perpendicular or oblique to the solar rays, 
and this is the case whatever be the shape of the aperture through 
which the light passes. 

435. Velocity of light. —Light moves with such a velocity that 
at the surface of the earth there is, to ordinary observation, no appre¬ 
ciable interval between the occurrence of any luminous phenomenon 












400 


ON LIGHT. 


[ 436 - 

and its perception by the eye. And accordingly, this velocity was first 
determined by means of astronomical observations. Homer, a Danish 
astronomer, in 1(375, first deduced the velocity of light from an obser¬ 
vation of the eclipses of Jupiter’s first satellite. 

Jupiter is a planet, round which four satellites revolve as the moon 
does round the earth. This first satellite, E (fig. 287), suffers occul- 
tation—that is, passes into Jupiter’s shadow—at equal intervals of 
time, which are 42 h. 28 m. 36 s. While the earth moves in that part 
of its orbit, ab , nearest Jupiter, its distance from that planet does not 
materially alter, and the intervals between two successive occultations 
of the satellite are approximately the same; but in proportion as the 
earth moves away in its revolution round the sun, S, the interval 
between two occultations increases, and when, at the end of six months, 
the earth has passed from the position T to the position T' a total 



Fig. 287. 


retardation of 16 m. 36 s. is observed between the time at which the 
phenomenon is seen and that at which it is calculated to take place. 
But when the earth was in the position T, the sun’s light reflected 
from the satellite E had to traverse the distance ET, while in the 
second position the light had to traverse the distance ET'. This 
distance exceeds the first by the quantity TT, for from the great 
distance of the satellite E, the rays ET and ET' may be considered 
parallel. Consequently, light requires 16 m. 36 s. to travel the diameter 
TT' of the terrestrial orbit, or twice the distance of the earth from the 
sun, which gives for its velocity 190,000 miles in a second. 

The stars nearest the earth are separated from it by at least 206,265 
times the distance of the sun. Consequently, the light which they send 
requires 3£ years to reach us. Those stars which are only visible by 
means of the telescope, are possibly at such a distance that thousands of 
years would be required for their light to reach our planetary system. 
They might have been extinguished for years without our knowing it. 

436. Foucault’s apparatus for determining the velocity of 
light. —Notwithstanding the prodigious velocity of light, M. Foucault 



VELOCITY OF LIGHT. 


401 


-436] 

has succeeded in determining it experimentally by the aid of an ingenious 
apparatus, based on the use of the rotating mirror, which has been 
adopted by Mr. Wheatstone in measuring the velocity of electricity. 

In the description of this apparatus, a knowledge of the principal 
properties of mirrors and of lenses is presupposed. Figure 288 
represents the principal parts of M. Foucault’s arrangement. The 
window shutter, K, of a dark chamber is perforated by a square 
aperture, behind which a platinum wire, o, is stretched vertically. A 
beam of solar light reflected from the outside upon a mirror enters 
the dark room by the square aperture, meets the platinum wire, and 
then traverses an achromatic lens, L, with a long focus, placed at a 
distance from the platinum wire less than double the principal focal 



Fig. 288. Fig. 289. 

distance. The image of the platinum wire, more or less magnified, 
would thus be formed on the axis of the lens; but the luminous 
pencil having traversed the lens, impinges on a plane mirror, m, 
rotating with great velocity; it is reflected from this, and forms in 
space an image of the platinum wire, which is displaced with an 
angular velocity double that of the mirror.* This image is reflected 
by a concave mirror, M, whose centre of curvature coincides with the 
axis of rotation of the mirror m, and with its centre of figure. The 

* To prove this, let mn (fig. 289) be the rotating mirror, O a fixed object placed in 
front, and forming its image at O'. When the mirror comes into the position mV. 
the image is formed at 0". But the arc O'm equals the arc Om, and the arc O'W 
equals the arc Om'; hence the arcs 00', 00", are respectively double the arc Om, 
Om'. Therefore, by subtraction, the arc O'O" is double the arc mm', or the angular 
velocity of the image is double that of the mirror. 








402 


ON LIGHT. 


[ 436 - 

pencil reflected from the mirror M returns upon itself, is again reflected 
from the mirror m, traverses the lens a second time, and forms an image 
of the platinum wire, which appears on the wire itself so long as the 
mirror m turns slowly. 

In order to see this image without hiding the pencil which enters by 
the aperture K, a mirror of unsilvered glass, V, with parallel faces, is 
placed between the lens and the wire, and is inclined so that the re¬ 
flected rays fall upon a powerful eyepiece, P. 

The apparatus being arranged, if the mirror m is at rest, the ray after 
meeting M is reflected to m, and from thence returns along its former 
path, till it meets the glass plate V in a , and being partially reflected, 
forms at d —the distance ad being equal to ao —an image of the wire, 
which the eye is enabled to observe by means of the eyepiece P. If 
the mirror, instead of being fixed, is moving slowly round—its axis being 
at right angles to the plane of the paper—there will be no sensible change 
in the position of the mirror m during the brief interval elapsing while 
light travels from m to M and back again, but the image will alternately 
disappear and reappear. If now the velocity of m is increased to upwards 
of 30 turns per second, the interval between the disappearance and re¬ 
appearance is so short that the impression on the eye is persistent, and 
the image appears perfectly steady. 

Lastly, if the mirror turns with sufficient velocity, there is an 
appreciable change in its position during the time which the light takes 
in making the double journey from in to M, and from M to m; the 
return ray, after its reflection from the mirror in, takes the direction mb, 
and forms its image at i ; that is, the image has undergone a total 
deviation, di. Speaking precisely, there is a deviation as soon as the 
mirror turns, even slowly, but it is only appreciable when it has acquired 
a certain magnitude, which is the case when the velocity of rotation is 
sufficiently rapid, or the distance Mm sufficiently great, for the deviation 
necessarily increases with the time which the light takes in returning on 
its own path. 

In M. Foucault’s experiment the distance Mm was only 13^ feet; when 
the mirror rotated with a velocity of 600 to 800 turns in a second, 
deviations of ~ to ~ of a millimeter were obtained. 

If Mm = l, Lm = V, oL = r, and representing by n the number of turns 
in a second, by 8 the absolute deviation di, and by V the velocity of 
light, M. Foucault arrived at the formula 

y_8 7 r P nr 

5 () 

from which the velocity of light is calculated at 185,157 miles in a 
second. 

In this apparatus liqu : ds can be experimented upon. For that purpose 



VELOCITY OF LIGHT. 


403 


- 438 ] 

a tube, AB, 10 feet long, and filled with distilled water, is placed 
between tbe turning mirror m, and a concave mirror M', identical with 
the mirror M. The luminous rays reflected by the rotating mirror, in 
the direction mW, traverse the column of water, AB, twice before 
returning to V. But the return ray then becomes reflected at c, and 
forms its image at h ; the deviation is consequently greater for rays ^yhich 
have traversed water than for those which have passed through air alone, 
hence the velocity of light is less in water than in air. 

This is the most important part of these experiments. For it had been 
shown theoretically that on the undulatory theory the velocity of light 
must be less in the more highly refracting medium, while the very 
opposite is a necessary consequence of the emission theory. Hence 
Foucault’s result may be regarded as a crucial test of the validity of the 
undulatory theory. 

The mechanism which M. Foucault uses to turn the mirror with great 
velocity consists of a small steam turbine, bearing a sort of resemblance 
to the syren, and, like that instrument, giving a higher sound as the 
rotation is more rapid; in fact, it is by the pitch of the note that the 
velocity of the rotation is determined. 

437. Experiments of XVI. Fizeau. —In 1849 M. Fizeau measured 
directly the velocity of light, by ascertaining the time it took to travel 
from Suresnes to Montmartre and back again. The apparatus employed 
was a toothed wheel, capable of being turned more or less quickly, and 
with a velocity that could be exactly ascertained. The teeth were made 
of precisely the same width as the intervals between them. The 
apparatus being placed at Suresnes, a pencil of parallel rays was trans¬ 
mitted through an interval between two teeth to a mirror placed at Mont¬ 
martre. The pencil, directed by a properly arranged system of tubes and 
lenses, returned to the wheel. As long as the apparatus was at rest the 
pencil returned exactly through the same interval as that through which 
it first set out. But when the wheel was turned sufficiently fast, a 
tooth was made to take the place of an interval, and the ray was inter¬ 
cepted. By causing the wheel to turn more rapidly, it reappeared when 
the interval between the next two teeth had taken the place of the 
former tooth at the instant of the return of the pencil. 

The distance between the two stations was 28,334 ft. By means of 
the data furnished by this distance, by the dimensions of the wheel, its 
velocity of rotation, etc., M. Fizeau found the velocity of light to be 
196,000 miles per second, a result agreeing with that given by astronomi¬ 
cal observation as closely as can be expected in a determination of this kind. 

438. Laws of the intensity of light.— The intensity of illumination 
is the quantity of light received on the unit of surface ; it is subject to 
the following laws :— 


404 ON LIGHT. [ 438 - 

• 

I. The intensity of illumination on a given surface is inversely as the 
square of its distance from the source of light. 

II. The intensity of illumination which is received obliquely is propor¬ 
tional to the cosine of the angle which the luminous rays make with the 
normal to the illuminated surface. 

In order to demonstrate the first law, let there he two circular screens, 
CD and AB (fig. 290), one placed at a certain distance from a luminous 
source L, and the other at double this distance, and let s and S be the 
areas of the two screens.' If a be the total quantity of light which is 
emitted by the source in the direction of the cone ALB, the intensity of 
the light on the screen CD, that is, the quantity which falls on the unit 

of surface, is a , and the intensity on the screen AB is %. Now, as the 

triangles ALB and CLD are similar, the diameter of AB is double 
that of CD; and as the surfaces of circles are as the squares of 
their diameters, the surface S is four times s, consequently the intensity 

^ is one-fourth of -. 
o 6’ 



Fig. 290. 

The same law may also be demonstrated by an experiment with the 
apparatus represented in figure 292. It is made by comparing the 
shadows of an opaque rod cast upon a glass plate, in one case by the light 
of a single candle, and in another by that of four candles, placed at 
double the distance of the first. In both cases the shadows have the 
same intensity. 

Figure 290 shows that it is owing to the divergence of the luminous 
rays emitted from the same source that the intensity of light is inversely 
as the square of the distance. The illumination of a surface placed in a 
beam of parallel luminous rays is the same at all distances, at any rate 
in a vacuum, for in air and in other transparent media the intensity of 
light decreases in consequence of absorption, but far more slowly than 
the square of the distance. 

The second law of intensity corresponds to the law which we have 
found to prevail for heat ; it may be theoretically deduced as follows: 






INTENSITY OF LIGHT. 


405 


- 439 ] 

let DA, EB (fig. 291), be a pencil of parallel rays falling obliquely on a 
surface, AB, and let om be the normal to this surface. If S is the 
i section of the pencil, a the total quantity of light which falls on the 
i surface AB, and I that which falls on the unit of surface (that is, the 

I intensity of illumination), we have I = * . But as S is only the pro- 

| jection of AB on a plane perpendicular to the pencil, we know from 



Fig. 291. 

Q 

trigonometry that S = AB cos a, from which AB = —_. This value 

cos a 

substituted in the above equation, gives I = ® cos a, a formula which 

demonstrates the law of the cosine, for as a and S are constant quantities, 
I is proportional to cos a. 

The law of the cosine applies also to rays emitted obliquely by a 
luminous surface; that is, the rays are less intense in proportion as they 



Fig. 292. 

are more inclined to the surface which emits them. In this respect they 
correspond to the third law of the intensity of radiant heat. 

439. Photometers.— A photometer is an apparatus for measuring the 
relative intensities of light. 

Rumford’s photometer. This consists of a ground glass screen, in front of 
which is fixed an opaque rod (fig. 292) ; the lights to be compared—for 



























406 


ON LIGHT. 


[ 439 - 

instance, a lamp and a candle—are placed at a certain distance in sucli a 
manner that each projects on the screen a shadow of the rod. The 
shadows thus projected are at first of unequal intensity, but by altering 
the position of the lamp, it may be so placed that the intensity of the 
two shadows is the same. Then, since the shadow thrown by the lamp 
is illuminated by the candle, and that thrown by the candle is illuminated 
by the lamp, the illumination of the screen due to each light is the same. 
The intensities of the two lights, that is, the illuminations which they 
would give at equal distances, are then directly proportional to the squares 
of their distances from the shadows; that is to say, that if the lamp is 
three times the distance of the candle, its illuminating power is nine 
times as ^great. 

For if i and i' are the intensities of the lamp and the candle at the 
unit of distance, and d and d' their distances from the shadows, it 
follows, from the first law of the intensity of light, that the intensity of 

i i' 

the lamp at the distance d is —-, and that of the candle — at the 

d 4 d n 

distance cT. On the screen these two intensities are equal; hence 
j 2 = ^9 ° r ; which was to be proved. 

Bunsen's photometer. When a grease spot is made on a piece of bibulous 
paper, the part appears translucent. If the paper be illuminated by a 
light placed in front, the spot appears darker than the surrounding space ; 
if, on the contrary, it be illuminated from behind, the spot appears light 
on a dark ground. If the greased part and the rest appear unchanged, 
the intensity of illumination on both sides is the same. Bunsen’s photo¬ 
meter depends on an application of this principle. A circular spot is 
made on a paper screen by means of a solution of spermaceti in naphtha; 
behind this is placed a light of a certain intensity, which serves as a 
standard ; in this country it is usually a wax candle of known dimensions. 
The light to be tested is then moved in a right line to such a distance in 
front of the diaphragm, that there is no difference in brightness between 
the greased part and the rest of the screen. By measuring the distances 
of the lights from the screen, their relative illuminating powers are 
deduced from what has been previously said. 

By this kind of determination great accuracy cannot be attained, more 
especially when the lights to be compared are of different colours, one, 
for instance, being yellow, and the other of a bluish tint. In this case, 
the determination of the relative brightness is quite uncertain. 

Wheatstone 1 s photometer. The principal part of this instrument is a 
steel bead, P (fig. 293), fixed on the edge of a disc, which rotates on a 
pinion, o, working in a larger toothed wheel. The wheel fits in a cylin¬ 
drical copper box, which is held in one hand, while the other works a 


REFLECTION OF LIGHT. 


407 


- 440 ] 

handle, A, which turns a central axis, the motion of which is transmitted 
by a spoke, a, to the pinion o. In this way the latter turns on itself, and 
at the same time revolves round the circumference of the box j the bead 
shares this double motion, and consequently describes a curve in the 
form of a rose (fig. 294). 




Fig. 293. 


Fig. 294. 


Now, let M and N be the two lights whose intensities are to be com¬ 
pared; the photometer is placed between them and rapidly rotated. The 
brilliant points produced by the reflection of the light on the two oppo¬ 
site sides of the bead give rise to two luminous bands, arranged as repre¬ 
sented in fig. 294. If one of them is more brilliant than the other, 
that which proceeds from the light M, for instance, the instrument is 
brought nearer the other light until the two bands .exhibit the same 
brightness. The distance of the photometer from each of the two lights 
being then measured, their intensities are proportional to the squares of 
the distances. 


CHAPTER II. 

REFLECTION OF LIGHT. MIRRORS. 

440. Laws of the reflection of light.— When a luminous ray meets 
a polished surface, it is reflected according to the following two laws, 
which, as we have seen, also prevail for heat:— 

I. The angle of reflection is equal to the angle of incidence. 

II. The incident and the reflected ray are both in the same plane , which 
is perpendicular to the reflecting surface. 

The -words are here used in the same sense as in article 357, and need 
no further explanation. 

First proof. The two laws may be demonstrated by the apparatus 
represented in fig. 295. It consists of a graduated circle in a vertical 
plane. Two brass slides move round the circumference ; on one of them 
there is a piece of ground glass, P, and on the other an opaque screen, N, 
in the centre of which is a small aperture. Fixed to the latter slide 




408 


ON LIGHT. 


[ 440 - 


there is also a mirror, M, which can be more or less inclined, but 
always remains in a plane perpendicular to the plane of the graduated 
circle. Lastly, there is a small polished metallic mirror, m, placed hori¬ 
zontally in the centre of the circle. 

In making the experiment, a pen¬ 
cil of solar light, S, is caused to 
impinge on the mirror M, which is 
so inclined that the reflected light 
passes through the aperture in N, 
and falls on the centre of the mirror 
The luminous pencil then ex¬ 



periences a second reflection in a 
direction mP, which is ascertained 
by moving P until an image of the 
aperture is found in its centre. The 
number of degrees comprised in the 
arc AN is then read off, and like¬ 
wise that in AP, these being equal, 
it follows that the angle of reflec¬ 
tion, AmP, is equal to the angle of 
incidence, AmM. 

The second law follows from the 
arrangement of the apparatus, the 
plane of the rays and waP being 
parallel to the plane of the graduated circle, and consequently, perpen¬ 
dicular to the mirror m. 



Fig. 296. 

Second proof. The law of the reflection of light may also be demon- 














REFLECTION OF LIGHT. 


409 


- 442 ] 

strated by the following experiment, which is susceptible of greater 
accuracy than that just described. In the centre of a graduated circle, 
M (tig. 296), placed in a vertical position, there is a small telescope 
moveable in a plane parallel to the limb ; at a suitable distance there is 
a vessel full of mercury, which forms a perfectly horizontal plane mirror. 
Some particular star of the first or second magnitude is viewed through 
the telescope in the direction AE, and the telescope is then inclined so as 
to receive the ray, AD, coming from the star after being reflected from 
the brilliant surface of the mercury. In this way the two angles formed 
by the rays EA and DA, with the horizontal AH, are found to be equal, 
from which it may easily be shown that the angle of incidence, E'DE, is 
equal to the angle of reflection, EDA. For if DE is the normal to the 
surface of the mercury, it is perpendicular to AH, and AED, ADE are 
the complements of the equal angles EAH, DAII; therefore AED, ADE 
are equal; but the two rays, AE and DE', may be considered parallel in 
consequence of the great distance of the star, and therefore the angles 
EDE'and DEA are equal, for they are alternate angles, and, consequently, 
the angle EDE' is equal to the angle EDA. 

REFLECTION OF LIGHT FROM PLANE SURFACES. 

441. Mirrors. Images. —Mirrors are bodies with polished surfaces, 
which show by reflection objects presented to them. The place at which 
objects appear is their imat/e. According to their shape, mirrors are 
divided into plane , concave , convex, spherical, parabolic, conical, kc. 



Fig. 29 6a. Fi S- 297< 

442. Formation of images by plane mirrors.— The determination 
of the position and size of images resolves itself into investigating the 
images of a series of points. And first, the case ot a single point. A. 
placed before a plane mirror, MN (fig. 296a), will be considered. Any 
ray, AB, incident from this point on the mirror, is reflected m the direc¬ 
tion BO. making the angle of reflection, DBG, equal to the angle of inci¬ 
dence, DBA. 


T 









410 


ON LIGHT. 


[ 443 - 

If now a perpendicular, AN, be let fall from the point A on the mirror, 
and if the raj, OB, be prolonged below the mirror until it meets this 
perpendicular on the point a, two triangles are formed, ABN and BNa, 
which are equal, for they have the side BN common to both, and the 
angles ANB, ABN, equal to the angles aNB, aBN, for the angles ANB 
and «NB are right angles, and the angles ABN and aBN are equal to the 
angle OBM. From the equality of these triangles it follows that «N is 
equal to AN; that is, that any ray, AB, takes such a direction after 
being reflected, that its prolongation below the mirror cuts the perpendi¬ 
cular, An, in the point a, which is at the same distance from the mirror 
as the point A. This applies also to the case of any other ray from the 
point A, AC, for example. From this the important consequence follows, 
that all rays from the point A, reflected from the mirror, folloio, after re¬ 
flection, the same direction as if they had all proceeded from thepoint a. The 
eye is deceived, and sees the point A at a, as if it were really situated at 
a. Hence in plane mirrors the image of any point is formed behind the 
mirror at a distance equal to that of the given point, and on the perpendicu¬ 
lar let fall from this point on the mirror. 

It is manifest that the image of any object will be obtained by con¬ 
structing according to this rule the image of each of its points, or, at least, 
of those which are sufficient to determine its form. Fig. 297 shows how 
the image, ab, of any object, AB, is formed. 

It follows from this construction that in plane mirrors the image is of 
the same size as the object, for if the trapezium ABCD be applied to the 
trapezium DC ab, they are seen to coincide, and the object AB agrees with 
its image. 

A further consequence from the above construction is, that in plane 
mirrors the image is symmetrical in reference to the object, and not in¬ 
verted. 

443. Virtual and real images.— There are two cases relative to the 
direction of rays reflected by mirrors, according as the rays after reflection 
are convergent or divergent. In the first case the reflected rays do not 
meet, but if they are supposed to be produced on the other side of the 
mirror their prolongations coincide in the same point, as shown in figs. 
296a and 297. The eye is then affected, just as if the rays proceeded from 
this point, and it sees an image. But the image has no real existence, 
the luminous rays do not come from the other side of the mirror; this 
appearance is called the virtual image. The images of real objects pro¬ 
duced by plane mirrors are of this kind. 

In the second case, where the reflected rays converge, of which we 
shall soon have an example in concave mirrors, the rays coincide at a 
point in front of the mirror, and on the same side as the object. They 
form there an image called the real image , for it can be received on a screen. 


REFLECTION OF LIGHT. 


411 


- 445 ] 

The distinction may be expressed by saying that real images are those 
formed hxj the reflected rays themselves , and virtual images those formed by 
their prolongations . 

444. Multiple images formed by glass mirrors.— Metallic mirrors 
which have but one reflecting surface only give one image; it is different 
with glass mirrors, they give rise to several images, which are readily 
observed when the image of a candle is looked 
at obliquely in a looking glass. A very feeble 
image is first seen, and then a very distinct one; 
behind this there are several others, whose inten¬ 
sities gradually decrease until they disappear. 

This phenomenon arises from the looking glass 
having two reflecting surfaces. When the rays 
from the point A meet the first surface, a part 
is reflected and forms an image, a, of the point 
A, on the prolongation of the ray 6E, reflected 
by this surface ; the other part passes into the 
glass, and is reflected at c, from the layer of metal which covers the 
hinder surface of the glass, and reaching the eye in the direction «TI, gives 
the image a'. This image is distant from the first by double the thickness 
of the glass. It is more intense, because metal reflects better than glass. 

In regard to the other images it will be remarked, that whenever light 
is transmitted from one medium to another, for instance, from glass to 
air, only some of the rays get through, the remainder are reflected at the 
surface which bounds the two media. Consequently when the pencil cd, 
reflected from c, attempts to leave the glass at d, most of the rays com¬ 
posing it pass into the air, but some are reflected at d, and continue 
within the glass. These are again reflected by the metallic surface, and 
form a third image of A ; after this reflection they come to MN, when 
many emerge and render the third image visible, but some are again re¬ 
flected within the glass, and in a similar manner give rise to a fourth, 
fifth, etc. image, thereby completing the series above described. It is 
manifest from the above explanation that each image must be much 
feebler than the one preceding it, and consequently not more than a 
small number are visible—ordinarily not more than eight or ten in all. 

This multiplicity of images is objectionable in observations, and, 
accordingly, metallic mirrors are preferable in optical instruments. 

445. Multiple images from two plane mirrors.— When an object 
is placed between two plane mirrors, which form an angle with each 
other either right or acute, images of the object are formed, the number 
of which increases with the inclination of the mirrors. If they are at 
light angles to each other, three images are seen, arranged as represented 
in fig. 299. The rays OC and OD from the point 0, after a single 

t 2 







412 


ON LIGHT. 


[ 446 - 

reflection, give the one an image O', and the other the image O'', while 
the ray OA, which has undergone two reflections at A and B, gives a 
third image, O'". When the angle of the mirrors is 60°, five images are 
produced, and seven if it is 45°. The number of images continues to in¬ 
crease in proportion as the angle diminishes, and when it is zero, that is, 

when the mirrors are parallel, the number 
of images is theoretically infinite. This 
multiplicity arises from the fact that the 
luminous rays undergo an increasing num¬ 
ber of reflections from one mirror to the 
other. 

The kaleidoscope, invented by Sir 1). 
Brewster, depends on this property of in¬ 
clined mirrors. It consists of a tube in 
which are three mirrors inclined at 60°; 
one end of the tube is closed by a piece of 
ground glass, and the other by "a cap 
provided with an aperture. Small irre¬ 
gular pieces of coloured glass are placed 
at one end between the ground glass and another glass disc, and on 
looking through the aperture, the other end being held towards the light, 
the objects and their images are seen arranged in beautiful symmetrical 
forms ; by turning the tube an endless variety of these shapes is obtained. 

446. Irregular reflection. —The reflection from the surfaces of 
polished bodies, the laws of which have just been stated, is called the 
regular or specular reflection : but the quantity thus reflected is less than 
the incident light. The light incident on an opaque body actually 
separates into three parts : one is reflected regularly, another irregularly, ] 
that is, in all directions; while a third is extinguished, or absorbed by 
the reflecting body. If light falls on a transparent body a considerable 
portion is transmitted with regularity. 

The irregularly reflected light is called scattered light : it is that which 
makes bodies visible. The light which is reflected regularly does not I 
give us the image of the reflecting surface, but that of the body from 
which the light proceeds. If, for example, a solar beam be incident on 
a well-polished mirror in a dark room, the more perfectly the light is 
reflected the less visible is the mirror in the different parts of the room. 
The eye does not perceive the image of the mirror, but that of the sun. 

If the reflecting power of the mirror be diminished by sprinkling on it a 
light powder, the solar image becomes feebler, and the mirror is visible 
from all parts of the room. Perfectly smooth polished reflecting surfaces, 
if such there were, would be invisible. 

447. Intensity of reflected light. —The intensity of the reflecting 





413 


- 449 ] REFLECTION OF LIGHT FROM CURVED SURFACES. 

power of a body increases with the degree of polish, and with the 
obliquity of the incident ray. For instance, if a sheet of white paper be 
placed before a candle, and be looked at very obliquely, an image of the 
flame is seen by reflection, which is not the case if the eye receives less 
oblique rays. 

The intensity of the reflection varies with different bodies, even when 
the degree of polish and the angle of incidence are the same. It also 
varies with the nature of the medium which the ray is traversing before 
and after reflection. Polished glass immersed in water loses a great part 
of its reflecting power. 

REFLECTION OE LIGHT FROM CURVED SURFACES. 

448. Spherical mirrors.— It has been already stated (441) that there 
are several kinds of curved mirrors j those most frequently employed are 
spherical and parabolic mirrors. 

Spherical mirrors are those whose curvature is that of a sphere; their 
surface may be supposed to be formed by the revolution of an arc MN 
(fig. 300) about the radius CA, which unites the middle of the arc to the 
centre of the circle of which it is a part. According as the reflection 
takes place from the internal or the external face of the mirror it is said 
to he concave or convex. C, the centre of the hollow sphere, of which the 
mirror forms part, is called the centre of curvature or geometrical centre : 
the point A is the centre of the figure. The infinite right line, AL, 
which passes through A and C, is the principal axis of the mirror: any 
right line which simply passes through the centre C, and not through the 
point A, is a secondary axis. The angle MCN, formed by joining the 
centre and extremities of the mirror, is the apeHure. A principal or 
meridional section is any section made by a plane through its principal 
axis. In speaking of mirrors those lines alone will be considered which 
lie in the same principal section. 

The theory of the reflection of light from curved mirrors is easily 
deduced from the laws of reflection from plane mirrors, by considering 
the surface of the former as made up of an infinitude of extremely small 
plane surfaces, which are its elements. The normal to the curved surface 
at a given point is the perpendicular to the corresponding element, or, 
what is the same thing, to its corresponding tangent plane. It is shown 
in geometry that in spheres all the normals pass through the centre of 
curvature, so that the normal may readily be drawn to any point of a 
spherical mirror. 

449. Focus of a spherical concave mirror. —In a curved mirror 
the focus is a point in which the reflected rays meet or tend to meet if 
produced either backwards or forwards ; there may either be a real focus 
or a virtual focus. 


414 


ON LIGHT. 


[ 449 - 

Real focus .—We shall first consider the case in which the luminous 
rays are parallel to the principal axis, which presupposes that the 
luminous body is at an infinite distance; let GD (fig. 300) be such a 
ray. 

From the hypothesis that curved mirrors are composed of a number of 
infinitely small plane elements, this ray would be reflected from the 
element corresponding to the point D, according to the laws of the re¬ 
flection from plane mirrors (440) ; that is, that CD being the normal at 
the point of incidence, D, the angle of reflection, CDF, is equal at the 


Fig. 300. 

angle of incidence, GDC, and is in the same plane. It follows from this 
that the point F, where the reflected ray cuts the principal axis, divides 
the radius of curvature, AC, very nearly into two equal parts. For in 
the triangle DFC, the angle DCF is equal to the angle CDG, for they are 
alternate and opposite angles; likewise the angle CDF is equal to the 
angle CDG, from the laws of reflection; therefore the angle FDC is 
equal to the angle FCD, and the sides FC and FD are equal as being 
opposite to equal angles. Now the smaller the arc, AD, the more nearly 
does DF equal AF ; and when the arc is only a small number of degrees 
the right lines AF and FC may be taken as approximately equal, and the 
point F may be taken as the middle of AC. So long as the aperture of 
the mirror does not exceed 8 to 10 degrees, any other ray, IIB, will after 
reflection pass very nearly through the point F. Hence, when a pencil 
of rays parallel to the axis falls on a concave mirror, the rays intersect 
after reflection in the same point, which is at an equal distance from the 
centre of curvature and from the mirror. This point is called the 
principal focus of the mirror, and the distance AF is the principal focal 
distance. 

All rays parallel to the axis meet in the point F ; and conversely if a 
luminous object be placed at F, the rays emitted by this object will after 
reflection take the directions DG, BH, parallel to the principal axis ; for 
in this case the angles of incidence and reflection have changed places, 
but these angles always remain equal. 

The case is now to be considered in which the rays are emitted from a 
luminous point, L (fig. 301), placed on the principal axis, but at such 







415 


- 449 ] REFLECTION OF LIGHT FROM CURVED SURFACES. 

a distance that they are not parallel, hut divergent. The angle LKC, 
which the incident ray LK forms with the normal KC, is smaller than 
the angle SKC, which the ray SK parallel to the axis forms with the 
same normal, and, consequently, the angle of reflection corresponding to 
the ray LK, must be smaller than the angle CKF, corresponding to the 
ray SK. And, therefore, the ray LK will meet the axis after reflection 
at a point l, between the centre, C, and the principal focus, F. So long 
as the aperture of the mirror does not exceed a small number of degrees, 
all the rays from the point L will intersect after reflection in the 
point l. This point is called the conjugate focus, in order to indicate 
the connection between the points L and l. These points are reciprocal 
to each other, that is, if the luminous point were transferred to l. its con¬ 
jugate focus would be at L, JK being the incident and KL the reflected 
ray. 



Fig. 301. 


On considering the figure 801 it will be seen that when the object, L, 
is brought near to or removed from the centre, C, its conjugate focus 
approaches or recedes in a corresponding manner, for the angles of 
incidence and reflection increase or decrease together. 

If the object L coincide with the centre C, the angle of incidence is 
null, and as the angle of reflection must be the same, the ray is reflected 
on itself, and the focus coincides with the object. When the luminous 
object is between the centre, C, and the principal focus, the conjugate 
focus in turn is on the other side of the centre, and is further from the 
centre according as the luminous point is nearer the principal focus. If 
the luminous point coincides with the principal focus, the reflected rays, 
being parallel to the axis, will not meet, and there is, consequently, no 
focus. 

Virtual focus .—There is, lastly, the case in which the object is placed 
at L, between the principal focus and the mirror (fig. 302). Any ray, 
LM, emitted from the point L, makes with the normal CM, an angle of 
incidence, LMC, greater than FMC j the angle of reflection must be 
greater than CMS, and therefore the reflected ray, ME, diverges 
from the axis, AK. This is also the case with all rays from the 
point L, and hence these rays do not intersect, and, consequently, form 




416 


ON LIGHT. 


[ 450 - 

no conjugate focus; but if they are conceived to be prolonged on the 
other side of the mirror their prolongations will intersect in the same 
point, l , on the axis, and the eye experiences the same impression as if the 
rays were emitted from the point, l. Hence a virtual focus is formed quite 
analogous to those formed by plane mirrors (443) 

In all these cases it is seen that the position of the principal focus is 
constant, while that of the conjugate foci and of the virtual foci vary. 



Fig. 302. Fig. 303. 

The principal and the conjugate foci are alivays on the same side of the 
mirror as the object, while the virtual focus is always on the other side of 
the mirror. 

Hitherto the luminous point has always been supposed to be placed on 
the principal axis itself, and then the focus is formed on this axis. In 
the case in which the luminous point is situate on a secondary axis, LB 
(fig. 303), by applying to this axis the same reasoning as in the preceding 
case it will.be seen that the focus of the point L is formed at a point 1, 
on the secondary axis, and that according to the distance of the point L, 
the focus may be either principal, conjugate, or virtual. 

450. Foci of convex mirrors. —In convex mirrors there are onlv 



Fig. 304. 

virtual foci. Let SI, TK ... (fig. 304), be rays parallel to the 
principal axis of a convex mirror. These rays, after reflection, take the 
diverging directions IM, KH, which, when continued, meet in a point, F, 
which is the principal virtual focus of the mirror. By means of the 




417 


- 451 ] REFLECTION OF LIGHT FROM CURVED SURFACES. 

triangle CKF, it may be shown in the same manner as with concave 
mirrors, that the point F is approximately the middle of the radius of 
curvature, CA. 

If the incident luminous rays, instead of being parallel to the axis, 
proceed from a point, L, situated on the axis at a finite distance, it is at 
once seen that a \ irtual focus will be formed between the principal focus, 
F, and the mirror. 

451. Determination of the principal focus.— In the applications 
of concave and convex mirrors it is often necessary to know the radius of 
curvature. This is tantamount to finding the principal focus; for being 
situated at the middle of the radius, it is simply necessary to double the 
focal distance. 

To find this focus with a concave mirror, it is exposed to the sun’s 
rays, so that its principal axis is parallel to them, and then with a small 
screen of ground glass the point is sought at which the image is formed 
with the greatest intensity: this is the principal focus. The radius of the 
mirror is double this distance. 

If the mirror is convex it is covered with paper, but two small portions, 
II and I, are left exposed at equal distances from the centre of the figure 
A, and on the same principal section (fig. 305). A screen, MN, in the 



Fig. 305. 

centre of which is an opening larger than the distance III, is placed before 
the mirror. If a pencil of solar rays, SH, ST, parallel to the axis, fall on the 
mirror, the light is reflected at H and I, on the parts where the mirror 
is left exposed, and forms on the screen two brilliant images at h and i. 
By moving the screen MN, nearer to or farther from the mirror, a posi¬ 
tion is found at which the distance hi is double that of III. The distance 
AD, from the screen to the mirror, then equals the principal focal 
distance. For the arc, HAI, does not sensibly differ from its chord, and 

HI FA 

because the triangles Fill and F hi are similar, but III is half 

hi 4 D 

of hi, and therefore also FA is the half of FD, and therefore AD is 
equal to AF. Further, FA is the principal focal distance; for the rays 

t 3 



418 ON LIGHT. [ 452 - 

SH and S'l are parallel to the axis: consequently also twice the distance 
AD equals the radius of curvature of the mirror. 

452. Formation of images in concave mirrors. —Hitherto it has 
been supposed that the luminous or illuminated object placed in front of 
the mirror was simply a point; but if this object has a certain magnitude, 
we can conceive a secondary axis drawn through each of its points, and 
thus a series of real or virtual foci could be determined, the collection of 
which composes the image of the object. By the aid of the constructions 
which have served for determining the foci, we shall investigate the 
position and magnitude of these images in concave and in convex 
mirrors. 

Real image .—We shall first take the case in which the mirror is con¬ 
cave, and the object AB (fig. 306), is on the other side of the centre. To 



Fig. 306. 


obtain the image or the focus of any point, A, a secondary axis, AE, is 
drawn from this point, and then drawing from the point A an incident 
ray, AD, the normal to this point CD is taken, and the angle of reflection, 
CD«, is made equal to the angle of incidence, ADC. The point a, where 
the reflected ray cuts the secondary axis, AE, is the conjugate focus of 
the point A, because every other ray drawn from this point passes 
through with a. Similarly if a secondary axis, BI, be drawn from 
the point B, the rays from this point meet after reflection in b, and form 
the conjugate fccus of B. And as the images of all the points of the 
object are formed between a and b, ab is the complete image of AB. From 
what has been said about foci (449) it appears that this image ispxd 
inverted, smaller than the object , and placed between the centre of curvature 
and the principal focus. This image may be seen in two ways ; by placing 
the eye in the continuation of the reflected rays, and then it is an aerial 
image which is seen j or the rays are collected on a screen, on which the 
image appears to be depicted. 

If the luminous or illuminated object is placed at ab, between the 
principal focus and the centre, its image is formed at AB. It is tlmn a 
real but inverted image ; it is greater than the object, and the greater as 
the object, ab, is nearer the focus . 





419 


- 453 ] REFLECTION OF LIGHT FROM CURVED SURFACES. 

If the object is placed in the principal focus itself, no image is pro¬ 
duced ; for then the rays emitted from each point form after reflection 
as many pencils respectively parallel to the secondary axis, which is 
drawn through the point from which they are emitted (449), and hence 
neither foci nor images are formed. ' 

When all points of the object, AB, are above the principal axis (fig. 



Fig. 307. 

307), by repeating the preceding construction, it is readily seen that the 
image of the object is formed at ab. 

Virtual image .—The case remains in which the object is placed 
between the principal focus and the mirror. Let AB be this object 
(fig. 308) ; the incident rays after reflection take the directions DI and KH, 
and their prolongations form a virtual image, a, of the point A, on the 



Fig. 308. 

secondary axis. Similarly, an image of B is formed at b, consequently 
the eye sees at ab the image of AB. This image is virtual, erect, and 
larger than the object. 

From what has been stated it is seen that according to the distance of 
the object concave mirrors produce two kinds of images, or none at all; 
a person notices this by placing himself before a concave mirror. At a 
certain distance he sees an image of himself inverted and smaller: this 
is the real image: at a less distance the image becomes confused and 
disappears when he is at the focus; still nearer the image appears erect, 
but larger—it is a virtual image. 

453. Formation of images in convex mirrors. —Let AB (fig. 309), 





420 


ON LIGHT. 


[ 454 - 

be an object placed before a mirror at any given distance, AC and BC 
are secondary axes, and it follows from what has been already stated, 
that all the rays from A are divergent after reflection, and that their 
prolongations pass through a point a, which is the virtual image of the 
point A. Similarly the rays from B form a virtual image of it in the 
point b. The eye which receives the divergent rays, DE, IvA, . . . 
sees in ab an image of AB. Hence, whatever the position of an object 



Fig. 309. 

before a convex mirror, the image is ahsmgs. virtual, erect , a nd smaller than 
the object. 

454. Formulae for spherical mirrors. —The relation between the 
position of an object and that of its image in spherical mirrors may be 
expressed by a very simple formula. In the case of concave mirrors let 
It be its radius of curvature, p the distance LA of the object, L (fig. 310), 



Fig. 310. 

and p' the distance IA of the image from the mirror. In the triangle 
LMZ, the normal MC divides the angle LMZ in two equal parts, and 
from geometry it follows that the two segments, LC, Cl, are to each 

other as the two sides containing the angle, that is ; therefore 

(JL LM 

Cl X LM = CL x ZM. 

If the arc, AM, does not exceed 5 or 6 degrees, the lines ML and MZ 
are approximately equal to AL and AZ, that is, to p and p'. 

Further, CZ = CA — AZ = II -p' f 

and also CL = AL — AC = p — R. 

These values substituted in the preceding equations give 
(R - p')p = (p - R )p', 

R/j — pp f = pp r - Rp'. 









- 455 ] 


REFLECTION OF LIGHT FROM CURVED SURFACES. 


420 


+ 1 
p ±c 




( 1 ) 


( 2 ) 


( 3 ) 


From which transposing and reducing we have 

Up += 2pp' . 

If the terms of this equation be all divided by /?/?'R, we obtain 
1 
P‘ 

which is the usual form of the equation. 

From the equation (1) we get 

1 2/? - R 

which gives the distance of the image from the mirror, in terms of the 
distance of the object, and of the radius of curvature. 

455. Discussion of the formulae for mirrors.— We shall now in¬ 
vestigate the different values of p', according to the values of p in the 
formula (3). 

i. Let the object be placed at an infinite distance on the axis, in 
which case the incident rays are parallel. To obtain the value of p' 
both terms of the fraction (3) must be divided by p, which gives 

R 

P' = 


2 _ 5 • • • (*> 

p 

as p is infinite — is zero, and we have p' = ~ ; that is, the image is 

formed in the principal focus, as ought to be the case, for the incident 
rays are parallel to the axis. 

ii. If the object approaches nearer the mirror, p decreases, and as 
the denominator of the formula (4) diminishes, the value ofjt?' increases: 
consequently the image approaches the centre at the same time as the 
object, but it is always between the principal focus and the centre, for 


R 


R 


so long as p is > R, we have —--p > ^ an( i < R- 

2 - - - " 

P 

iii. When the object coincides with the centre, p — R, and, conse¬ 
quently, p' = R, that is, the image coincides with the object. 

iv. When the luminous object is between the centre and the 
principal focus, p < R, and hence from the formula (4), /?' > R, that is, 
the image is formed on the other side of the centre. When the object 

is in the focus, p = which gives/?' = oo, that is, the image is 
Z U 

at an infinite distance, for the reflected rays are parallel to the axis. 

v. Lastly, if the object is between the principal focus and the 

mirror, we get p < p is then negative, because the denominator 

z 




422 


ON LIGHT. 


[ 456 - 


of tbe formula (4) is negative. Therefore, the distance p' of the mirror 
from the image must be calculated on the axis in a direction opposite to 
p. The image is then virtual, and is on the other side of the mirror. 

1 1 2 

Making p' negative in the formula (2) it becomes--= ; m this 

° ° p p li 

form it comprehends all cases of virtual images in concave mirrors. 

In the case of convex mirrors the image is always virtual (453); p' 

and R are of the same sign, since the image and the centre are on the same 

side of the mirror, while the object being on the opposite side, is of the 

contrary sign; hence in the formula (2) we get 


1 

P' 



(o) 


as the formula for convex mirrors. It may also be found directly by the 
same geometrical considerations as those which have led to the formula 
(2) for concave mirrors. 

It must be observed that the preceding formulae are not rigorously 
true, inasmuch as they depend upon the hypothesis that the lines LM 
and ZM (fig. 310), are equal to LA and A/; although this is not true he 
error diminishes without limit with the angle MCA ; and when this angle 
does not exceed a few degrees, the error is so small that it may, in prac¬ 
tice, be neglected. 

456. Calculation of the magnitude of images. —By means of the 
above formulae the magnitude of an image may be calculated, when the 
distance of the object, its magnitude, and the radius of the mirror are 
given. For if BD be the object (fig. 311), bd its image, and if the 



Fig. 311. 


distance KA, and the radius AC be known, Ao can be calculated bv 
means of formula (3) of article 454. Ao known, oC can be calculated. 
But as the triangles BCD and dCb are similar, their bases and heights 
are in the proportion bd : BD = Co : CK, or 

Length of the image : length of the object 
= distance from image to centre : distance from the object to centre. 
457. Spherical aberration. Caustics.— In the foregoing theory of 
the foci and images of spherical mirrors, it has already been observed 



- 459 ] REFLECTION OF LIGHT FROM CURVED SURFACES. 423 

that the reflected rays only pass through a single point when the aperture 
of the mirror does not exceed 8 or 10 degrees (449). With a larger 
aperture, the rays reflected near the edges meet the axis nearer the 
mirror than those which are reflected at a small distance from the neigh¬ 
bourhood of the centre of the mirror. Hence arises a want of precision 
in these images, which is called spherical aberration by reflection, to dis¬ 
tinguish it from the spherical aberration by refraction, which occurs in 
the case of lenses. 

Every reflected ray cuts the one next to it (fig. 312), and their points 
of intersection form in space a curved surface, which is called the caustic 



Fig. 312. 

by reflection. The curve FM represents one of the branches of a section 
of this surface made by the plane of the paper. When the light of a 
candle is reflected from the inside of a cup or tumbler, a section of the 
caustic surface can be seen by partly filling the cup or tumbler with 
milk. 

458. Applications of mirrors. —The applications of plane mirrors 
in domestic economy are well known. Mirrors are also frequently used 
in physical apparatus for sending light in a certain direction. The solar 
light can only be sent in a constant direction by making the mirror move- 
able. It must have a motion which compensates for the continual 
change in the direction of the sun’s rays produced by the apparent diurnal 
motion of the sun. This result is obtained by means of a clock-work 
motion, to which the mirror is fixed, and which causes it to follow the 
course of the sun. This apparatus is called the heliostat. The reflection 
of light is also used to measure the angles of crystals by means of the 
instruments known as reflecting goniometers. , 

Concave spherical mirrors are also often used. They are applied for 
magnifying mirrors , as in a shaving mirror. They have been employed 
for burning mirrors, and are still used in telescopes. They also serve as 
reflectors, for conveying light to great distances, by placing a luminous 
object in their principal focus. For this purpose, however, parabolic 
mirrors are preferable. 

459. Parabolic mirrors. —Parabolic mirrors are concave mirrors, 



ON LIGHT. 


424 


[ 459 - 


whose surface is generated by the revolution of the arc of a parabola, AM 
about its axis, AX (fig. 313). 

It has been already stated that in spherical mirrors the rays parallel 
to the axis converge only approximately to the principal focus, and 
reciprocally when a source of light is placed in the principal focus of 

these mirrors, the reflected rays 
are not exactly parallel to the axis. 
Parabolic mirrors are free from 
this defect; they are more difficult 
to construct, but are far better for 
reflectors. It is a well-known 
property of a parabola that the 
right line FM, drawn from the 
focus F, to any point, M, of the 
curve, and the line ML, parallel 
to the axis AF, make equal 
angles with the tangent TT' at 
this point. Consequently, all rays 
parallel to the axis after reflection in the focus of the mirror, F, and 
reciprocally, when a source of light is placed in the focus, the rays 

incident on the mirror, are reflected exactly 
parallel to the axis. The light thus reflected 
tends to maintain its intensity even at a 
great distance, for it has been seen (438) 
that it is the divergence of the luminous 
rays which principally weakens the inten¬ 
sity of light. 

It is from this property that parabolic 
mirrors are used in carriage lamps, and in 
the lamps placed in front of and behind 
railway trains. These reflectors were for¬ 
merly used for lighthouses, but have been 
replaced by lenticular glasses. 

When two equal parabolic mirrors are 
cut by a plane perpendicular to the axis 
passing through the focus, and are then 
united at their intersections, as shown in the 
figure 314, so that their foci coincide, a 
system of reflectors is obtained with which a single lamp illuminates in 
two directions at once. This arrangement is used in lighting stair¬ 
cases. 



Fig. 314 . 





-4S1] 


SINGLE REFRACTION. 


425 


CHAPTER III. 



Fig. 315. 


SINGLE REFRACTION. LENSES. 

460. Phenomenon of refraction. —Refraction is the deflection which 
luminous rays experience in passing obliquely from one medium to 
another; for instance, from air into water. We say obliquely , because if 
the incident ray is perpendicular to the surface separating the two media, 
it is not deflected, and continues its course in a right line. 

The incident ray being represented by SO (fig. 315), the refracted ray 
is the direction OH which light takes in the second medium ; and of the 
angles SOA and HOB, which these rays form 
with the line AB, at right angles to the sur¬ 
face which separates the two media, the first 
is the angle of incidence, and the other the 
angle of refraction. According as the refracted 
ray approaches or deviates from the normal, 
the second medium is said to be more or less 
refringent or refracting than the first. 

All the light which falls on a refracting 
surface does not completely pass into it; one part is reflected and scattered, 
while another penetrates into the medium. 

Analysis shows that the direction of refraction depends on the relative 
velocity of light in the two media. On the undulatory theory the more 
highly refracting medium is that in which the velocity of propagation is 
least. 

In uncrystallised media, such as air, liquids, ordinary glass, the luminous 
ray is singly refracted; but in certain crystallised bodies, such as Iceland 
spar, selenite, &c., the incident ray gives rise to two refracted rays. The 
latter phenomenon is called double refraction , and will be discussed in 
another part of the book. We shall here deal exclusively with single 
refraction. 

461. Laws of single refraction.— When a luminous ray is refracted 
in passing from one medium into another of a different refractive power 
the following laws prevail:— 

I. Whatever the obliquity of the incident ray , the ratio which the sine of 
the incident angle bears to the sine of the angle of refraction, is constant for 
the same two media, but varies with different media. 

II. The incident and the refracted ray are in the same plane which is. 
perpendicular to the surface separating the two media. 

These are known as Descartes' laws, and are demonstrated by the 








426 


ON LIGHT. 


[ 462 - 

same apparatus as that used for the laws of reflection (440). The plane 
mirror in the centre of the graduated circle is replaced by a semi-cylin- 

drical glass vessel filled with water 
to such a height that its level is 
exactly the height of the centre 
(fig. 316). If the mirror, M, be 
then so inclined, that a reflected 
ray, MO, is directed towards the 
centre, it is refracted on passing 
into the water, but it passes out 
without refraction, because then 
its direction is at right angles to 
the curved sides of the vessel. In 
order to observe the course of the 
refracted ray it is received on a 
screen, P, which is moved until the 
image of the aperture in the screen 
N is formed in its centre. In all 
positions of the screens N and P 
the sines of the angles of incidence 
and refraction are measured by 
means of two graduated rules move- 
able so as to be always horizontal, and hence perpendicular to the dia¬ 
meter AD. 

On reading off the lengths of the sines of the angles MOA and DOP 
in the scales I and It, the numbers are found to vary with the position 
of the screens, but their ratio is constant; that is, if the sine of incidence 
becomes twice or three times as large, the sine of refraction increases in 
the same ratio, which demonstrates the first law. The second law 
follows from the arrangement of the apparatus, for the plane of the 
graduated limb is perpendicular to the surface of the liquid in the semi- 
cylindrical vessel. 

462. Index of refraction.— The ratio between the sines of the in¬ 
cident and refracted angle is called index of refraction or refractive index. 
It varies with the media; for example, from air to water it is f, and from 
air to glass it is §. 

If the media are considered in an inverse order, that is, if light passes 
from water to air, or from glass to air, it follows the same course, but in 
a contrary direction, PO becoming the incident, and OM the refracted 
ra}L Consequently, the index of refraction is reversed ; from water to 
air it is then §, and from glass to air §. 

463. Effects produced by refraction.— In consequence of refraction, 
bodies immersed in a medium more highly refracting than air appear 














SINGLE REFRACTION. 


427 


- 464 ] 

nearer the surface of this medium, but they appear to be more distant if 
immersed in a less refracting medium. Let L (fig. 317) be an object im¬ 
mersed in a mass of water. In passing thence into air the rays LA, LB 
. . . diverge from the normal to the point of incidence, and assume the 
direction AC, BD . . . the prolongations of which intersect approximately 
in the point L', placed on the perpendicular L'K. The eye receiving 
these rays sees the object L at L'. The greater the obliquity of the rays 
LA, LB . . . the higher the object appears. 

It is for the same reason that a stick plunged obliquely into water 
appears bent (fig. 318), the immersed part appearing raised. 



Fig. 317. Fig. 318. Fig. 319. 


Owing to an effect of refraction stars are visible to us even when they 
are below the horizon. For as the layers of the atmosphere are denser 
in proportion as they are nearer the earth, and as the refractive power of 
a gas increases with its density (473), it follows that on entering the 
atmosphere the luminous rays become bent, as seen in the fig. 319, 
describing a curve before reaching the eye, so that we see the star at S' 
along the tangent of this curve instead of at S. In our climate the 
atmospheric refraction does not raise the stars when on the horizon more 
than half a degree. 

464. Total reflection. Critical angle. —When a luminous ray- 
passes from one medium into another which is less refracting, as from 
water into air, it has been seen that the angle of incidence is greater than 
the angle of refraction. Hence, when light is propagated in a mass of 
water from S to 0 (fig. 320), there is always a value of the angle of in¬ 
cidence, SOB, such that the angle of refraction, AOR, is a right angle, 
in which case the refracted ray emerges parallel to the surface of the 
water. 

This angle, SOB, is called the critical angle , because for any greater 
angle, POB, the incident ray cannot emerge, but undergoes an internal 
reflection, which is called total reflection , because the incident light is 
entirely reflected. From water to air the critical angle is 48° 35'; from, 
glass to air, 41° 48'. 









428 


ON LIGHT. 


[ 465 - 

The occurrence of this internal reflection may be observed by the 
following experiment. An object, A, is placed before a glass vessel filled 
with water (fig. 321) ; the surface of the liquid is then looked at as 



Fig. 320. Fig. 321. 


shown in the figure, and an image of the object A is seen at a, formed 
by the rays reflected at m, in the ordinary manner of a mirror. 

465. Mirage.— The mirage is an optical illusion by which inverted 
images of distant objects are seen as if below the ground or in the 
atmosphere. This phenomenon is of most frequent occurrence in hot 
climates, and more especially on the sandy plains of Egypt. The ground 
there has often the aspect of a tranquil lake, on which are reflected trees 
and the surrounding villages. The phenomenon has long been known, 



Fig. 322. 


but Monge, who accompanied Napoleon’s expedition to Egypt, was the 
first to give an explanation of it. 

It is a phenomenon of refraction, which results from the unequal 
density of the different layers of the air when they are expanded by 























TRANSMISSION OF LIGHT. 


429 


-467] 

contact with the heated soil. The least dense layers are then the lowest, 
and a luminous ray from an elevated object, A (fig. 322), traverses layers 
which are gradually less refracting; for, as will be shown presently 
(473), the refracting power of a gas diminishes with lessened density. 
The angle of incidence accordingly increases from one layer to the other, 
and ultimately reaches the critical angle, beyond which, internal reflec¬ 
tion succeeds to refraction (464). The ray then rises, as seen in the 
figure, and undergoes a series of successive refractions, but in a direction 
contrary to the first, for it now passes through layers which are gradually 
more refracting. The luminous ray then reaches the eye with the same 
direction as if it had proceeded from a point below the ground, and hence 
it gives an inverted image of the object, just as if it had been reflected at 
the point 0, from the surface of a tranquil lake. 

Mariners sometimes see images in the air of the shores or of distant 
vessels. This is due to the same cause as the mirage, but in a contrary 
direction, only occurring when the temperature of the air is above that 
of the sea, for then the inferior layers of the atmosphere are denser, owing 
to their contact with the surface of the water. 


TRANSMISSION OF LIGHT THROUGH TRANSPARENT MEDIA. 


466. Media with parallel faces. —When light traverses a medium 
with parallel faces, the emei'yent rays are parallel to the incident rays. 

Let MN (fig. 323) be a glass plate with parallel faces, let SA be the 
incident, and LB the emergent ray, i and r the angles of incidence and 
of refraction at the entrance of the ray, and, lastly, i' and r the same 
angles at its emergence. At A the 
light undergoes a first refraction, the 


index of which is 


sin i 


(462). At 1) 


sin r 

it is refracted a second time, and the 

index is then - 81I1 -4-. But we have 
sin r 

seen that the index of refraction of glass 
to air is the reciprocal of its refraction 
from air to glass; hence 

sin i' sin r 

sin r' sin i 



Fig. 323. 


But as the two normals, AG and DE, are parallel, the angles r and %' 
are equal, as being alternate interior angles. As the numerators in the 
above equation are equal, the denominators must be also equal; the 
angles r' and i are therefore equal, and hence DB is parallel to SA. 

467. Prism. —In optics a prism is any transparent medium comprised 








430 


ON LIGHT. 


[4S8- 


between two plane faces inclined to each other. The intersection of 
these two faces is the edge of the prism, and their inclination is its 
refracting angle. Every section perpendicular to the edge is called a 
principal section. 

The prisms used for experiments are generally right triangular prisms 
of glass, as shown in the fig. 324, and their principal section is a tri¬ 
angle (fig. 325). In this section the point A is called the summit of 
the prism, and the right line, BC, is called the base ; these expressions 
have reference to the triangle ABO, and not to the prism. 



Fig. 324. Fig. 325. 


468. Path of rays in prisms. —When the laws of refraction are 
known, the passage of rays in a prism is readily determined. Let 0 be 
a luminous point (fig. 325) in the same plane as the principal section, 
ABC, of a prism, and let OD be an incident ray. This ray is refracted 
at D, and approaches the normal, because it passes into a more highlv 
refracting medium. At K it experiences a second refraction, but it then 
deviates from the normal, for it passes into air, which is less refractive 
than glass. The light is thus refracted twice in the same direction, so 
that the ray is deflected towards the base , and consequently the eye which 
receives the emergent ray, KII, sees the object O at O'; that is, objects 
seen through a prism appear deflected towards its summit. The angle OEO', 
which the incident and emergent rays form with each other, expresses the 
deviation of light caused by the prism, and is called the angle of deviation. 

Besides this, objects seen through a prism appear in all the colours 
of the rainbow j this phenomenon will be described under the name of 
dispersion. 

469. Conditions of emergence in prisms.— In order that any 
luminous rays refracted at the first face of a prism may emerge from the 
second, it is necessary that the refractive angle of the prism be less than 
twice the critical angle of the substance of which the prism is composed. 
For if LI (fig. 326) be the ray incident on the first face, IE the refracted 
ray, PI and PE the normals, the ray IE can only emerge from the 
second face when the incident angle, IEP, is less than the critical angle 
(464). But as the incident angle LIN increases, the angle EIP also 













TRANSMISSION OF LIGHT. 


431 


- 470 ] 

increases, while IEP diminishes. Hence, according as the direction of 
the ray LI tends to become parallel with the face AB, does this ray tend 
to emerge at the second face. 

Let LI be now parallel to AB, the angle r is then equal to the critical 
angle l of the prism, because it 
has its maximum value. Fur¬ 
ther, the angle EPK, the exterior 
angle of the triangle IPE, is 
equal to r -f i '; but the angles 
EPK and A are equal, because 
their sides are perpendicular, and 
therefore A = r -f- i'; there¬ 
fore also A = l for in this 
case r = l. Hence, if A = 21 or 
is > 21, we shall have i' — l or 
> l, and therefore the ray would 
not emerge at the second face, 
but would undergo internal reflection, and would emerge at a third face, 
BC. This would be much more the case with rays whose incident 
angle is less than BIN, because we have already seen that i' continually 
increases. Thus in the case in which the refracting angle of a prism is 
equal to 21 or is greater, no luminous ray could pass through the faces of 
the refracting angle. 

As the critical angle of glass is 41° 48', twice this angle is less than 
90°, and, accordingly, objects cannot be seen through a glass prism whose 
refracting angle is a right angle. As the critical angle of water is 48° 35', 
light could pass through a hollow rectangular prism formed of three glass 
plates, and tilled with water. 

If we suppose A to be greater than l and less than 21, then of rays in¬ 
cident at I some within the angle NIB will emerge from AO, others 
will not emerge, nor will any emerge that are incident within the angle 
NIA. If we suppose A to have any magnitude less than l, all rays in¬ 
cident at I within the angle NIB will emerge from AC, as also will 
some of those incident within the angle NIA. 

470. Minimum deviation. —When a pencil of solar light passes 
through an aperture, A, in the side of a dark chamber (fig. 327), the 
pencil is projected in a straight line, AC, on a distant screen. But if 
a vertical prism be interposed between the aperture and the screen, the 
pencil is deviated towards the base of the prism, and the image is pro¬ 
jected at D, at some distance from the point C. If the prism be turned, 
so that the incident angle decreases, the luminous disc approaches the 
point C, up to a certain position, E, from which it reverts to its original 
position even when the prism is rotated in the same direction. Hence 



Fig. 326. 



432 


ON LIGHT. 


[ 471 - 

there is a deviation, EBC, less than any other. It may be demonstrated 
mathematically that this minimum deviation takes place when the angles 
of incidence and of emergence are equal. 

The angle of minimum deviation may be calculated when the incident 
angle and the refracting angle of the prism are known. For, when the 
deviation is least, as the angle of emergence r' is equal to the incident 
angle i (fig. 326), r must = i'. But it has been shown above (469) that 
A = r i '; consequently, 

A = 2r .(1) 

If the minimum angle of deviation C'DL be called d, this angle being 
exterior to the triangle DIE, we readily obtain the equation 
d — i-r -\-r' — i' = 2* — 2 r, 

whence d = 2i— A.(2) 

which gives the angle d , when i and A are known. 

From the formulae (1) and (2) a third may be obtained, which serves 



Fig. 327. 

to calculate the index of refraction of a prism, when its refracting augle 
and the minimum deviation are known. The index of refraction, n is 
the ratio of the sines of the angles of incidence and refraction ; hence 

n — sm 1 ; replacing i and r from their values in the above equations 
sm r 1 

(1) and (2), we get 



471. Measurement of the index of refraction in solids.— By 

means of the preceding formula (3) the refractive index of a solid may be 
calculated when the angles A and d are known. 

In order to determine the angle A, the substance is cut in the form 
°f a triangular prism, and the angle measured bv means of a goniometer 
(458). 












TRANSMISSION OF LIGHT. 


433 


- 473 ] 

The angle d is measured in the following manner: a ray LI emitted 
from a distant object (fig. 328) is received on the prism, which is turned 
in order to obtain the minimum deviation EDL'. By means of a 
telescope with a graduated circle, the angle EDL is read off, which the 
refracted ray DE makes with the ray DL', coming directly from the 
object,* now this is the angle of minimum deviation, assuming that the 



Fig. 328 


object is so distant that the two rays, LI and L'D, are approximately 
parallel. These values then only need to be substituted in the equation 
(3) to give the value of n. 

This method is due to Newton. Under many circumstances it cannot 
be employed, for instance, when the refractive index of a mere drop of 
fluid is required. In this case, use may be made of a method due to 
Wollaston, which depends on the determination of the critical angle of 
the substance. 

472. Measurement of the index of refraction of liquids. —M. 

Biot has applied Newton’s method to determining the refractive index 
of liquids. For this purpose a cylindrical 
cavity, 0, of about 075 in. in diameter, is 
perforated in a glass prism, PQ, (fig. 329), 
from the incident face to the face of emer¬ 
gence. This cavity is closed by two plates 
of glass which are cemented on the sides of 
this prism. Liquids are introduced through 
a small stoppered aperture, B. The re¬ 
fracting angle and the minimum deviation 
of the liquid prism in the cavity 0 having 
been determined, their values are introduced into the formula (3), which 
gives the index. 

473. Measurement of the index of refraction of grases. A 

method for this purpose founded on that of Newton has been devised by 
MM. Biot and Arago. The apparatus which they use consists of a glass 
tube (fig. 330), bevelled at its two extremities, and closed by glass plates, 
which are at an angle of 143°. This tube is connected with a belljar, II, 

u 







434 


ON LIGHT. 


[ 473 - 


in which there is a siphon barometer, and with a stopcock by means of 

which the apparatus can be exhausted, 
and different gases introduced. After 
having exhausted the tube AB, a ray of 
light, SA, is transmitted, which is bent 
away from the normal through an angle 
r — i at the first incidence, and towards 
it through an angle i' — r' at the second. 
These two deviations being added, 
the total deviation d is r—i + i'— r'. 
In the case of a minimum deviation, 
i = r' and r — i ', whence d = A — 2/, 
since r + %' = A (469). The index from 

vacuum to air, which is evidently ~ r , 

sin i 

has therefore the value 

_!li_«, 

Fig. 330. Hence, in order to deduce the re¬ 

fractive index from vacuum into air, 
which is the absolute index , or principal index , it is simply necessary to 
know the refracting angle A, and the angle of minimum deviation d. 

To obtain the absolute index of any other gas, after having produced 
a vacuum, this gas is introduced ; the angles A and d having been mea¬ 
sured, the above formula gives the index of refraction from gas to air. 
Dividing the index of refraction from vacuum to air by the index of re¬ 
fraction from the gas to air, we obtain the index of refraction from vacuum 
to the gas, that is, its absolute index. 

By means of this apparatus Biot and Arago have found that the re¬ 
fractive indices of gases are very small as compared with those of solids 
and liquids, and that for the same gas the refractive power is proportional 
to the density ; meaning by the refractive action of a substance the square 
of its refractive index less unity, that is, ri* —1. The refractive action 
divided by the density, or 

w 2 —1 



cl 

is called the absolute reflective power. 



Ci t, Is 


Table of the absolute indices of ref raction. 

Diamond .... 2-47 to 2*75 Ruby. . 

Phosphorus. 2*224 Bisulphide of carbon . . 

Sulphur.2*115 Iceland spar, ordinary ray 


1*779 

1*678 

1*654 


















-474] 

LENSES. 

435 

Iceland spar, extraordinary 

Alcohol .... 

. . 1-374 

ray. 


Albumen .... 

. . 1-360 

Flint glass .... 


Ether. 


Rock salt .... 


Crystalline lens . . 

. . 1-384 

,, crystal . . . 

. . 1*548 

Vitreous „ . . 

. . 1-339 

Plate glass, St. Gobin 

. . 1-543 

Aqueous „ . . 

. . 1-337 

Crown glass . . . 

. . 1-500 

Water. 

. . 1-336 

Turpentine . . . 

, . 1-470 

Ice. 

. . 1-310 


Refractive indices of gases. 


Vacuum .... 

. 1-000000 

Carbonic acid . . 

. 1-000449 

Hydrogen .... 

. 1-000138 

Hydrochloric acid . 

. 1-000449 

Oxygen .... 

, 1-000272 

Nitrous oxide . . 

. 1-000503 

Air. 

. 1-000294 

Sulphurous acid . 

. 1-000665 

Nitrogen . . . . 

. 1-000300 

Olefiant gas . . . 

. 1-000678 

Ammonia .... 

. 1-000385 

Chlorine .... 

. 1-000772 


LENSES. THEIR EFFECTS. 



474. Different kinds of lenses. — Lenses are transparent media, 
which, from the curvature of their surfaces, have the property of 
causing the luminous rays which traverse them either to converge or 
to diverge. According to their curvature they are either spherical, 
cylindrical, elliptical, or parabolic. Those used in optics are always 
spherical. They are usually made either of crown glass, which is free 
from lead, or of Jlint glass, which contains lead, and is more refractive 
than crown glass. 

The combination of spherical surfaces, either with each other or with 
plane surfaces, gives rise to six kinds of lenses, sections of which are 




Fig. 331. 


represented in fig. 331; four are formed by two spherical surfaces, and 
two by a plane and a spherical surface. 

A is a doable convex, B is a plano-convex, C is a converging concavo- 
convex, D is a double concave, E is a plano-concave, and F is a diverging 

xj 2 




















ON LIGHT. 


436 


[ 475 - 


concavo-convex. The lens C is also called the converging meniscus , and 
the lens F the diverging meniscus. 

The first three, which are thicker at the centre than at the borders, are 
converging ; the others, which are thinner in the centre, are diverging. 
In the first group, the double convex lens only need be considered, and 
in the second the double concave, as the properties of each of these lenses 
apply to all those of the same group. 

In lenses whose two surfaces are spherical the centres for these surfaces 
are called centres of curvature , and the right line which passes through 
these two centres is the ’principal axis. In a plano-concave or plano¬ 
convex lens, the principal axis is the perpendicular let fall from the centre 
of the spherical face on the plane face. 

In order to compare the path of a luminous ray in a lens with that 
in a prism, the same hypothesis is made as for curved mirrors (449), that 
is, the surfaces of these lenses are supposed to be formed of an infinity of 
small plane surfaces or elements; the normal at any point is then the 
perpendicular to th.e plane of the corresponding element. It is a geo¬ 
metrical principle that all the normals to the same spherical surface pass 
through its centre. On the above hypothesis we can always conceive 
two plane surfaces at the points of incidence and convergence, which are 
inclined to each other, and thus produce the effect of a prism. Pursuing 
this comparison, the three lenses, A, B, and C, may be compared to a 
succession of prisms having their summits outwards, and the lenses, D, 
E, and F, to a series having their summits inwards; from this we see 
that the first ought to condense the rays, and the latter to disperse them, 
for we have already seen that when a luminous ray traverses a prism it 
is deflected towards the base (498). 

475. Foci in double convex lenses.— The focus of a lens is the 
point where the refracted rays, or their prolongations, meet. Double 
convex lenses have the same kind of foci as concave mirrors; that is, 
real foci and virtual foci. 

Real foci. We shall first consider the case in which the luminous 
rays which fall on the lens are parallel to its principal axis, as shown in 
the fig. 332. In this case, any incident ray, LB, in approaching the 
normal of the point of incidence, B, and in diverging from it at the 
point of emergence, D, is twice refracted towards the axis, which it cuts 
at F. As all rays parallel to the axis are refracted in the same manner, 
it can be shown by calculation that they all pass very nearly through 
the point F, so long as the arc, DE, does not exceed 10° to 12°. This 
point is called the principal focus , and the distance FA is the principal 
focal distance. It is constant in the same lens, but varies with the radii 
of curvature and the index of refraction. In ordinary lenses, which are 
of crown glass, and in which the radii of the two surfaces are nearly 


LENSES. 


437 


- 475 ] 

equal, the principal tocus coincides very closely with the centre of 
curvature. 


V 


Fig. 332. 

We shall now consider the case in which the luminous object is out¬ 
side the principal focus, but so near that all incident rays form a diver¬ 
gent pencil, as shown in fig. 333. The luminous point being at L, by 
comparing the path of a diverging ray, LB, with that of a ray, SB, 



Fig. 333. 

parallel to the axis, the former is found to make with the normal an 
angle, LB n, greater than the angle SBra; consequently, after traversing 
the lens, the ray cuts the axis at a point, /, which is more distant than 
the principal focus, F. As all rays from the point L intersect approxi- 


J 




Fig. 334. 

mately in the same point /, this latter is the conjugate focus of the point 
L j this term has the same meaning here as in the cases of mirrors, and 








438 


ON LIGHT. 


[476- 

expresses the relation existing between the two points L and l , which 
is of such a nature, that if the luminous point is moved to l, the focus 
passes to L. 

According as the object comes near the lenses, the convergence of the 
emergent rays decreases, and the focus l becomes more distant; when the 
object L coincides with the principal focus, the emergent rays on the 
other side are parallel to the axis, and there is no focus, or, what is the 
same thing, it is infinitely distant. As the refracted rays are parallel in 
this case, the intensity of light only decreases slowly, and a simple lamp 
can illuminate great distances. It is merely necessary to place it in the 
focus of a double concave lens, as shown in fig. 334. 

Virtual foci. A double convex lens has a virtual focus, when the 
luminous object is placed between the lens and the principal focus, as 
shown in fig. 335. In this case the incident rays make with the normal 



7 L 



Bj§ 


F... 







Fig. 335. 

greater angles than those made by the rays FI from the principal focus; 
hence, when the former rays emerge, they move farther from the axis 
than the latter, and form a diverging pencil, HK, GM. These rays 
cannot produce a real focus, but their prolongations intersect in some 
point / on the axis, and this point is the virtual focus of the point L 
(443). 

476. Foci in double concave lenses.— In double concave lenses 
there are only virtual foci, whatever the distance of the object. Let 



336. Fig. 337. 

SI be any pencil of rays parallel to the axis (fig. 336), any ray, SI, is 
refracted at the point of incidence, I, and approaches the normal, CL 





LENSES. ' 


439 


-478] 

At the point of emergence it is refracted, but diverges from the normal, 
CrC , so that it is twice refracted in a direction which moves it from 
the axis, CC'. As the same thing takes place for every other ray, 
S'KMN, it follows that the rays, after traversing the lens, form a diverg¬ 
ing pencil, GH, MN. Hence there is no real focus, but the prolonga¬ 
tions of these rays cut one another in a point F, which is the principal 
virtual focus. 

In the case'in which the rays proceed from a point, L (fig. 337), on 
the axis, it is found by the same construction that a virtual focus is 
formed at l, which is between the principal focus and the lens. 

477. Experimental determination of the principal focus of 
lenses.— To determine the principal focus of a double convex lens, it may 
be exposed to the sun’s rays so that they are parallel to its axis. The 
emergent pencil being received on a ground glass screen, the point to 
which the rays converge is readily seen; it is the principal focus. 

With a double concave lens, the face, ab (fig. 338), is covered with an 
opaque substance, such as lampblack, two small apertures, a and b, being 


Fig. 338. 

left in the same principal section, and at an equal distance from the 
axis ; a pencil of solar light is then received on the other face, and the 
screen, P, which receives the emergent rays, is moved nearer to or 
farther from the lens, until A and B, the spots of light from the small 
apertures, a and b , are distant from each other by twice ab. The distance 
I) I is then equal to the focal distance FD, because the triangles Fa& and 
FAB are similar. 

478. Optical centre, secondary axis. —In every lens there is a 
point called the optical centre , which is situated on the axis, and which 
has the property that any luminous ray passing through it experiences 
no angular deviation, that is, that the emergent ray is parallel to the 
incident ray. The existence of this point may be demonstrated in the 
following manner: Let two parallel radii of curvature, CA and C'A' 
(fig. 339), be drawn to the two surfaces of a double convex lens. As 
the two plane elements of the lens A and k! are parallel, as being per¬ 
pendicular to two parallel right lines, it will be granted that the 





440 


ON LIGHT. 


[ 479 - 

refracted ray, KA, A'K', is propagated in a medium with parallel faces. 
Hence, a ray which reaches A at such an inclination, that after refrac¬ 
tion it takes the direction A A', will emerge parallel to its first direction 
(466) ; the point O, at which the right line cuts the axis, is therefore 
the optical centre. The position of this point may he determined for 
the case in which the curvature of the two faces is the same, which is 
the usual condition, by observing that the triangles COA and C'O A 7 are 
equal, and therefore that OC=OC' which gives the point O. If the cur¬ 
vatures are unequal, the triangles COA and C'OA 7 rre similar, and either 
CO or C'O may be found, and therefore also the point O. 

In double concave or concavo-convex lenses, the optical centre may 
be determined by the same construction. In lenses with a plane face, 
this point is at the intersection of the axis by the curved face. 


Fig. 339. 

Every right line, PP 7 (fig. 340), which passes through the optical 
centre without passing through the centres of curvature, is a secondary 
axis. From the property of the optical centre, every secondary axis 
represents a luminous rectilinear ray passing through this point, for 
from the slight thickness of the lenses, it may be assumed that rays 
passing through the optical centre are in a right line, that is, that the 
small deviation may be neglected which rays experience in traversing 
a medium with parallel faces (fig. 323). 

So long as the secondary axes only make a small angle with the prin¬ 
cipal axis, all that has hitherto been said about the principal axis is appli¬ 
cable to them; that is, that rays emitted from a point, P (fig. 340), on the 
secondary axis, PP 7 , nearly converge to a certain point of this axis, P', 
and according as the distance from the point P to the lens is greater or 
less than the principal focal distance, the focus thus formed will be con- 
jugate or virtual. This principle is the foundation of what follows as to 
the formation of images. 

479. Formation of images in double convex lenses. —In lenses 
as well as in mirrors the image of an object is the collection of the foci 
of its several points ; hence the images furnished by lenses are real or 
virtual in the same case as the foci, and their construction resolves itself 



Fig. 340. 






- 479 ] LENSES. 441 

into determining a series of points, as was the case with mirrors 
(452). 

i. Real image. Let AB (fig. 341) be placed beyond the principal focus. 
If a secondary axis, A a, be drawn from the outside point, A, any ray, 
AC, from this point, will be twice refracted at C and D, and both times 
in the same direction, approaching the secondary axis, which it cuts at a. 
From what has been said in the last paragraph, the other rays from the 
point A will intersect in the point a , which is accordingly the con¬ 
jugate focus of the point A. If the secondary axis be drawn from the 
point B, it will be seen, in like manner, that the rays from this point 
intersect in the point b, and as the points between A and B have their 
foci between a and b, a real but inverted image of AB will be formed at 
ab. 

In order to see this image, it may be received on a white screen, on 
which it will be depicted, or the eye may be placed in the path of the 
rays emerging from it. 



Fig. 341. 


Conversely, if a b were the luminous or illuminated object which 
emitted rays, its image would be formed at AB. Two consequences 
important for the theory of optical instruments follow from this : that, 
1st, If an object, even a very large one , is at a sufficient distance from a 
double convex lens, the real and inverted image which is obtained of it is very 
small, it is near the principal focus, but somewhat farther from the lens 
than this is ; 2nd, if a very small object be placed near the principal focus, 
but a little before it, the image which is formed is at a great distance, it is 
much larger, and that in proportion as the object is nearer the principal 
focus. In all cases the object and the image have the same proportion as 
their distances from the lens. 

These two principles are experimentally confirmed by receiving on a 
screen the image of a lighted candle, placed successively at various 
distances from a double convex lens. 

ii. ViHual image. There is another case in which the object, AB 
(fig. 342), is placed between the lens and its principal focus. If a secon¬ 
dary axis, Oa, be drawn from the point A, every ray, AC, after having 

u 3 





442 


ON LIGHT. 


[ 480 - 


been twice refracted on emerging, diverges from this axis, since the 
point A is at a less distance than the principal focal distance (475). This 
ray, continued in an opposite direction, will cut the axis Oa, in the point 
«, which is the virtual focus of the point A. Tracing the secondary axis 
of the point B, it will be found, in the same manner, that the virtual 



Tig. 342. 

' 

focus of this point is formed at b. There is, therefore, an image of AB 
at ab. This is a virtual image , it is erect, and larger than the object. 

The magnifying power is greater in proportion as the lens is more con¬ 
vex, and the object nearer the principal focus. We shall presently show 
how the magnifying power may be calculated by means of the formula 
relating to lenses (502). Double convex lenses, used in this manner as 
magnifying glasses, are called simple microscopes. 

480. Formation of images in double concave lenses. —Double 
concave lenses, like convex mirrors, only give virtual images, whatever 
the distance of the object. 

Let AB (fig. 343) be an object placed in front of such a lens. If the 

secondary axis be drawn from the 
point A, all rays, AC, AI, from 
this point are twice refracted in 
the same direction, diverging 
from the axis AO; so that the 
eye, receiving the emergent rays, 
DE and GH, supposes them to 
proceed from the point where 
their prolongations cut the se¬ 
condary axis AO, in the point a. 
In like manner, drawing a secon¬ 
dary axis from the point B, the 
rays from this point form a pencil of divergent rays, the directions of 
which, prolonged, intersect in b. Hence the eye sees at ab a virtual 
image of AB, which is ahcays erect and smaller than the object. 



Fig. 343. 






LENSES. 


-482J 


443 


481. Spherical aberration. Caustics.— In the theory of the foci, 
and of the images formed by different kinds of spherical lenses, it has 
been hitherto assumed, that the rays emitted from a single point intersect 
also after refraction in a single point. This is virtually the case with a 
lens whose aperture, that is, the angle obtained by joining the edges to 
the principal focus, does not exceed 10° or 12°. 

Where the aperture is larger, the rays which traverse the lens near 
the edge are refracted to a point nearer the lens than the rays which pass 
near the axis. The phenomenon thus produced is named spherical aber¬ 
ration by refraction ; it is analogous to the spherical aberration produced 
by reflection. The luminous surfaces formed by the intersection of the 
refracted rays are termed caustics by refraction. 

Spherical aberration is prejudicial to the sharpness and definition of 
an image. If a ground glass screen be placed exactly in the focus of a 
lens, the image of an object will be sharply defined in the centre, but 
indistinct at the edges; and, vice versa , if the image is sharp at the edges, 
it will be indistinct in the centre. This defect is very objectionable, 
more especially in lenses used for photography. It is partially obviated 
by placing before the lenses diaphragms provided with a central aperture 



Fig. 344. 

which admits the rays passing near the centre, but cuts off. those which 
pass near the edges. Also by combining two lenses of suitable curvature, 
the spherical aberration may be destroyed. 

482. Formulae relating: to lenses. —In all lenses, the relation 
between the distances of the image and object, the radii of curvature, and 
the refractive index, may be expressed by a formula. In the case of a 
double convex lens let P be a luminous point, situate on the axis fig. 
344, let PI be an incident ray, IE its direction within the lens, EP' the 
emergent ray, so that P' is the conjugate focus of P. Further, let CT 
and CE be the normals to the points of incidence and emergence, and 
IPA be put equal to a, EP'A' = /J, ECA' = y, IC'A = S, NIP = i, 
EIO = r, IEO = i', N'EP' = r'. 

Because the angle i is the exterior angle of the triangle PIC'', and the 



444 


ON LIGHT. 


[ 482 - 


angle r' the exterior angle of the triangle CEP', therefore, i = a -f 5 ? 
and r' = 7 -J- £, whence 

i+r> = a + J3 + 7 + 5 . . • (1) 

But at the point I, sin i = n sin r, and at the point E, sin r' = n sin V 
(462), n being the refractive index of the lens. Now if the arc AI is 
only a small number of degrees, these sines may be considered as pro¬ 
portional to the angles i, r, i', and r', whence, in the above formula, we 
may replace the sines by their angles, which gives i =■ nr and r' = ni' 
from which i + r' = n (r -f- V). Further, because the two triangles IOE 
and COC' have a common equal angle, O, therefore r -f i' = y + 5 , from 
which i + v* = n (7 + 5). Introducing this value into the equation (1) 
we obtain 

n ( 7 + 8 ) = a+j 6 -f y+5, from which (n- 1) (y-f- 8 ) = a-f/3 ... (2) 

Let CA' be denoted by R, C'A by R', PA by p, and P'A' by p\ 
Then with centre P and radius PA describe the arc Ad, and with centre 
P' and radius P'A' describe the arc An. Now when an angle at the 
centre of a circle subtends a certain arc of the circumference, the quo¬ 
tient of the arc divided by the radius measures the angle, consequently 
_A d Ad A'n A'E , _ AI 

• = ES"7’* = 7'*=-H-'“ d, = S'- 

Therefore by substitution in ( 2 ) 

(—i) ( A ^+i I )= Ad + A ' n . 

v R E'/ P P 

Now since the thickness of the lens is very small, and the angles also 
small, Ad, AI, A'E, and A'n, differ but little from coincident straight 
lines, and are therefore sensibly equal. Hence the above equation 
becomes 


(M_1) (s+E'H+,1' • 


p P' 


(3) 


This is the formula for double convex lenses; if p be = 00 , we have 
p’ being the principal focal distance. If this be represented by/, we get 




(4) 


from which the value of /is easily deduced. Considered in reference to 
formula (4), the formula (3) assumes the form 


1 + 1=1 
P P' f 


(5) 


which is that in which it is usually employed. When the image is 
virtual, p' changes its sign, and formula (5) takes the form 

l_l = i 
P P' f 


( 6 ) 


- 483 ] DISPERSION OF LIGHT. 445 

In double concave lenses, p' and / retain the same sign, but that of p 
changes; the formula (5) becomes then 


1 _ 1 __ 1 

P P' f 




The formula (7) may be obtained by the same reasonings as the other. 


CHAPTER IV. 

DISPERSION AND ACHROMATISM. 

483. Decomposition of white light. Solar spectrum.— The phe¬ 
nomenon of refraction is by no means so simple as we have hitherto as¬ 
sumed ; when white light, or that which reaches us from the sun, passes 
from one medium into another, it is decomposed into several kinds of lights , 
a phenomenon to which the name dispersion is given. 

In order to show that white light is decomposed by refraction, a pencil 
of solar light, SA (fig. 334), is allowed to pass through a small aperture 
in the window shutter of a dark chamber. This pencil tends to form a 



Fig. 345. 

round and colourless image of the sun at K; but if a flint glass prism 
arranged horizontally be interposed in its passage, the beam, on emerg¬ 
ing from the prism, becomes refracted towards its base, and produces 
on a distant screen a vertical band, coloured in all the tints of the 
rainbow, which is called the solar spectrum. In this spectrum there 
is, in reality, an infinity of different tints, which imperceptibly merge 
into each other, but it is customary to distinguish seven principal colours. 














446 


ON LIGHT. 


[ 484 - 


These are violet, indigo , blue, green, yellow, orange, red ; they are arranged 
in this order in the spectrum, the violet being the most refrangible, and 
the red the least so. They do not all occupy an equal extent in the 
spectrum, violet having the greatest extent, and orange the least. 

With transparent prisms of different substances, or with hollow glass 
prisms filled with various liquids, spectra are obtained formed of the 
same colours, and in the same order; but when the deviation produced 
is the same, the length of the spectrum varies with the substance of 
which the prism is made. The angle of separation of two selected rays 
(say in the red and the violet) produced by a prism is called the disper¬ 
sion, and the ratio of this angle to the mean deviation of the two rays 
is called the dispei'sive power. This ratio is constant for the same sub¬ 
stance so long as the refracting angle of the prism is small. For the 
deviations of the two rays are proportional to the refracting angle; their 
difference and their mean vary in the same manner, and, therefore, the 
ratio of their difference to their mean is constant. For flint-glass this is 
0 043, for crown-glass it is 0 0246, or the dispersive power of flint is 
almost double that of crown-glass. 

The spectra which are formed by artificial lights rarely contain all 
the colours of the solar spectrum j but their colours are found in the solar 
spectrum, and in the same order. Their relative intensity is also modi¬ 
fied. The shade of colour which predominates in the flame predominates 
also in the spectrum; yellow, red, and green flames produce spectra in 
which the dominant tint is yellow, red, or green. 

In order to produce a solar spectrum in which the seven principal tints 
are distinctly seen, the aperture by which light enters ought not to be 
more than a few millimeters in diameter, and if the refracting angle of 
the prism, as is usually the case, is 60°, the screen on which the spectrum 
is caught must be 5 or 6 yards distant. 



Fig. 346. 

484. The colours of the spectrum are simple, and unequally 
refrangible.— If one of the colours of the spectrum be isolated by in¬ 
tercepting the others by means of a screen, E, as shown in fig. 346, 
and if the light thus intercepted be allowed to pass through a second 




DISPERSION OF LIGHT. 


447 


- 484 ] 

prism, B, a refraction will be observed, but the light remains unchanged; 
that is, the image received on the screen H is violet if the violet pencil 
has been allowed to pass,, blue if the blue pencil, and so on. Hence the 
colours of the spectrum are simple ; that is, they cannot further be de¬ 
composed by the prism. 

Moreover, the colours of the spectrum are unequally refrangible ; that 
is, they possess different refractive indices. The elongated shape of the 
spectrum would be sufficient to prove the unequal refrangibility of the 
simple colours, for it is clear that the violet, which is most deflected 
towards the base of the prism, is also most refrangible, and that red 
which is least deflected is least refrangible. But the unequal refrangi¬ 
bility of simple colours may be shown by numerous experiments, of 
which the two following may be adduced : 

i. Two narrow strips of coloured paper, one red and the other violet, 
are fastened close to each other on a sheet of black paper. On looking 
at them through a prism, they are seen to be unequally displaced, the 

. red band to a less extent than the violet; hence the red rays are less 
refrangible than the violet. 

ii. The same conclusion may be drawn from Newton’s experiment 
with crossed prisms. On a prism, A (fig. 347), in a horizontal position, 



Fig. 347. 


a pencil of white light, S, is received, which, if it had merely traversed 
the prism, A, would form the spectrum, rv, on a distant screen. But if 
a second prism, B, be placed in a vertical position behind the first, in 
such a manner that the refracted pencil passes through it, the spectrum 
vr becomes deflected towards the base of the vertical prism, but instead 
of being deflected in a direction parallel to itself, as would be the case 
if the colours of the spectrum were equally refracted, it is obliquely 















448 ON LIGHT. [ 485 - 

refracted in the direction rV, proving that from red to violet the colours 
are more and more refrangible. 

These different experiments show that the refractive index differs in 
different colours; even rays which are to perception undistinguishable 
have not the same refractive index. In the red band, for instance, the 
rays at the extremity of the spectrum are less refracted than those which 
are nearer the orange zone. In calculating indices of refraction (462), 
it is usual to take as the index of a substance the refrangibility of the 
yellow ray in a prism formed of that substance. 

485. Recomposition of white light.— Not merely can white light 
be resolved into lights of various colours, but by combining the different 
pencils separated by the prism, white light can be reproduced. This 
may be effected in various ways: 



Fig. 349. 


Fig. 350. 


i. If the spectrum produced by one prism be allowed to fall upon 
a second prism of the same material, and the same refracting angle as 
the first, but inverted, as shown in fig. 350, the latter reunites the 
different colours of the spectrum, and it is seen that the emergent pencil 
E, which is parallel to the pencil, S, is colourless. 

ii. If the spectrum falls upon a double convex lens (fig. 349), a 

white image of the sun will be formed 
on a white screen placed in the focus of 
the lens ; a glass globe filled with water 
produces the same effect as the lens. 

iii. When the spectrum falls upon a 
concave mirror a white image is formed 
on a screen of ground glass placed in its 
focus (fig. 351). 

iv. Light may be recomposed by 
means of a pretty experiment, which consists in receiving the seven 
colours of the spectrum on seven small glass mirrors with plane faces, 
and which can be so inclined in all positions that the reflected light may 
be transmitted in any given direction (fig. 352). When these mirrors 
are suitably arranged, the seven reflected pencils may be caused to fall 
on the ceiling in such a manner as to form seven distinct images—red, 








DISPERSION OF LIGHT. 


449 


- 485 ] 

orange, yellow, etc. When the mirrors are moved so that the separate 
images become superposed a single image is obtained, which is white. 



Fig. 352. 

v. By means of Newton’s disc it may be shown that the seven 
colours of the spectrum form white. This is a cardboard disc of about 



Fig. 354. 


a foot in diameter, the centre and the edges are covered with black 
paper, while in the space between there are pasted strips of papers of 


















450 


ON LIGHT. 


[ 486 - 

tke colours of the spectrum. They proceed from the centre to the cir¬ 
cumference, and their relative dimensions and tints are such as to repre¬ 
sent five spectra (fig. 353). When this disc is rapidly rotated, the retina 
receives simultaneously the impression of the seven colours, and the 
disc appears white (fig. 354), or at all events of a greyish-white, for the 
colours which cover it cannot be arranged exactly in the same dimensions 
or of the same tints as those of the spectrum. 

486. Wewton’s theory of the composition of light and the 
colour of bodies.— Newton was the first to decompose white light by 
the prism, and to recompose it. From the various experiments which 
we have described he concluded that white light was not homogeneous, 
but formed of seven lights unequally refrangible, which he called simple 
or primitive lights. It is owing to their difference in refrangibility that 
they become separated in traversing the prism. 

On this theory bodies also decompose light by reflection, and their 
colour depends on their reflecting power for the different simple colours. 
Those which reflect all colours in the proportion in which they exist in 
the spectrum are white; those which reflect none are black. Between 
these two limits there are infinite tints, according to the greater or less 
extent to which bodies reflect some colours, and absorb others. Hence 
bodies have no colours of themselves, but are coloured by the kind of 
light which they reflect. In fact, if in a dark room the same body is 
successively illuminated by each of the colours of the spectrum, the body 
has no special colour; it appears red, orange, green, etc., according to the 
position in which it is placed. The colour of bodies also varies with the 
nature of the light. This is the case with the light of gas, and of a candle 
in which yellow predominates, and which communicates this tint to the 
objects which it illuminates. 

487. Complementary colours. —If in white light any colour be 
suppressed, a mixture of the remainder is called the complementary 
colour , for it is the colour needed to complete the sensation of white 
light. A mixture of blue and yellow produces a green , and, accordingly, 
green is the complementary colour to red. In like manner a mixture of 

' red and yellow produces orange , which is complementary to blue. Simi¬ 
larly indigo is the complementary colour to yellow, and yellowish green 
to violet. 

488. Homogeneous light.— The light emitted from luminous bodies 
is never quite pure. In optical researches it is frequently of great im¬ 
portance to procure homogeneous or monochromatic light. Common salt 
in the flame of a Bunsen’s lamp gives a yellow of great purity. For red 
light, ordinary light is transmitted through glass coloured with suboxide 
of copper, which absorbs nearly all the rays excepting the red. A very 
pure blue is obtained by transmitting ordinary light through a glass 


- 489 ] DISPERSION OF LIGHT. 451 

trough with parallel sides, containing an ammoniacal solution of sulphate 
of copper. 

489. Properties of the spectrum.— Besides its luminous properties, 
the spectrum is found to produce calorific and chemical effects. 

Luminous properties. It appears from the experiments of Fraunhofer 
and of Herschel, that the light in the yellow part of the spectrum has 
the greatest intensity, and that in the violet the least. 

Calorific effects. It was long known that the various parts of the 
spectrum differed in their calorific effects. Leslie found that a thermo¬ 
meter placed in different parts of the spectrum indicated a higher tem¬ 
perature as it moved from violet towards red. Herschel fixed the 
maximum intensity of the heating effects just outside the red; Berard 
in the red itself. Seebeck showed that those different effects depend on 
the nature of a prism : with a prism of water the greatest calorific effect 
is produced in the yellow; with one of alcohol it is in the orange-yellow; 
and with a prism of crown glass it is in the middle of the red. 

Melloni, by using prisms and lenses of rock salt, and by availing him¬ 
self of the extreme delicacy of the thermo-electric apparatus, first made 
a complete investigation of the calorific properties of the thermal spec¬ 
trum. This result led, as we have seen, to the confirmation and exten¬ 
sion of Seebeck’s observation. 

Chemical properties. In numerous phenomena light acts as a chemical 
agent. For instance, chloride of silver blackens under the influence of 
light, transparent phosphorus becomes opaque, vegetable colouring- 
matters fade, hydrogen and chlorine gases, when mixed, combine slowly 
in diffused light, and with explosive violence when exposed to direct 
sunlight. The chemical action differs in different parts of the spectrum. 
Scheele found that when chloride of silver was placed in the violet, the 
action was more energetic than in any other part. Wollaston observed 
that the action extended beyond the violet, and concluded that, besides 
the visible rays, there are some invisible and more highly refrangible 
rays. These are the chemical or actinic rays. 

There is a curious difference in the action of the different rays. Moser 
placed an engraving on an iodised silver plate, and exposed it to the 
light until an action had commenced, and then placed it under a violet 
glass in the sunlight. After a few minutes a picture was seen with great 
distinctness, while when placed under a red or yellow glass it required a 
very long time, and was very indistinct.^ When, however, the iodised 
silver plate was first exposed in a camera obscura to blue light for two 
minutes, and was then brought under a red or yellow glass, an image 
quickly appeared, but not when placed under a green glass. It appears 
as if there are vibrations of a certain velocity which could commence an 
action, and that there are others which are devoid of the property of 


452 


ON LIGHT. 


[ 490 - 

commencing, but can continue and complete an action when once set up. 
Becquerel, who discovered these properties in luminous rays, called the 
former exciting rays , and the latter continuing or phosphorogenie rays. 
The phosphorogenie rays, for instance, have the property of rendering 
certain objects self-luminous in the dark after they have been exposed 
for some time to the light. Becquerel found that the phosphorogenie 
spectrum extended from indigo to beyond the violet. 

490. Dark lines of the spectrum. —The colours of the solar spec- 
trum are not continuous. For several grades of refrangibility rays are 
wanting, and in consequence, throughout the whole extent of the spec¬ 
trum, there are a great number of very narrow dark lines. To observe 
them, a pencil of solar rays is admitted into a darkened room, through a 
narrow slit. At a distance of three or four yards, we look at this slit 
through a prism of flint glass, which must be very free from flaws, taking 
care to hold its edge parallel to the slit. We then observe a great 
number of very delicate dark lines parallel to the edge of the prism, and 
at very unequal intervals. 

The existence of the dark lines was first observed by Wollaston in 
1802; but Fraunhofer, a celebrated optician of Munich, first studied and 
gave a detailed description of them. Fraunhofer mapped the lines, and 
indicated the most obvious of them by the letters A, a, B, C, D, E, 6, 

F, G, H; they are therefore generally known as Fraunhofer’s lines. 

The dark line A (see fig. I. of the coloured plate), is at the extremity 

and B in the middle of the red rgy; C, at the boundary of the red and 
orange ray; D is in the orange ray ; E, in the green; F, in the blue; 

G, in the indigo; H, in the violet. There are certain other noticeable i 
dark lines, such as a in the red, and b in the green. In the case of solar j 
light the positions of the dark lines are fixed and definite; on this ac¬ 
count they are used for obtaining an exact determination of the refractive | 
index (471) of each colour; for example, the refractive index of 
the blue ray is, strictly speaking, that of the dark line F. In the spectra 
of artificial lights, and of the stars, the relative positions of the dark lines 
are changed. In the electric light the dark lines are replaced by brilliant 
lines. In coloured flames, that is to say, flames in which certain chemi¬ 
cal substances undergo evaporation, the dark lines are replaced by very 1 
brilliant lines of light, which differ for different substances. Lastly, of i 
the dark lines, some are constant in position and distinctness, such are 
Fraunhofer’s lines, but some of the feebler lines are seen or not according j 
to the height of the sun above the horizon, and the state of the atmo- I 
sphere. The fixed lines are due to the sun ; the variable lines are J 
thought by some to be due to the absorption of the air, and are accord- i 
ingly called atmospheric or telluric lines. 

Fraunhofer counted in the spectrum more than 600 dark lines, more or . 
less distinct, distributed irregularly from the extreme red to the extreme i 



SPECTROSCOPE. 


453 


- 492 ] 

violet ray. Brewster counted 2000. By causing the refracted rays to 
pass successively through several analysing prisms, not merely has the 
existence of 3000 dark lines been ascertained, hut several which had been 
supposed single have been shown to be double. 

491. Applications of Fraunhofer’s lines.— Subsequently to Fraun¬ 
hofer, several physicists studied the dark lines of the spectrum. In 1822 
Sir J. Herschel remarked that by volatilising substances in a flame a very 
delicate means is afforded of detecting certain ingredients by the colours 
they impart to certain of the dark lines of the spectrum ; and Fox Talbot 
in 1834 suggests optical analysis as probably the most delicate means of 
detecting minute portions of a substance. To Kirchhoff* and Bunsen, 
however, is really due the merit of basing on the observation of the lines 
of the spectrum a method of analysis. They ascertained that the salts 
of the same metal, when introduced into a flame, always produce lines 
identical in colour and position, but different in colour, position, or num¬ 
ber for different metals, and finally that an exceedingly small quantity of 
a metal suffices to disclose its existence. Hence has arisen a new method 
of analysis, known by the name of spectral analysis. 

492. Spectroscope. —The name of spectroscope has been given to 
the apparatus employed by Kirchhoff and Bunsen for the study of the 
spectrum. One of the forms of this apparatus as modified by MM. 
Duboscq and Grandeau is represented in fig. 355. It is composed of three 
telescopes mounted on a common foot, and whose axes converge towards 
a prism, P, of flint-glass. The telescope A is the only one which can 
turn round the prism. It is fixed in any required position by a clamping 
screw, n. The screw head, m, is used to shift the position of the eye¬ 
piece, so that a clear image of the spectrum may be obtained, or, in other 
words, to focus the eye-piece. The screw head n is used to change the 
inclination of the axis. 

To explain the use of the telescopes B and C, we must refer to fig. 
356, which shows the passage of the light through the apparatus. The 
rays emitted by the flame G fall on the lens a, and are caused to converge 
to a point, b, which is the principal focus of a second lens, c. Consequently 
the pencil, on leaving the telescope, B, is formed of parallel rays. This 
pencil enters the prism P. On leaving the prism, the light is decomposed, 
and in this state falls on the lens x. By the lens x, a real and reversed 
image of the spectrum is formed at i. This image is seen by the observer 
through a magnifying glass which forms at ss' a virtual image of the 
spectrum magnified about eight times. 

The telescope C serves to measure the relative distances of the lines of 
the spectrum. For this purpose there is placed at m a micrometer 
divided into 25 equal parts. The micrometer is formed thus:—A scale 
of 250 millimeters is divided with great exactness into 25 equal 


454 


ON LIGHT. 


[ 492 - 

parts. A photographic negative on glass of this scale is taken reduced 
to 15 millimeters. The negative is taken because then the scale is 



Fig. 355. 

light on a dark ground. The scale is then placed at m in the principal 
focus of the lens e , consequently, when the scale is lighted by the candle 



Fig. 356. 

F, the rays emitted from it leave the lens e in parallel pencils; a portion 











































SPECTROSCOPE. 


455 


- 492 ] 

of these, being reflected from a face of the prism, passes through the lens 
x, and forms a perfectly distinct image of the micrometer at i, thereby 
furnishing the means of measuring exactly the relative distances of the 
different spectral lines. 

The micrometric telescope C (fig. 355) is furnished with several adjust¬ 
ing screws i, o, r: of these i adjusts the locus; o displaces the micrometer 
in the direction of the spectrum laterally; r raises or lowers the micro¬ 
meter, which it does by giving different inclinations to the telescope. 

The opening whereby the light of 
the flame G enters the telescope B, 
consists of a narrow vertical slit, 
which can be opened more or less by 
causing the moveable piece a to 
advance or recede by means of the 
screw v (fig. 357). When for pur¬ 
poses of comparison two spectra are 
to be examined simultaneously, 
there is placed over the upper part 
of the slit a small prism whose re¬ 
fracting angle is 60°. Rays from 
one of the flames, H, fell at right Big. 357. 

angles on one face of the prism, they 

then experience total reflection on a second face, and leave the prism by 
the third face, and in a direction at right angles to that face. By this 
means they pass into the telescope in a direction parallel to its axis, 
without in any degree mixing with the rays which proceed from the 
second flame, G. Consequently the two pencils of rays traverse the 
prism P (fig. 356), and form two horizontal spectra which are viewed 
simultaneously through the telescope A. In the flames G and H are 
platinum wires, e, e\ These wires have been dipped beforehand into 
solutions of the salts of the metals on which experiment is to be made ; 
and by the vaporisation of these salts the metals modify the transmitted 
light, and give rise to definite lines. 

Each of the flames H and G is a jet of ordinary gas. The apparatus 
through which the gas is supplied is known as a JBtmsen's burner. The 
gas comes through the hollow stem k (fig. 355). At the lower part of 
this there is a lateral orifice to admit air to support the combustion of 
the gas. This orifice can be more or less closed by a small diaphragm 
which acts as a regulator. If we allow a moderate amount of air to enter, 
the gas burns with a luminous flame, and the lines are obscured. But if 
a strong and steady current of air enters, the carbon is rapidly oxidised, 
the flame loses its brightness, and burns with a pale blue light, but with 
an intense heat. In this state it no longer yields a spectrum. If, how- 









456 


ON LIGHT. 


[ 493 - 

ever, a metallic salt is introduced either in a solid state or in a state of 
solution, the spectrum of the metal makes its appearance, and in a fit 
state for observation. 

493. Experiments with the spectroscope. —The coloured plate at 
the beginning shows certain spectra observed by means of the spectro¬ 
scope. Fig. I. represents the solar spectrum. 

Fig. II. shows the spectrum of potassium. It is continuous, that is, it 
contains all the colours of the solar spectrum ; moreover it is marked by 
two brilliant lines, one in the extreme red, corresponding to Fraunhofer’s 
dark line A, the other in the extreme violet. 

Fig. III. shows the spectrum of sodium. This spectrum contains neither 
red, orange, green, blue, nor violet. It is marked by a very brilliant 
yellow ray in exactly the same position as Fraunhofer’s dark line D. Of 
all metals sodium is that which possesses the greatest spectral sensibility. 
In fact, it has been ascertained that one two hundred millionth of a grain 
of soda is enough to cause the appearance of the yellow line of sodium. 
Consequently it is very difficult to avoid the appearance of this line. A 
very little dust scattered in the apartment is enough to produce it,—a 
circumstance which shows how abundantly sodium is scattered through¬ 
out nature. 

Figs. IV. and V. show the spectra of ccesium and rubidium , metals dis¬ 
covered by MM. Bunsen and Kirchhoff by means of spectral analysis. 
The former is distinguished by two blue lines, the latter by two very 
brilliant red lines and by two less intense violet lines. A third metal 
thallium , has been discovered by the same method by Mr. Crookes in 
England, and independently by M. Lamy in Franee. Thallium is cha¬ 
racterised by a single green line. 

Still more recently Richter and Reich have discovered a new metal 
associated with zinc, and which they call indium from a couple of charac¬ 
teristic lines which it forms in the indigo. 

The extreme delicacy of the spectrum reactions, and the ease with 
which they are produced, constitute them a most valuable help in the 
quantitative analysis of the alkalis and alkaline earths. It is sufficient to 
place a small portion of the substance under examination on platinum 
wire as represented in fig. 357, and compare the spectrum thus obtained 
with the charts in which the positions of the lines produced by th& 
various metals are laid down. 

With other metals the production of their spectrum is more difficult,' 
especially in the case of some of their compounds. The heat of a Bunsen’s 
burner is insufficient to vaporise the metals, and a more intense temperature 
must be used. This is effected by taking electric sparks between wires 
consisting of the metal whose spectrum is required, and the electric sparks 
are most conveniently obtained by means of Ruhmkorff’s coil. Thus all 
the metals may be brought within the sphere of spectrum observations. 


SPECTROSCOPE. 


457 


- 494 ] 

It has been observed that the character of the spectrum changes with 
the temperature; thus chloride of lithium in the flame of a Bunsen’s 
burner gives a single intense line ; in a hotter flame, as that of hydrogen, it 
gives an additional orange line; while in the oxyhydrogen jet or the 
voltaic arc a broad brilliant blue band comes out in addition. Sometimes 
also in addition to the appearance of new lines an increase in temperature 
resolves those bands which exist into a number of fine lines , which in 
some cases are more and in some less refrangible than the bands from 
which they are formed. It may be supposed that the glowing vapour 
found at the low temperature consists of the oxide or some difficultly 
reducible metal, whereas at the enormously high temperature of the 
spark these compounds are decomposed, and the true bright lines of the 
spectrum are formed. 

The spectra of the gases are obtained by taking the electric spark 
through glass tubes of a special construction, provided with electrodes of 
platinum and filled with the gas in question in a state of great attenuation ; 
if the spark be passed through hydrogen, the light emitted is bright 
red, and its spectrum consists of one bright red, one green, and one blue 
line; whilst in nitrogen the spark is purple and the spectrum very com¬ 
plicated. If the electric discharge takes place through a compound gas or 
vapour the spectra are those of the elementary constituents of the gas. 
It seems as if at very intense temperatures chemical combination was im¬ 
possible, and oxygen and hydrogen, chlorine and the metals, could co¬ 
exist in a separate form, although mechanically mixed with each other. 

494. Explanation of the dark lines of the solar spectrum.— It has 
been already seen that incandescent sodium vapour gives a bright yellow 
line corresponding to the dark line I) of the solar spectrum. Kirchhoff 
found that, when the brilliant light produced by incandescent lime passes 
through a flame coloured by sodium in the usual manner, a spectrum is 
produced in which is a dark line coinciding with the dark line D of the 
solar spectrum; what would have been a bright yellow line becomes a 
dark line when formed on the background of the lime light. By 
allowing in a similar manner the limelight to traverse vapours of potas¬ 
sium, barium, strontium, etc., the bright lines which they would have 
■formed were found to be converted into dark lines. 

It appears then that the vapour of sodium has the power of absorbing 
rays of the same refrangibility as that which it emits. And the same is 
true of the vapours of potassium, barium, strontium, etc. This absorptive 
power is by no means an isolated phenomenon. These substances share 
it, for example, with the vapour of nitrous acid, which Brewster found 
to possess the following property: when a tube filled with this vapour is 
placed in the path of the light either of the sun or of a gas flame, and 
the light is subsequently decomposed by a prism, a spectrum is produced 

x 


ON LIGHT. 


458 


[ 494 - 


which is full of dark lines; and Miller showed that iodine and bromine 
vapour produced analogous effects. 

Hence the origin of the above phenomenon is, doubtless, the absorption 
by the sodium vapour of rays of the same kind, that is, of the same re- 
frangibility, as those which it has itself the power of emitting. Other 
rays it allows to pass unchanged, but these it either totally or in great 
part suppresses. Thus the particular lines in the spectrum to which 
these rays would converge are illuminated only by the feebly luminous 
sodium flame, and accordingly -appear dark by contrast with the other 
portions of the spectrum which receive light from the powerful flame 
behind. 

By replacing one of the flames, G or H (fig. 357), by a ray of solar light 
reflected from a heliostat, Kirchhoff ascertained by direct comparison 
that the bright lines which characterise iron correspond to dark lines in 
the solar spectrum. He also found the same to be the case with sodium, 
magnesium, calcium, nickel, and some other metals. 

From these observations we may draw important conclusions with respect 
to the constitution of the sun. Since the solar spectrum has dark lines 
where sodium, iron, etc., give bright ones, it is probable that around the 
solid, or more probably liquid, body of the sun, which throws out the 
light, there exists a vaporous envelope which, like the sodium flame 
in the experiment described above, absorbs certain rays, namely, those 
which the envelope itself emits. Hence those parts of the spectrum 
which, but for this absorption, would have been illuminated by these 
particular rays, appear feebly luminous in comparison with the other 
parts, since they are illuminated only by the light emitted by 
the envelope, and not by the solar nucleus; and we are at the same 
time led to conclude that in this vapour there exist the metals sodium, 
iron, etc. 

Huggins and Miller have applied spectrum analysis to the investigation 
of the heavenly bodies. The spectra of the moon and planets, whose 
light is reflected from the sun, give the same lines as those of the sun. 
The spectra of the fixed stars contain, however, dark lines differing from 
the solar lines, and from one another. The red star Aldebaran gave lines 
corresponding with sodium, magnesium, calcium, iron, bismuth, tellurium, 
antimony, and mercury. In the spectrum of the orange-tinted star 
a Orionis the lines of magnesium, sodium, calcium, and bismuth were 
observed. The brilliant white star Sirius gave evidence of the presence 
of sodium, magnesium, hydrogen, and iron. It would thus appear that 
these fixed stars, while differing from one another in the matter of which 
they are composed, are constructed on the same general plan as our sun. 
Huggins has observed a striking difference in the spectra of the nebula ; i 
where they can at all be observed, they are found to consist generally of 
bright lines, like the spectra of the ignited gases, instead of like the 



FLUORESCENCE. 


459 


- 495 ] 

spectra of the sun and stars consisting of a bright ground intersected by 
dark lines. It is hence probable that the nebulae are masses of glowing 
gas, and do not consist, like the sun and stars, of a photosphere sur¬ 
rounded by a gaseous atmosphere. 

495. Fluorescence.— Professor Stokes has made the remarkable dis¬ 
covery that under certain circumstances the rays of light are capable of 
undergoing a change of refrangibility. The discovery originated in the 
study of a phenomenon observed by Sir J. Herschel, that certain solutions 
when looked at by transmitted light appear colourless, but when viewed 
in reflected light present a bluish appearance. Stokes has found that this 
property, which he calls fluorescence , is characteristic of a large class of 
bodies. 

The phenomenon is best seen when a solution of sulphate of quinine, 
contained in a trough with parallel sides, is placed in different positions 
in the solar spectrum. No change is observed in the upper part of the 
spectrum, but from about the middle of the lines G and H (frontispiece) 
to some distance beyond the extreme range of the violet, rays of a beau¬ 
tiful sky blue colour are seen to proceed. These invisible ultra-violet rays 
also become visible when the spectrum is allowed to fall on paper im¬ 
pregnated with a solution of cesculine (a substance extracted from horse 
chestnut), an alcoholic solution of stramonium, or a plate of canary glass 
(which is coloured by means of uranium). This change arises from a 
diminution in the refrangibility of those rays outside the violet, which 
are ordinarily too refrangible to affect the eye. 

Glass appears to absorb many of these more refrangible rays, which is 
not the case nearly to the same extent with quartz. When prisms and 
troughs formed of plates of quartz are used, a spectrum may be obtained 
which, outside the line H, is double the length of the visible spectrum. 
In the spectrum thus made visible dark lines may be seen like those in 
the ordinary spectrum. 

The phenomena may be observed without the use of a prism. When 
an aperture in a dark room is closed by means of a piece of blue glass, 
and the light is allowed to fall upon a piece of canary glass, it instantly 
appears self-luminous from the emission of the altered rays. 

In most cases it is the violet and ultra-violet rays which undergo an 
alteration of refrangibility, but the phenomenon is not confined to them. 
A decoction of madder in alum gives yellow and violet light from about 
the line D to beyond the violet; an alcoholic solution of chlorophylle gives 
red light from the line B to the limit of the spectrum. In these cases 
the yellow, the green, and the blue rays experience diminution of refran- 
gibility; the change never produces more highly refrangible rays. 

The electric light gives a very remarkable spectrum. With quartz 
apparatus Stokes obtained a spectrum six or eight times as long as the 


460 


ON LIGHT. 


[ 496 - 

ordinary one. Several flames of no great illuminating power emit very 
peculiar light. Characters traced on paper with solution of stramonium, 
which are almost invisible in daylight, appear instantaneously when il¬ 
luminated by the flame of burning sulphur. Bobinson has found that 
the light of the aurora is peculiarly rich in rays of high refrangibility. 

496. Chromatic aberration.— The various lenses hitherto described 
(474) possess the inconvenience that, when at a certain distance from the 
eye, they give images with coloured edges. This defect, which is most 
observable in condensing lenses, is due to the unequal refrangibility of the 
simple colours (484), and is called chromatic aberration. 

For, as lenses may be compared to a series of prisms with infinitely 
small faces, and united at their bases, they not only refract light, but 
also decompose it like a prism. On account of this dispersion, therefore, 
lenses have really a distinct focus for each colour. In condensing lenses, 
for example, the red rays, which are the least refrangible, form their focus 
at a point r on the axis of the lens (fig. 358), while the violet rays, which 
are most refrangible, coincide in the nearest 
point v. The foci of the orange, yellow, green, 
blue, and indigo are between these points. The 
chromatic aberration is more perceptible in pro¬ 
portion as the lenses are more convex, and as the 
point at which the rays are incident is further 
from the axis; for then the deviation and there- 
Fig. 358. tore the dispersion are increased. 

497. Achromatism.— By combining prisms which have different re¬ 
fracting angles (467), and are formed of substances of unequal dispersive 
powers (483), white light may be refracted without being dispersed. The 
same result is attained by combining lenses of different substances, the 
curvatures of which are suitably combined. The images of objects viewed 
through such lenses do not appear coloured, and they are accordingly 
called achromatic lenses; achromatism being* the term applied to the phe¬ 
nomenon of the refraction of light without decomposition. 

By observing the phenomenon of the dispersion of colours in prisms of 
water, of oil of turpentine, and of crown-glass, Newton was led to suppose 
that dispersion w r as proportional to refraction. He concluded that there 
could be no refraction without dispersion, and, therefore, that achroma¬ 
tism was impossible. Almost half a century elapsed before this was 
found to be incorrect. Hall, an English philosopher, in 1733, was the 
first to construct achromatic lenses, but he did not publish his discovery. 
It is to Dollond, an optician in London, that we owe the greatest im¬ 
provement which has been made in optical instruments. He showed in 
1757 that by combining two lenses, one a double convex crown-glass lens, 
the other a concavo-convex lens of flint-glass (fig. 359), a lens is obtained 
which is virtually achromatic. 




ACHROMATISM. 


461 


-497] 

To explain this result, let two prisms, BFC and CDF, be joined and 
turned in a contrary direction, as shown in fig. 360. Let us suppose, in 
the first case, that both prisms are of the same material, but that the 
refracting angle of the second, CDF, is less than the refracting angle of 
the first: the two prisms will produce the same effect as a single prism, 
BAF, that is to say, tha,t white light which traverses it will not only be 
refracted but also decomposed. If, on the contrary, the first prism, BCF, 



• Fig. 359. Fig. 360. 

were of crown-glass, and the other of flint-glass, the dispersion might be 
destroyed without destroying the refraction. For as flint-glass is more 
dispersive than crown, and as the dispersion produced by a prism dimi¬ 
nishes with its refracting angle (483), it follows that by suitably lessening 
the refracting angle of the flint-glass prism, CFD, as compared with the 
refracting angle of the crown-glass prism, BCF, the dispersive power of 
these prisms may be equalised ; and as, from their position, the dispersion 
takes place in a contrary direction, it .is neutralised, that is, the emergent 
rays, EO, are parallel, and therefore give white light. Nevertheless, 
the ratio of the angles BCF and CFD, which is suitable for the parallelism 
of the red rays and violet rays, is not so for the intermediate rays, and, 
consequently, only two of the rays of the spectrum can be exactly com¬ 
bined, and the achromatism is not quite perfect. To obtain perfect achro¬ 
matism several prisms would be necessary of unequally dispersive materials, 
and the angles of which were suitably combined. 

The refraction is not destroyed at the same time as the dispersion; that 
could only happen if the refracting power of a body varied in the same 
ratio as its dispersive power, which is not the case. Consequently the 
emergent ray, EO, is not exactly parallel to the incident ray, and there is 
a refraction without appreciable decomposition. 

Achromatic lenses are made of two lenses of unequally dispersive ma¬ 
terials : one, A, of flint-glass, is a diverging concavo-convex (fig. 359) ; 
the other, B, of crown-glass, is double convex, and one of its faces may 
exactly coincide with the concave face of the first. As with prisms, 
several lenses would be necessary to obtain perfect achromatism; but for 
optical instruments two are sufficient, their curvature being such as to 
combine the blue and orange rays. 



462 


ON LIGHT. 


[ 498 - 


CHAPTER V. 

OPTICAL INSTRUMENTS. 

498. The different kinds of optical instruments. —By the term 

optical instrument is meant any combination of lenses, or of lenses and 
mirrors. Optical instruments may be divided into three classes accord¬ 
ing to the ends they are intended to answer, viz.:—i. Microscopes , 
which are designed to obtain a magnified image of any object whose real 
dimensions are too small to admit of its being seen distinctly by the 
naked eye. ii. Telescopes , by which very distant objects, whether 
celestial or terrestrial, may be observed, iii. Instruments designed 
to project on a screen a magnified or diminished image of any object 
which can thereby be either depicted or rendered visible to a crowd of 
spectators; such as the camera lucida , the camera obscura , photographic 
apparatus , the magic lantern, the solar microscope, the photo-electric mict'o- 
scope , etc. The two former classes yield virtual images, the last, with 
the exception of the camei'a lucida , yield real images. 

MICROSCOPES. 

499. The simple microscope. —The simple microscope or magnifying 
glass is merely a convex lens of short focal length, by means of which we 
look at objects placed between the lens and its principal focus. Let AB 
(fig. 361) be the object to be observed placed between the lens and its 



Pig. 361. 

principal focus, F. Draw the secondary axes AO and BO, and also from 
A and B rays parallel to the axis of the lens FO. Now these rays, on 
passing out of the lens, tend to pass through the second principal focus 
F', consequently they are divergent with reference to the secondary axes, 



MICROSCOPES. 


463 


- 499 ] 

and therefore, when produced,will cut those axes in A' and B' respectively. 
These points are the virtual foci of A and B respectively. The lens 
therefore produces at A'B' an erect and magnified virtual image of the 
object AB. 

The position and magnitude of this image depend on the distance of 
the object from the focus. Thus, if AB is moved to ab nearer the lens, 
the secondary axes will contain a greater angle, and the image will be 
formed at a'b ', and will be much smaller, and nearer the eye. On the 
other hand, if the object is moved farther from the lens, the angle 
between the secondary axes is diminished, and their intersection with the 
prolongation of the refracted rays taking place beyond A'B', the image is 
formed farther from the lens, and is larger. 

In a simple microscope both chromatic aberration and spherical 



Fig. 362. 

aberration increase with the degree of magnification. We have already 
seen that the former can be corrected by using achromatic lenses 
(art. 497), and the latter by using diaphragms which allow the passage of 
such rays only as are nearly parallel to the axis, the spherical aberration 


of these rays being nearly insensible. 
Spherical aberration may be still 
further corrected by using two plano¬ 
convex lenses instead of one very 
convergent lens. When this is 
done, the plane face of each lens is 
turned towards the object (fig. 362). 
Although each lens is less convex 
than the simple lens which they 
replace, yet their joint magnifying 
power is as great, and with a less 
amount of spherical aberration, since 
the first lens draws towards the axis 
the rays which fall on the second 
lens. This combination of lenses is 
known as Wollaston’s doublet. 

There are many forms of the 
simple microscope. One of the best 
is that represented in fig. 363. 



Fig. 363. 

On a horizontal support, E, which 







404 


UN LIGHT. 


[ 500 - 

ean be raised and lowered by a rack and pinion, there is a black eye¬ 
piece, 7n, in the centre of which is fitted a small convex lens. Below 
this is the stage , which is fixed, and on which the object is placed be¬ 
tween glass plates. In order to illuminate the object powerfully, 
diffused light is reflected from a concave glass mirror, M, so that the 
reflected rays fall upon the object. In using this microscope, the eye is 
placed very near the lens, which is lowered or raised until the position 
is found at which the object appears in its greatest distinctness. 

500. Conditions of distinctness of the images.— In order that 
objects looked at through a microscope should be seen with distinctness 
they must have a strong light thrown upon them, but this is by no 
means enough. It is necessary that the image be formed at a determinate 
distance from the eye. In fact, there is for each person a distance of 
most distinct vision, a distance, that is to say, at which an object must be 
placed from an observer’s eye, in order to be seen with greatest dis¬ 
tinctness. This distance is different for different observers, but ordi¬ 
narily is between 10 and 12 inches. It is, therefore, at this distance 
from the eye that the image ought to be formed. Moreover, this is why 
each observer has to focus the instrument, that is, to adapt the microscope 
to his own distance of most distinct vision. This is effected by slightly 
varying the distance from the lens to the object, for we have seen above 

Fig. 364. 



that a slight displacement of the object causes a great displacement of 
the image. With a common magnifying glass, such as is held in the hand, 
the adjustment is effected by merely moving it nearer to or further from 
the object. In the microscope the adjustment is effected by means of a 
rack and pinion, which in the case of the instrument shown in fig. 363 
moves the instrument, but moves the object in the case of the instrument 
depicted in fig. 368, What has been said about focussing the microscope 














MICROSCOPES. 


465 


- 502 ] 


applies equally to telescopes. In the latter instruments the eyepiece is 
generally adjusted with respect to the image formed in the focus of the* 
object glass. 

501. Apparent magnitude of an object. —The apparent magnitude 
or apparent diameter of a body is the angle it subtends at the eye of the 
observer. Thus, if AB is the object, and 0 the observer’s eye (figs. 364, 
365), the apparent magnitude of the object, is the angle AOB contained 
by two visual rays drawn from the centre of the pupil to the extremities 
of the object. 

In the case of objects seen through optical instruments, the angles 
which they subtend are so small that the arcs which measure the angles 
do not differ sensibly from their tangents. The ratio of two such angles 
is therefore the same as that of their tangents. Hence we deduce the 
two following principles:— 

I. When the same object is seen at unequal distances , the apparent 
diameter varies inversely as the distance from the observer's eye. 

II. In the case of two objects seen at the same distance , the ratio of the 
apparent diameters is the same as that of their absolute magnitudes. 

These principles may be proved as follows:—i. In fig. 364, let AB 
be the object in its first position, and ab the same object in its second 
position. For the sake of distinctness these are represented in such 
positions that the line. OC passes at right angles through their middle 
points C and c respectively. It is, however, sufficient that ab and AB 
should be the bases of isosceles triangles having a common vertex at O. 
Now by what has been said above, AB is sensibly an arc of a circle 
described with centre 0 and radius OC ; likewise ab is sensibly an arc of 
a circle whose centre is O, and radius Oc. Therefore 

a at) . a i_AB ab 1 1 

AOB • a0b ~ oc : oi = 0C : 0? 


Therefore AOB varies inversely as OC. 

ii. Let AB and A'B' be two objects placed at the same perpendicular 
distance, OC, from the eye, 0, of the observer (fig. 365). Then they are 
sensibly arcs of a circle whose centre is 0, and radius OC. Therefore 

AB VB' 

AOB : AW = gg ; = AB : A'B, 

a proportion which expresses the second principle. 

502. Measure of magnification. —In the simple microscope, the 
measure of the magnification produced is the ratio of the apparent 
diameter of the image to that of the object, both being at the distance 
of most distinct vision.* The same rule holds good for other microscopes. 

* A simpler and more general definition may be stated thus :—Let a be the angular 
magnitude of the object as seen by the naked eye, p the angular magnitude of the 
image, whether real or virtual, actually present to the eye, then the magnification 
is p+a. This rule applies to telescopes. 

x 3 


466 


ON LIGHT. 


[ 503 - 

It is, however, important to obtain an expression for the magnification 
‘depending on data that are of easier determination. 

In fig. 366 let AB be the object, and A'B' its image formed at the 
distance of most distinct vision. Let a'b' be the projection of AB on 
A'B'. Then, since the eye is very near the glass, the magnification equals 

, or 4 that is —But since the triangles A'OB' and AOB 

are similar, A'B' : AB = DO : CO. Now DO is the distance of most 



Fig. 366. 

distinct vision, and CO is very nearly equal to FO, the focal length of the 
lens. Therefore the magnification equals the ratio of the distance of 
most distinct vision to the focal length of the lens. Hence we conclude 
that the magnification is greater:—1st. as the focal length of the lens is 
smaller, in other words, as the lens is more convergent; 2ndly, as the 
observer’s distance of most distinct vision is greater. 

By changing the lens the magnification can be increased, but only 
within certain limits if we wish to obtain a distinct image. By means of 
a simple microscope distinct magnification may be obtained up to 120 
diameters. 

The magnification we have now considered is linear magnification. 
Siqierficial magnification equals the square of the linear magnification, 
for instance, the former will be 1600 when the latter is 40. 

503. Compound microscope. —The compound microscope in its 
simplest form consists of two condensing lenses ; one with a short focus is 
called the object glass or objective, because it is turned towards the object; 
the other is less condensing, and is called the eyepiece or powei', because 
it is close to the observer’s eye. 

Fig. 367 represents the path of the luminous rays, and the formation 
of the image in the simplest form of a compound microscope. An object, 





COMPOUND MICROSCOPE. 


467 


- 504 ] 


AB, being placed very near the principal focus of the object glass, M, but 
a little farther from the glass, a real image, ab, inverted and somewhat 
magnified, is formed on the other side of the object glass (479). Now 
the distance of the two lenses, M and N, is such that the position of the 
image, ab, is between the eyepiece N, and its focus, F. From this it 



Fig. 367. 


follows that for the eye at E, looking at the image through the eye¬ 
piece, this glass produces the same effect as a simple microscope, and 
instead of this image, ab, another image, alb', is seen, which is virtual, 
and still more magnified. This second image, although erect as regards 
the first, is inverted in reference to the object. It may thus be said, 
that the compound microscope is nothing more than a simple micro¬ 
scope applied not to the object, but to its image already magnified by 
the first lens. 

504. Amici’s compound microscope. —The principle of the com¬ 
pound microscope has been already (503) explained; the principal ac¬ 
cessories to the instrument remain to be described. 

Fig. 368 represents the essential parts of the microscope known as 
Amici's or Chevallier's microscope. In the older microscopes the tube, 
A, was always vertical, and the lenses were not achromatic. Amici 
was the first to adopt an arrangement by which the tube could be 
placed either vertically or horizontally, and Chevallier was the first to 
introduce into France the use of achromatic lenses. The figure shows 
the microscope in a horizontal position, which is less fatiguing for the 
sight ; but it can also be placed vertically. This is effected by removing 
the tube G, and putting the long tube A, which contains the eyepiece, 
in its place over the object glass, E. The microscope may also be 
placed in an inclined position by removing a pin, m, which fixes the 
apparatus at the lower part; the whole system then moves on a hinge, 
a, which supports the microscope on a cylindrical column. 

On a rectangular rod, parallel to this column, is the stage, B. This 
can be raised or lowered by a pinion working in a rack by means of a 
milled head. The object, o , to be observed is placed on the stage be¬ 
tween two pieces of glass, C. The diffused light of the atmosphere is 
reflected through the object by means of a concave glass reflector, M; 




468 


ON LIGHT. 


[ 504 - 

tlie powerful illumination thus attained is indispensable with high mag¬ 
nifying powers. In the centre of the stage there is an aperture through 
which passes the light sent by the reflector. 



Fig. 368. 


Fig. 369 shows the position of the glasses, and the path of the 
rays in the microscope. The object glass, E, may be formed of one, 
two, or three lenses ; in this case there are three, whose principal focal 
distances are 8 to 10 millimeters. The eyepiece is formed of two plano¬ 
convex lenses, m and n. The path of the rays is easily followed. The 
luminous rays, after being reflected from the mirror, M, converge to¬ 
wards the object, o, and are thence directed towards the object glass, E. 
Having traversed it, they fall on a glass prism, p , on whose hypothenuse 
they experience total reflection (464). The luminous rays then traverse 
the tube AB, and, falling on the lens w, form at be a real and magnified 
































































COMPOUND MICROSCOPE. 


469 


- 504 ] 

image of the object. The last lens, m , acts as a simple microscope, and 
instead of this first image forms a second virtual image, b'c', which is 
still more magnified. 



Fig. 369. 


The object of the intermediate lens, n, is to condense the rays which 
are too oblique, and which would not fall on the eyeglass, m. It 
enlarges the Jield of the microscope, making the image smaller and 
more defined. The spherical aberration is corrected by the diaphragms 
e and e '; they intercept the rays which pass the lenses too near the 
edges. In order to extinguish the internal reflection, which might 
injure the precision of the images, the inside of the tube is blackened. 

The illumination of the microscope varies according as the object is 
transparent or opaque. In the former case the object is illuminated as 
above by means of a reflector placed below the stage. In the second 
case a condensing lens called the bull's eye is used ; it is placed on the 
stage, and concentrates the rays S on the object. 

The microscope possesses numerous eyepieces and object glasses, by 
means of which a great variety of magnifying power is obtained. A 
small magnifying power is also obtained by removing one or two of the 
lenses of the object glass. 

The above contains the essential features of the microscope; it is 
made in a great variety of forms, which differ mainly in the construction 
of the stand, the arrangement of the lenses, and in the illumination. 
For descriptions of these the student is referred to special works on the 
microscope. 






















470 


ON LIGHT. 


[505- 

505. Achromatism of the microscope. Campani’s eyepiece.— 

When a compound microscope consists of two single lenses, as in fig. 370, 
not only is the spherical aberration uncorrected, but also the chromatic 
aberration, the latter defect causing the images to be surrounded by 
fringes of the prismatic colours, these fringes being larger as the 
magnification is greater. It is with a view to correcting these aberra¬ 
tions that the object glass (see fig. 369) is composed of thiee achromatic 
lenses, and the eyepiece of two lenses, n and in, for the first of these, 
n, would be enough to produce colour unless the magnifying power were 
low. 

The effect of this eyepiece in correcting the colour may be explained 
as follows. It will be borne in mind that with respect to red rays the 



focal length of a lens is greater than the focal length of the same lens 
with reference to the violet rays. 

T> 

In fact, if, equation (4), p. 444, we write R' = oo, we obtain/=-_ 

n— 1 

which gives the focal length of a plano-convex lens whose refractive 
index is n. Now, in flint-glass, and for the red ray, n —1 equals 0*63, 
and for the violet ray n —1 equals 0*67. 

Let ab be the object, 0 the object glass which is corrected for colour. 
Consequently a pencil of rays falling from a on O would converge to a 
focus, A, without any separation of colours, but falling on the Jieldglass 
C, the red rays would converge to r, the violet rays to v, and inter¬ 
mediate colours to intermediate points. In like manner the rays from b , 
after passing through the fieldglass, would converge to r f , v ', and inter¬ 
mediate points. So that on the whole there would be formed a succes¬ 
sion of coloured images of ab, viz., a red image at it', a violet image at 
vv', and between them images of intermediate colours. Let d be the 
point of the object which is situated on the axis. The rays from d will 
converge to R, V, and intermediate points. Now suppose the eyeglass O' 
to be placed in such a manner that R is the principal focus of O' for 
the red rays, then will Y be its principal focus for the violet rays. 
Consequently the red rays, after emerging from O', will be parallel to the 
axis, and so will the violet rays emerging from V, and so of any other 
colour. Consequently, the colours of d, which are separated by C, are 






COMPOUND MICROSCOPE. 


471 


-507] 

again combined by O'. The same is very nearly true of r and v, and of 
r' and v'. Hence combination of the lenses C and 0' corrects the chro¬ 
matic aberration that would be produced by the use of a single eyeglass. 
Moreover, by drawing the rays towards the axis, it diminishes the 
spherical aberration, and, as we shall see in the next article, enlarges the 
field of view. 

In all eyepieces consisting of two lenses the lens to which the eye is 
applied is called the eyelens , the one towards the object glass is called 
the jieldlens . The eyepiece above described was invented by Huyghens, 
who was not, however, aware of its property of achromatism. He de¬ 
signed it for use with the telescope. It was applied to the microscope 
by Campani. The relation between the focal lengths of the lenses is as 
follows. The focal length of the fieldglass is three times that of the 
eyelens, and the distance between their centres is half the sum of the 
focal length. It easily follows from this that the image of the point d 
would, but for the interposition of the fieldlens, be formed at D, which 
is so situated that CD is three times DO', then the mean of the coloured 
images will be formed midway between C and O'. 

506. Field of view. —By the field of view of an optical instrument 
is meant all those points which are visible through the eyepiece. The 
advantage obtained by the use of an eyepiece in enlarging the field of 
view will be readily understood by an inspection of the accompanying 
figure. As before, 0 is the object glass, C the fieldlens, O' the eye¬ 
lens, and E the eye placed on the axis of the instrument. Let a be a 



point of the object; if we suppose the fieldlens removed, the pencil of 
rays from a would be brought to a focus at A, and none of them would 
fall on the eyelens O', nor pass into the eye E. Consequently a is 
beyond the field of view. But when the fieldglass C is interposed, the 
pencil of rays is brought to a focus at A', and emerges from O' into the 
eye. Consequently a is now within the field of view. It is in this 
manner that the substitution of an eyepiece for a single eyelens enlarges 
the field of view. 

507. Magnifying power. Micrometer.— The magnifying power of 
any optical instrument is the ratio of the magnitude of the image to the 
magnitude of the object. The magnifying power in a compound micro- 








472 


ON LIGHT. 


[507- 

scope is the product of the respective magnifying powers of the object glass 
and of the eyepiece ; that is, if the first of these magnifies 20 times, and 
the other 10, the total magnifying power is 200. The magnifying power 
depends on the greater or less convexity of the object glass and of the 
eyepiece, as well as on the distance between these two glasses, together 
with the distance of the object from the object glass. A magnifying 
power of 1500 and even upwards has been obtained; but the image 
then loses in sharpness what it gains in extent. To obtain precise and 
well illuminated images, the magnifying power ought not to exceed 500 
to 000 diameters, which gives a superficial enlargement 250,000 to 
360,000 times that of the object. 

The magnifying power is determined experimentally by means of the 
micrometer ; this is a small glass plate, on which, by means of a diamond, 
a series of lines is drawn at a distance from each other of ~ or of 
a millimeter. The micrometer is placed in front of the object glass, and 
then instead of viewing directly the rays emerging from the eyepiece, O, 
they are received on a piece of glass, A (fig. 372), inclined at an angle 
of 45°, and the eye is placed above so as to 
see the image of the micrometer lines which 
is formed by reflection on a screen, E, on 
which is a scale divided into millimeters. By 
counting the number of divisions of this scale 
corresponding to a certain number of lines of 
the image, the magnifying power may be de¬ 
duced. Thus, if the image occupies a space of 
45 millimeters on the scale, and contains 15 
lines of the micrometer, the distance between 
each of which shall be assumed at milli¬ 
meter, the absolute magnitude of the object 
will be ~ millimeter, and as the image oc¬ 
cupies a space of 45 millimeters, the magnification will be the quotient 
of 45 by — or 300. The eye in this experiment ought to be at such a 
distance from the screen, E, that the screen is distinctly visible : this 
distance varies with different observers, but is usually 10 to 12 inches. 
The magnifying power of the microscope can also be determined by means 
of the camera lucida. 

When once the magnifying power is known, the absolute magnitude 
of objects placed before the microscope is easily deduced. For, as the 
magnifying power is nothing more than the quotient of the size of the 
image by the size of the object, it follows that the size of the image 
divided by the magnifying power gives the size of the object; it is in this 
manner that the diameter of all microscopic objects is determined. 














—508] 


TELESCOPES. 


473 


TELESCOPES. 


508. Astronomical telescope. —The astronomical telescope is used for 
observing the heavenly bodies; like the microscope, it consists of a 
condensing eyepiece and object glass. The object glass, M (fig. 373), 
forms between the eyepiece, N, and its principal focus an inverted 



Fig. 373. 


image of the heavenly body, and this eyepiece, which acts as a magni¬ 
fying glass, then gives a virtual and highly magnified image, a'b', of the 
image ab. The astronomical telescope appears, therefore, analogous to 
the microscope, but the two instruments differ in this respect: that in 
the microscope, the object being very near the objective, the image is 
formed much beyond the principal focus, and is greatly magnified, so 
that both the object glass and the eyepiece magnify; while in the 
astronomical telescope, the heavenly body being at a great distance, the 
incident rays are parallel, and the image formed in the principal focus of 
the object glass is much smaller than the object. There is, therefore, no 
magnification except by the eyepiece, and this ought, therefore, to be of 
very short focal length. 

Fig. 374 shows an astronomical telescope mounted on its stand. Above 
it there is a small telescope, which is called the finder. Telescopes with a 
large magnifying power are not convenient for finding a star, as they 
have but a small field of view : the position of the star is, accordingly, 
first sought by the finder, which has a much larger field of view, that is, 
takes in a far greater extent of the heavens : it is then viewed by means 
of the telescope. 

a m 

The magnification (note, p. 465) equals ——— (fig. 373), that is, it equals 

a uo 


inn Qp 

and therefore is approximately equal to F being the focus of 


the object glass, M, and being supposed very nearly to coincide with 
the focus of the eyepiece, N j it may, therefore, be concluded that the 



474 ON LIGHT. 1 . 509 - 

magnifying power is greater in proportion as the object glass is less con¬ 
vergent, and the eyepiece more so. 



Fig. 374. 


When the telescope is used to make an accurate observation of the 
stars, for example, their zenith distance, or their passage 
over the meridian, a cross wire is added. This consists of 
two very fine metallic wires or spider threads stretched 
across a circular aperture in a small metal plate (fig. 375). 
The wires ought to be placed n the position where the 
inverted image is produced by the object glass, and the 
point where the wires cross ought to be on the optical axis 



Fig. 375. 


of the telescope, which thus becomes the line of sight or collimation. 

509. Terrestrial telescope. —The terrestrial telescope differs from the 
astronomical telescope in producing images in their right positions. 
This is effected by means of two condensing glasses, P and Q (fig. 376), 
placed between the object glass, M, and the eyepiece, R. The object 
being supposed to be at AB, at a greater distance than can be shown in 
the drawing, an inveffed and much smaller image is formed at ba on the 
other side of the object glass. But the second lens, P, is at such a 
distance that its principal focus coincides with the image ab; from 
which it follows that the luminous rays which pass through 6, for 
example, after traversing the lens, P, take a direction parallel to the 




TELESCOPES. 


- 510 ] 


475 


secondary axis, bO (475). Similarly the rays passing by a take a 
direction parallel to the axis, aO. After crossing on H, these various 
rays traverse a third lens, Q, whose principal focus coincides with the 
point H. The pencil, B&H, converges towards b', on a secondary axis, 



Fig. 376. 

O'b, parallel to its direction; the pencil A«II, converging in the same 
manner at an erect image of the object, AB, is produced at o7/. 
This image is viewed, as in the astronomical telescope, through a 
condensing eyepiece, R, so placed that it acts as a magnifying glass, 
that is, its distance from the image, a'b', is less than the principal focal 
distance ; hence, there is formed, at a"b", a virtual image of a'b', erect, 
and much magnified. The lenses P and Q, which only serve to rectify 
the position of the image, are fixed in a brass tube, at a constant 
distance, which is equal to the sum of their principal focal distances. 
The object glass, M, moves in a tube, and can be moved to or from the 
lens P, so that the image, ab, is always formed in the focus of the lens 
whatever be the distance of the object. The distance of the lens R 
may also be varied so that the image a"b" may be formed at the distance 
of distinct vision. 

This instrument may also be used as an astronomical telescope by 
using a different eyepiece ; this must have a much greater magnifying 
power than in the former cases. 

In the terrestrial telescope the magnifying power is the same as in 
the astronomical telescope, provided always that the correcting glasses, 
P and Q, have the same convexity. 

510. Galilean telescope.— The Galilean telescope is the simplest 
of all telescopes, for it only consists of two lenses, namely, an 
object glass, M, and a diverging or double concave eyepiece, R (fig. 
377), and it gives at once an erect image. Opera glasses are constructed 
on this principle. 

If the object be represented by the right line, AB, a real but inverted 
and smaller image would be formed at ba j but in traversing the eyepiece, 
R, the rays emitted from the points A and B are refracted, and diverge 
from the secondary axes, bO' and aO', which correspond to the points b and 
a of the image. Hence, these rays produced backward meet their axes in 



476 


ON LIGHT. 


[ 511 - 

«' and b '; the eye which receives them sees accordingly an erect and 
magnified image in a'b', which appears nearer because it is seen under an 
angle, a'Ob', greater than the angle, AO'B, under which the object is 
seen. 

The magnifying power is equal to the ratio of the angle a'O'b' to the 
angle AO'B, and is usually from 2 to 4. 

The distance of the eyepiece R' from the image ab is pretty nearly 



Fig. 377. 

equal to the principal focal distance of this eyepiece ; it follows, there¬ 
fore, that the distance between the two lenses is the difference between 
their respective focal distances: hence, Galileo’s telescope is very short 
and portable. It has the advantage of showing objects in their right 
position, and, further, as it has only two lenses, it absorbs very little 
light: in consequence, however, of the divergence of the emergent rays 
it has only a small field of view, and in using it the eye must be placed 
very near the eyepiece. The eyepiece can be moved to or from the 
object glass, so that the image a'b' is always formed at the distance of 
distinct vision. 

The opera glass is usually double, so as to produce an image in each 
eye, by which greater brightness is attained. 

The time at which telescopes were invented is not known. Some at¬ 
tribute their invention to Roger Bacon in the 13th century; others to 
J. B. Porta at the end of the 16th ; others again to a Dutchman, Jacques 
Metius, who, in 1609, accidentally found that by combining two glasses, 
one concave and the other convex, distant objects appeared nearer and 
much larger. 

Galileo’s was the first telescope directed towards the heavens. By its 
means Galileo discovered the mountains of the moon, Jupiter’s satellites, 
and the spots on the sun. 

511. Reflecting: telescopes.— The telescopes previously described are 
refracting or dioptric telescopes. It is, however, only in recent times that 
it has been possible to construct achromatic lenses of large size; before 
this, a concave metallic mirror was used instead of the object glass. 
Telescopes of this kind are called receding or catoptric telescopes. The 
principal forms are those devised by Gregory, Newton, Herschel and 
Cassegrain. 




TELESCOPES. 


477 


- 512 ] 

512. The Gregorian telescope. —Figure 378 is a representation of 
Gregory’s telescope ; it is mounted on a stand, about which it is move- 
able, and can be inclined at any angle. This mode of mounting is 



optional; it may be equatorially mounted. Fig. 379 gives a longitudinal 
section. It consists of a long brass tube closed at one end by a concave 
metallic mirror, M, which is perforated in the centre by a round aperture 



through which rays reach the eye. There is a second concave metal 
mirror, N, near the end of the tube : it is somewhat larger than the 
central aperture in the large mirror, and its radius of curvature is much 
smaller than that of the large mirror. The axes of both mirrors coincide 
with the axis of the tube. As the centre of curvature of the large 
mirror is at O, and its focus at ab, rays, such as SA, emitted from a 










478 


ON LIGHT. 


[ 513 - 

heavenly body, are reflected from the mirror M, and form at ab an in¬ 
verted and very small image of the heavenly body. The distance of the 
mirrors and their curvatures is so arranged that the position of this 
image is between the centre, o, and the focus, /, of the small mirror; 
hence the rays, after being reflected a second time from the mirror N, 
form at a'b' a magnified and inverted image of ab, and therefore in the 
true position of the heavenly body. This image is viewed through an 
eyepiece, P, which may either be single or compound, its object being to 
magnify it again so that it is seen at a"b". 

As the objects viewed are not always at the same distance, the focus 
of the large mirror, and therefore that of the small one, vary in position. 
And as the distance of distinct vision is not the same with all eyes, the 
image a ,f b" ought to be formed at different distances. The required ad¬ 
justments may be obtained by bringing the small mirror nearer or farther 
from the larger one ; this is effected by means of a milled head, A (fig. 
368), which turns a rod, and this by a screw moves a piece to which the 
mirror is fixed. 

513. The Newtonian telescope. —This instrument does not differ 
much from that of Gregory ; the large mirror is not perforated, and there 
is a small plane mirror inclined at an angle of 45° towards an eyepiece 
placed in the side of the telescope. The difficulty of constructing metallic 
mirrors has caused telescopes of Gregorian and Newtonian construction 
to fall into disuse. Of late, however, the process of silvering glass 
mirrors has been carried to a high state of perfection, and M. Foucault 
has applied these mirrors to Newtonian telescopes with great success. 
His first mirror was only four inches in diameter, but he has successively 
constructed mirrors of 8, 12, 13 inches, and at the time of his death 
had completed one of 32 inches diameter. 



Fig. 381 represents a Newtonian telescope mounted on an equatorial 
stand, and fig. 380 gives a horizontal section of it. This section shows 
how the luminous rays reflected from the parabolic mirror, M, meet a small 
rectangular prism, mn, which replaces the inclined plane mirror used in 
the old form of Newtonian telescope. After undergoing a total reflection 
















TELESCOPES. 


479 


- 513 ] 

from ?nn, the rays form at ah a very small image of the heavenly body. 
This image is viewed through an eyepiece with four lenses placed on 
the side of the telescope, and magnifying from 50 to 800 times, according 
to the size of the silvered mirror. 

In reflectors the mirror acts as object glass, but there is, of course, no 
chromatic aberration. 

The spherical aberration is corrected by the form given to the re¬ 
flector, which is paraboloid, but slightly modified by trial to suit the 
eyepiece fitted to the telescope. 

The mirror once polished is immersed in a silvering liquid, which 
consists essentially of ammoniacal solution of nitrate of silver, to which 
some reducing agent is added. When a polished glass surface is im¬ 
mersed in this solution, silver is deposited on the surface in the form of 
a brilliant metallic layer, which adheres so firmly that it can be polished 
with rouge in the usual manner. 

These new telescopes 'with glass mirrors have the advantage over the 
old ones that they give purer images, they weigh less, and are much 
shorter, their focal distance being only about six times the diameter of 
the mirror. 

These details known, the whole apparatus remains to be described. 
The body of the telescope (fig. 381) consists of an octagonal wooden 
tube. The end, G, is open; the mirror is at the other end. At a certain 
distance from this end two axles are fixed, which rest on bearings sup¬ 
ported by two wooden uprights, A and B. These are themselves fixed 
to a table, PQ, which turns on a fixed plate, RS, placed exactly parallel 
to the equator. On the circumference of the turning table there is a 
brass circle, divided into ‘360 degrees, and beneath it, but also fixed to 
the turning table, there is a circular toothed wheel, in which an endless 
screw, V, works. By moving this in either direction by means of the 
handle m, the table PQ, and with it the telescope, can be turned. A 
vernier, x, fixed to the plate RS, gives the fractions of a degree. On the 
axis of the motion of the telescope there is a graduated circle, O, which 
serves to measure the declination of the star, that is, its angular distance 
from the equator; while the degrees traced round the table, RS, serve to 
measure the right ascension , that is, the angle which the declination circle 
of the star makes with the declination circle passing through the first 
point of Aries. 

In order to fix the telescope in declination, there is a brass plate, E, 
fixed to the upright; it is provided with a clamp, in which the limb O 
works, and which can be screwed tight by means of a screw with milled 
head, r. On the side of the apparatus there is the eyepiece, o, which is 
mounted on a sliding copper plate, on which there is also the small prism 
mn, represented in the section fig. 380. To bring the image to the right 


480 


ON LIGHT. 


514 - 


place, this plate may be moved by means of a rack and a milled head, a. 
The handle, n, serves to damp or undamp the screw, V. The drawing 



was one taken from a telescope, the mirror of which is only 6^ inches 
in diameter, and which gives a magnifying power of 150 to 200. 

514. The Herschelian telescope. —Sir W. Herschel’s telescope, 
which, until recently, was the most celebrated instrument of modern 













TELESCOPES. 


481 


- 515 ] 

times, was constructed on a method differing from those described. 
The mirror was so inclined that the image of the star was formed 
at ab on the side of the telescope near the eyepiece, o, hence it is 



termed the front vieiv telescope. As the rays in this telescope only 
undergo a single reflection, the loss of light is less than in either of the 
preceding cases, and the image is therefore brighter. The magnifying 
power is the quotient of the principal focal distance of the mirror by the 
focal distance of the eyepiece. 

Herschel’s great telescope was constructed in 1789; it was 40 feet in 
length, the great mirror was 50 inches in diameter. The quantity of 
light obtained by this instrument was so great as to enable its inventor 
to use magnifying powers far higher than anything which had hitherto 
been attempted. 

Herschel’s telescope has been exceeded by one constructed by the late 
Earl of Rosse. This magnificent instrument has a focal length of 53 
feet, the diameter of the speculum being 6 feet. It is at present used as 
a Newtonian telescope, but it can also be arranged as a front view 
telescope. 


instruments for forming pictures of objects. 

515. Camera obscura. —The camei'a obscura (dark chamber) is, as 
its name implies, a closed space impervious to light. There is, however, 
a small aperture by which luminous rays enter, as shown in fig. 383. 
The ray, proceeding from external objects, and entering by this aperture, 
forms on the opposite side an image of the object in its natural colours, 
but of reduced dimensions, and in an inverted position. 

Porta, a Neapolitan physician, the inventor of this instrument, found 
that by fixing a double convex lens in the aperture, and placing a white 
screen in the focus, the image was much brighter, and more definite. 

Eig. 383 represents a camera obscura, such as is used for drawing. 
It consists of a rectangular wooden box, formed of two parts which 

¥ 







4g2 0N light. [515- 

slide in and out. The luminous rays, R, pass into the box by a lens, B, 
and form an image on the opposite side, 0, which is at the focal distance 



of the lens. But the rays are reflected from a glass mirror, M, inclined 

at an angle of 45°, and form 
an image on a ground glass 
plate, N. When a piece of 
tracing paper is placed on this 
screen, a drawing of the image 
is easily made. A wooden 
door, A, cuts off extraneous 
light. 

The box is formed of two 
parts, sliding one within the 
other, like the joints of a 
telescope, so that, by elongat¬ 
ing it more or less, the re¬ 
flected image may be made 
to fall exactly on the screen, 
N, at whatever distance the 
object may be situated. 

Fig. 384 shows another 
kind of camera obscura which 
is occasionally erected in sum¬ 
mer houses. In a brass case 
Fig. 384. A, there is a triangular prism, 














CAMERA LUCIDA. 


483 


- 516 ] 

P (fig. 385), which acts both as condensing lens and as mirror. One 
of its faces is plane, but the others have such curvatures that the com¬ 
bined refractions on entering and emerging from 
the prism produce the effect of a meniscus lens. 

Hence rays from an object, AB, after passing 
into the prism, and undergoing total reflec¬ 
tion from the face cd, form at ab a real image 
of AB. 

In fig. 384, the small table B corresponds 
to the focus of the prism in the case A, and an 
image forms on a piece of paper placed on 
the table. The whole is surrounded by a 
black curtain, so that the designer can place 
himself in complete darkness. 

516. Camera lucida. —The camera lucida is a small instrument de¬ 
pending on internal reflection, and serves for taking an outline of any 
object. It was invented by Dr. Wollaston, in 1804. It consists of a 
small four-sided glass prism, of which fig. 386 gives a section perpendi¬ 
cular to the edges. A is a right angle, and C an angle of 135 °; the other 
angles, B and D, are 67 j°. The prism rests on a stand, on which it can 





be raised or lowered, and turned more or less about an axis parallel to 
the prismatic edges. When the face, AB, is turned towards the object, 
the rays from the object fall nearly perpendicular on this face, pass into the 
prism without any appreciable refraction, and are totally reflected from 
BC ; for as the line ab is perpendicular to BC, and wL to AB, the angle 
anL will equal the angle B, that is, it will contain 67 j°, and this being 
greater than the critical angle of glass (464), the ray Ln will undergo 
total reflection. The rays are again totally reflected from o, and emerge 
near the summit, D, in a direction almost perpendicular to the face DA, 
so that the eye which receives the rays sees at L' an image of the 

Y 2 

















484 


ON LIGHT. 


[517- 

object L. If the outlines of the image are traced with a pencil, a very- 
correct design is obtained; but unfortunately there is a great difficulty 
in seeing both the image and the point of the pencil, for the rays from 
the object give an image which is farther from the eye than the pencil. 
This is corrected by placing between the eye and prism a lens, I, which 
gives to the rays from the pencil and those from the object the same 
divergence. In this case, however, it is necessary to place the eye very 
near the edge of the prism, so that the aperture of the pupil is divided 
into two parts, one of which sees the image, and the other the pencil. 

Amici’s camera lucida, represented in fig. 387, is preferable to that of 
Wollaston, inasmuch as it allows the eye to change its direction to a con¬ 
siderable extent, without ceasing to see the image and the pencil at the 
same time. It consists of a rectangular glass prism, ABC, having one of 
its perpendicular faces turned towards the object to be depicted, while 
the other is at right angles to an inclined plate of glass, mn. The rays, 
LI, proceeding from the object, and entering the prism, are totally re¬ 
flected from its base at D, and emerge in the direction KH. They are 
then partially reflected from the glass plate mn at H, and form a vertical 
image of the object, L, which is seen by the eye in the direction OL'. The 
eye, at the same time, sees through the glass the point of a pencil applied 
to the paper, and thus the outline of the picture may be traced with great 
exactness. 


Fig. 388. 



Fig. 389. 


517. Magic lantern. —This is an apparatus by which a magnified 
image of small objects may be projected on a white screen in a dark 
room. It consists of a tin plate box, in which there is a lamp placed in 
the focus of a concave mirror, A (fig. 388)* The reflected rays fall upon 
























SOLAR MICROSCOPE. 


485 


- 518 ] 


a condensing- lens, B (fig. 388), which concentrates them on the figure 
painted on a glass plate, Y. There is a double convex lens, C, at a dis¬ 
tance from V of rather more than its focal distance, and, consequently, a 
real and very much magnified image of the figure on the glass is produced 
on the screen (479). 

Dissolving views are obtained by arranging two magic lanterns, which 
are quite alike, with different pictures, in such a manner that both pictures 
are produced on exactly the same part of a screen. The object glasses of 
both lanterns are closed by screens, which are so arranged that according 
as one is raised the other is lowered, and vice versa. In this way one 
picture is gradually seen to change into the other. 

The magnifying power of the magic lantern is obtained by dividing 
the distance of the lens C from the image by its distance from the object. 
If the image is 100 or 1000 times farther from the lens than the object, 
the image will be 100 or 1000 times as large. Hence a lens with a very 
short focus can produce a very large image, provided the screen is suffi¬ 
ciently large. 

518. Solar microscope. —The solar microscope is in reality a magic 
lantern illuminated by the solar rays ; it serves to produce highly mag- 



rig. 390. 


nified images of very small objects. It is worked in a dark room; fig. 
390 represents it fitted in the shutter of a room, and fig. 391 gives the 
internal details. 

The solar rays fall on a plane mirror, M, placed outside the room, and 
are reflected towards a condensing lens, l , and from thence to a second 


















486 


ON LIGHT. 


[ 518 - 

lens, o (fig. 391), by which they are concentrated at its focus. The object 
to be magnified is at this point; it is placed between two glass plates, 
which, by means of a spring, n, are kept in a firm position between two 
metal plates, m. The object thus strongly illuminated is very near the 
focus of a system of three condensing lenses, x, which forms upon a screen 
at a suitable distance an inverted and greatly magnified image, ab. The 
distance of the lenses, o and x, from the object is regulated by means of 
screws, C and D. 

As the direction of the solar light is continually varying, the position 
of the mirror outside the shutter must also be changed, so that the re¬ 
flection is always in the direction of the axis of the microscope. The 
most exact apparatus for this purpose is the heliostat (458) ; but as this 



instrument is very expensive, the object is usually attained by inclining 
the mirror to a greater or less extent by means of an endless screw, B, 
and at the same time turning the mirror itself round the lens l, by a knob, 
A, which moves in a fixed slide. 

The solar microscope labours under the objection of concentrating 
great heat on the object, which soon alters it. This is partially obviated 
by interposing a layer of a saturated solution of alum, which, being a 
powerfully athermanous substance, cuts off a considerable portion of the 
heat. 

The magnifying power of the solar microscope maybe deduced experi¬ 
mentally by substituting for the object a glass plate marked with lines at 
a distance of ^ or ~ of a millimeter. Knowing the distance of these 
lines on the image, the magnifying power may be calculated. The same 
method is used with the photoelectric light. According to the magnify¬ 
ing power which it is desired to obtain, the objective x is formed of one, 
two, or three lenses, which are all achromatic. 

The solar microscope furnishes the means of exhibiting to a large 




















PHOTOELECTRIC MICROSCOPE. 


487 


- 519 ] 

audience many curious phenomena, such, for instance, as the circulation 
of blood in the smaller animals, the crystallisation of salts, the occur¬ 
rence of animalculse in water, vinegar, etc., etc. 

519. Photoelectric microscope. —This is nothing more than the 
solar microscope, but is illuminated by the electric light instead of by 
the sun’s rays. The electric light, by its intensity, its steadiness, and the 



Fig. 392. 


readiness with which it can be procured at any time of the day, is far 
preferable to the solar light. The photoelectric microscope alone will be 
described here: the electric light will be considered under the head of 
galvanism. 

Fig. 392 represents the arrangement devised by M. Duboscq. A 
solar microscope, ABD, identical with that already described, is fixed on 
the outside of a brass box. In the interior are two charcoal points which 



















488 


ON LIGHT. 


[ 520 - 

do not quite touch, the space between them being exactly on the axis 
of the lenses. The electricity of one end of a powerful battery reaches 
the charcoal a by means of a copper wire, K; while the electricity 
from the opposite end of the battery reaches c by a second copper 
wire H. 

During the passage of the electricity, a luminous arc is formed between 
the two ends of the carbons, which gives a most brilliant light, and 
powerfully illuminates the microscope. This is effected by placing at D 
in the inside of the tube a condensing lens, whose principal focus corre¬ 
sponds to the space between the two charcoals. In this manner the 
luminous rays, which enter the tubes D and B, are parallel to their axis, 
and the same effects are produced as with the ordinary solar microscope: 
a magnified image of the object placed between two plates of glass is 
produced on the screen. 

In continuing the experiment, the two carbons become consumed, and 
to an unequal extent, a more quickly than c. Hence, their distance 
increasing, the light becomes weaker and is ultimately extinguished. In 
speaking afterwards of this electric light, the working of the apparatus 
P, which keeps these charcoals at a constant distance, and thus ensures a 
constant light, will be explained. 

The part of the apparatus, MN, may be considered as a universal 
photogenic apparatus. The microscope can be replaced by the head pieces 
of the phantasmagoria, the polyorama, the megascope, by polarising ap¬ 
paratus, etc., and in this manner is admirably adapted for exhibiting 
optical phenomena to a large auditory. Instead of the electric light 
we may use with this apparatus the oxy-hydrogen or Drummond's light, 
which is obtained by heating a cylinder of lime in the flame produced 
by the combustion of a mixture of hydrogen and oxygen gases. 

520. lighthouse lenses.— Lenses of large dimensions are very dif¬ 
ficult of construction ; they further produce a considerable spherical aber¬ 
ration, and their thickness causes the loss of much light. In order to 
avoid these inconveniences, ichelon lenses have been constructed. Thev 
consist of a plano-convex lens, C (figs. 393 and 394), surrounded by a 
series of annular and concentric segments, A, B, each of which has a 
plane face on the same side as the plane face of the central lens, while the 
faces on the other side have such a curvature that the foci of the different 
segments coincide in the same point. These rings form, together with the 
central lens, a single lens, a section of which is represented in figure 394. 
The drawing was made from a lens of about 2 feet in diameter, the 
segments of which are formed of a single piece of glass ; but with larger 
lenses, each segment is likewise formed of several pieces. 

Behind the lens there is a support fixed by three rods, on which a body 
can be placed and submitted to the sun’s rays. As the centre of the 



- 520 ] LENSES FOR LIGHTHOUSES. 489 

support coincides with the focus of the lens, the substances placed there 
are melted and volatilised by the high temperature produced. Gold, 
platinum, and quartz are rapidly melted. This experiment proves that 
heat is refracted in the same way as light: for the position of the calo¬ 
rific focus is identical with that of the luminous focus. 


Fig. 394 


Fig. 393. 

Formerly parabolic mirrors were used in sending the light of beacons 
and lighthouses to great distances, but they have been supplanted by the 
use of lenses of the above construction. In most cases, oil is used in a 
lamp of peculiar construction, which gives as much light as 20 moderators. 
The light is placed in the principal focus of the lens on the side of the 
plane face. The emergent rays consequently form a parallel beam 
(fig. 334), which loses intensity only by passing through the atmo¬ 
sphere, and can be seen at a distance of above 40 miles. In order that 

y 3 
















490 


ON LIGHT. 


[ 521 - 

all points of the horizon may be successively illuminated, the lens is 
continually moved round the lamp by a clock-work motion, the rate of 
wbicji varies with different lighthouses. Hence, in different parts, the 
light alternately appears and disappears after equal intervals of time. 
These alternations serve to distinguish lighthouses from an accidental 
fire or a star. By means too of the number of times the light disappears in 
a given time, and by the colour of the light, sailors are enabled to distin¬ 
guish the lighthouses from one another, and hence to know their position. 

Of late years the use of the- electric light has been substituted for that 
of oil lamps ; a description of the apparatus will be given in a subse¬ 
quent chapter. 


PHOTOGRAPHY. 

521. Daguerreotype.— Photography is the art of fixing the images of 
the camera obscura on substances sensitive to light. The various photo¬ 
graphic processes may be classed under three heads : photography on 
metal, photography on paper, and photography on glass. 

Wedgewood was the first to suggest the use of chloride of silver in 
fixing the image, and Davy, by means of the solar microscope, obtained 
images of small objects on paper impregnated with chloride of silver; 
but no method was known of preserving the images thus obtained, by 
preventing the further action of light. Niepce, in 1814, obtained per¬ 
manent images of the camera by coating glass plates with a layer of 
a varnish composed of bitumen dissolved in oil of lavender. This pro¬ 
cess was tedious and inefficient, and it was not until 1839 that the pro¬ 
blem was solved. In that year, Daguerre described a method of fixing 
the images of the camera, which, with the subsequent improvements 
of Talbot and Archer, has rendered the art of photography one of the 
most marvellous discoveries ever made, either as to the beauty and per¬ 
fection of the results, or as to the celerity with which they are produced. 

In Daguerre’s process, the Daguerreotype, the picture is produced on 
a plate of copper coated with silver. This is first very carefully polished, 
an operation on which much of the success of the subsequent operations 
depends. It is then rendered sensitive by exposing it to the action of 
iodine vapour, which forms a thin layer of iodide of silver on the surface.' 
The plate is now fit to be exposed in the camera; it is sensitive enough for 
views which require an exposure of ten minutes in the camera, but when 
greater rapidity is required, as for portraits, etc., it is further exposed 
to the action of an accelerator, such as bromine or hypobromite of calcium. 
All these operations must be performed in a room lighted by a candle, 
or by the daylight admitted through yellow glass, which cuts off all 
chemical rays. The plate is preserved from the action of light by placing 
it in a small wooden case provided with a slide on the sensitive side. 


PHOTOGRAPHY. 


491 


-S21] 

The third operation consists in exposing the sensitive plate to the 
action of light, placing it in that position in the camera where the image 
is produced with greatest delicacy. For photographic purposes a camera 
obscura of peculiar construction is used. The brass tube A (fig. 395) 
contains an achromatic condensing lens, which can be moved by means 
of a rackwork motion, to which is fitted a milled head, D. At the op¬ 
posite end of the box is a ground glass plate, E, which slides in a groove, 



Fig. 395. 

in which the case containing the plate also fits. The camera 
placed in a proper position before the object, the sliding part of the box 
is adjusted until the image is produced on the glass with the utmost 
sharpness ; this is when the glass slide is exactly in the focus. The final 
adjustment is made by means of the milled head, D. 
f* The glass slide is then replaced by the case containing the sensitive 
plate ; the slide which protects it is raised ; and the plate exposed for a 
time, the duration of which varies in different cases, and can only be 
hit exactly by great practice. The plate is then removed to a dark room. 
No change is perceptible to the eye, but those parts on which the light 
has acted have acquired the property of condensing mercury: the plate 
is next placed in a box and exposed to the action of mercurial vapour at 
60 or 70 degrees. 

The mercury is deposited on the parts affected in the form of globules 
imperceptible to the naked eye. The shadows, or those parts on which 
the light has not acted, remain covered with the layer of iodide of silver. 
This is removed by treatment with hyposulphite of sodium, which dissolves 
iodide of silver without affecting the rest of the plate. The plate is next 
immersed in a solution of chloride of gold in hyposulphite of sodium, which 
dissolves the silver, while some gold combines with the mercury and silver 
of the parts attacked, and greatly increases the intensity of the lustre. 




492 


ON LIGHT. 


[ 522 - 

Hence the light parts of the image are those on which the mercury 
has been deposited, and the shaded those on which the metal has retained 
its reflecting lustre. 

Fig. 396 represents a section of the object glass. At first it consisted 
of a double convex lens, but now double achromatic lenses are used as 
object glasses. They act more quickly than ob¬ 
jectives with a single lens, and can be more easily 
focussed by moving the lens B, by means of the 
rack and pinion D. 

•522. Photographs on paper.— In Daguerre’s 
process, which has just been described, the images 
are produced directly on metallic plates. With 
paper and glass, photographs of two kinds may be obtained: those in 
which an image is obtained with reversed tints, so that the lightest parts 
have become the darkest on paper, and vice versa; and those in which 
the lights and shades are in their natural position. The former are 
called negative and the latter positive pictures. 

A negative may be taken either on glass or on paper; it serves to pro¬ 
duce a positive picture. 

Negatives on glass. A glass plate of the proper size is carefully cleaned; 
collodion impregnated with iodide of potassium is then poured upon it, 
and the plate moved about till a layer of collodion of uniform thickness 
is obtained. The plate is then immersed for about a minute in a bath of 
nitrate of silver containing 30 grains of the salt in an ounce of water. 
This operation must be performed in a dark room. The plate is then 
removed, allowed to drain, and when somewhat dry, placed in the closed 
frame, and afterwards exposed in the camera, for a shorter time than in 
the case of a Daguerreotype." On removing the plate to a dark room, 
no change is visible, but on pouring over it a solution called the developer , 
an image gradually appears. The principal substances used for developing 
are protosulphate of iron and pyrogallic acid. The action of light on 
iodide of silver appears to produce some molecular change, in virtue of 
which the developers have the property of reducing to the metallic state, 
those parts of the iodide of silver which have been most acted upon 
by the light. When the picture is sufficiently brought out, water is 
poured over the plate, in order to prevent the further action of the de¬ 
veloper. The parts on which light has not acted are still covered with 
iodide of silver, which would be affected if the plate were now exposed 
to the light. It is, accordingly, washed with solution of hyposulphite 
of sodium, which dissolves the iodide of silver and leaves the image un¬ 
altered. The picture is then coated with a thin layer of spirit-varnish, 
to protect it from mechanical injury. 

When once the negative is obtained, it may be used for printing an 



Fig. 396. 













STRUCTURE OF THE HUMAN EYE. 


493 


- 525 ] 

indefinite number of positive pictures. For this purpose, paper is impreg¬ 
nated with chloride of silver, by immersing it first in solution of nitrate 
of silver and then in one of chloride of sodium ; chloride of silver is thus 
formed on the paper by double decomposition. The negative is placed on 
a sheet of this paper in a copying frame, and exposed to the action of light 
for a certain time. The chloride of silver becomes acted upon—the light 
parts of the negative being most affected, and the dark parts least so. A 
copy is thus obtained, on which the lights of the negative are replaced by 
shades, and inversely. In order to fix the picture, it is washed in a solu¬ 
tion of hyposulphite of sodium, which dissolves the unaltered chloride of 
silver. The picture is afterwards immersed in a bath of chloride of gold, 
which gives it tone. 

523. Positives on glass. —Very beautiful positives are obtained by 
preparing the plates as in the preceding cases; the exposure in the camera, 
however, is not nearly so long as for the negatives. The picture is then 
developed by pouring over it a solution of protosulphate of iron, which 
produces a negative image; and by afterwards pouring a solution of 
cyanide of potassium over the plate, this negative is rapidly converted 
into a positive. It is then washed and dried, and a coating of varnish 
poured over the picture. 

524. Photographs on albumenised paper and glass. —In some 
cases, paper impregnated with a solution of albumen containing iodide of 
potassium is used instead of collodion, over which it has the advantage 
that it can be prepared for some time before it is used, and that it pro¬ 
duces certain effects in the middle tints. It has the disadvantage of not 
being nearly so sensitive. It requires, therefore, longer exposure, and is 
unsuitable for portraits, but can be advantageously used for views. 


CHAPTER VI. 

THE EYE CONSIDERED AS AN OPTICAL INSTRUMENT. 

525. Structure of the human eye. —The eye is the organ of vision, 
that is to say, of the phenomenon by virtue of which the light emitted 
or reflected from bodies excites in us the sensation which reveals their 
presence. 

The eye is placed in a bony cavity called the orbit; it is maintained 
in its position by the muscles which serve to move it, by the optic nerve, 
the conjunctiva, and the eyelids. Its size is much the same in all persons: 
it is the varying aperture of the eyelids that makes the eye appear larger 
or smaller. 





494 


ON LIGHT. 


[ 525 - 

Fig. 397 represents a transverse section of the eye from back to front. 
The general shape is that of a spheroid, the curvature of which is greater 
in the anterior than in the posterior part. It is composed of the follow¬ 
ing parts: the cornea, the sclerotica, the iris, the pupil, the aqueous humour, 
the crystalline, the vitreous body, the hyaloid membrane, the choroid, the 
retina, and the optic nerve. 



Fig 397. 


Cornea. The cornea, a, is a transparent membrane situated in front of 
the hall of the eye. In shape it resembles a small watch glass, and it fits 
into the sclerotica, i ; in fact, these membranes are so connected that some 
anatomists have considered them as one and the same, and have distin¬ 
guished them by calling the cornea the transparent, and the sclerotica the 
opaque cornea. 

Sclerotica. The sclerotica, i, or sclerotic coat, is a membrane which, 
together with the cornea, envelopes all parts of the eye. In front there 
is an almost circular aperture into which the cornea fits; behind it is 
perforated so as to give passage to the optic nerve. 

Iris. The iris, d, is an annular, opaque diaphragm, placed between 
the cornea and the crystalline lens. It constitutes the coloured part of 
the eye, and is perforated by an aperture called the pupil, which in man 
is circular. In some animals, especially those belonging to the genus 
felis, it is narrow and elongated in a vertical direction : in the ruminants 
it is elongated in a transverse direction. It is a contractile membrane, 
and its diameter varies in the same individual between 042 and 0*28 of 
an inch; but these limits may be exceeded. The luminous rays pass into 
the eye through the pupil. The pupil enlarges in darkness, but contracts 
under the influence of a bright light. These alternations of contraction 
and enlargement take place with extreme rapidity ; they are very frequent, 




- 525 ] STRUCTURE OF THE HUMAN EYE. 495 . 

and play an important part in the act of vision. The movements of the 
iris are involuntary. 

It appears from this description that the iris is a screen with a variable 
aperture, whose function is to regulate the quantity of light which pene¬ 
trates into the eye : for the size of the pupil diminishes as the intensity 
of light increases. The iris serves also to correct the spherical aberration 
as it prevents the marginal rays from passing through the edges of the 
crystalline lens. It thus plays the same part with reference to the eye 
that a diaphragm does in optical instruments (481). 

Aqueous humour. Between the posterior part of the cornea and the 
front of the crystalline, there is a transparent liquid called the aqueous 
humour. The space, e , occupied by this humour is divided into two 
parts by the iris; the part 6, between the cornea and the iris, is called 
the anterior chamber ; the part c, which is between the iris and the 
crystalline, is the posterior chamber. 

Crystalline. The crystalline or crystalline lens is a lens-shaped body, 
/, placed behind the iris, but very near it. The crystalline is remarkable 
for its transparence; it is enclosed in a similar transparent membrane 
called the capsule , which adheres by its edge to an annular wreath called 
the ciliary ligament , g. 

The convexity of the anterior face of the crystalline is less than that 
of the posterior. It is made up of a series of layers which are almost 
concentric, and are harder at the centre than at the circumference. The 
outermost layers are so soft as to be almost liquid. They have been 
called Morgagni’s humour. The refracting power of these layers decreases 
from the centre to the circumference. 

Vitreous body. Hyaloid membrane. The vitreous body, or vitreous 
humour, is a transparent mass resembling the white of an egg, which 
occupies all the part of the ball of the eye, h, behind the crystalline. 
The vitreous humour is surrounded by the hyaloid membrane , l, which 
lines the posterior face of the crystalline capsule, and also the internal 
face of another membrane called the retina. 

Retina. Optic nerve. The retina, m 1 is a membrane which receives the 
impression of light, and transmits it to the brain by the intervention of 
a nerve, n, called the optic nerve, which, proceeding from the brain, 
penetrates into the eye, and extends over the retina in the form of a 
nervous network. 

The only property of the retina and optic nerve is that of receiving 
and transmitting to the brain the impression of objects. These organs 
have been cut and picked without causing any pain to the animals sub¬ 
mitted to these experiments. 

Choroid. The choroid, k } is a membrane between the retina and the 
sclerotica. It is completely vascular, and is covered on the internal face 


496 


ON LIGHT. 


[526- 

by a black substance wbicb resembles the colouring matter of a negro’s 
skin, and which absorb all rays not intended to co-operate in producing 
vision. 

The choroid elongates in front, and forms a series of convoluted folds 
called ciliary processes, which penetrate between the iris and the crystal¬ 
line capsule to which they adhere, forming round it a disc, resembling a 
radiated flower. By its vascular tissue, the choroid serves to carry the 
blood into the interior of the eye, and especially to the ciliary processes. 

526. Refractive indices of the transparent media of the eye. 
—The refractive indices from air into the transparent parts of the eye 
have been determined by Brewster. His results are contained in the 
following table, compared with water as a standard : 


Water. 

. 1-3358 

Aqueous humour . . 

. 1-3366 

Vitreous humour. 

. 1-3394 

Exterior coating of the crystalline 

. 1-3767 

Centre of the crystalline .... 

. 1-3990 

Mean refraction of the crystalline 

. 1-3839 


527. Curvatures and dimensions of various parts of the human 
eye. 


Radius of curvature of the sclerotica 


0-40 to 0-44 in, 

„ „ cornea . 


0-28 to 0-32 „ 

,, „ anterior face of the 


crystalline . 


0-28 to 0-40 „ 

„ „ posterior face 


0-20 to 0-24 „ 

Diameter of the iris .... 


0-44 to 0-48 „ 

„ „ pupil .... 


0-12 to 0-28 „ 

,, „ crystalline 


0-40 „ 

Thickness of the crystalline . 


0-20 „ 

Distance from the pupil to the cornea . 


0-08 „ 

Length of the axis of the eye 


0-88 to 0 96 „ 


The curvature of the cornea, according to M. Chossat, is that of an 
ellipsoid of revolution round its major axis, and the curvature of the 
crystalline that of an ellipsoid of revolution round its minor axis. 

528. Path of rays in the eye, —From what has been said as to 
the structure of the eye, it may be compared to a camera obscura (515), 
of which the pupil is the aperture, the crystalline is the condensing lens, 
and the retina is the screen on which the image is formed. Hence, the 
effect is the same as when the image of an object placed in front of a 
double convex lens is formed in its conjugate focus. Let AB (fig. 898) 
be an object placed before the eye, and let us consider the rays emitted 
from any point of the object A. Of all these rays those which are 
directed towards the pupil are the only ones which penetrate the eye, 





STRUCTURE OF THE HUMAN EYE. 


497 


- 530 ] 

and are operative in producing vision. These rays, on passing into the 
aqueous humour, experience a first refraction which brings them near the 
secondary axis, A a, drawn through the optic centre of the crystalline; 
they then traverse the crystalline, which again refracts them like a double 
convex lens, and having experienced a final refraction by the vitreous 



humour, they meet in a point a , and form the image of the point A. 
The rays issuing from the point B form in like manner an image of it at 
the point b, so that a very small, real, and inverted image is formed 
exactly on the retina, provided the eye is in its normal condition. 

529. inversion of images. —In order to show that the images 
formed on the retina are really inverted, the eye of an albino or any 
animal with pink eyes may be taken; this has the advantage that, as the 
choroid is destitute of pigment, light can traverse it without loss. This 
is then deprived at its posterior part of the cellular tissue surrounding it, 
and fixed in a hole in the shutter of a dark room ; by means of a lens it 
may be seen that inverted images of external objects are depicted on the 
retina. 

The inversion of images in the eye has greatly occupied both 
physicists and physiologists, and many theories have been proposed to 
explain how it is that we do not see inverted images of objects. Some 
have supposed that it is by custom, and by a regular education of the 
eye, that we see objects in their true position, that is to say, in their 
position relative to us. The visual impression becomes corrected by the 
impression of other senses, such as that of touch. Miiller, Volkmann, 
and others contended that, as we see everything inverted, and not simply 
one object among others, nothing can appear inverted, because terms of 
comparison are wanting. It must, however, be admitted that none of 
these theories is quite satisfactory. 

530. Optic axis, optic angle, visual angle.— The principal optic axis 
of an eye is the axis of its figure ; that is to say, the straight line in re¬ 
ference to which it is symmetrical. In a well-shaped eye it is the 
straight line passing through the centre of the pupil and of the crystal¬ 
line, such as the line Oo (fig. 398). The lines A a, B b, which are almost 
rectilinear, are secondaiy axes. The eye sees objects most distinctly in 
the direction of the principal optic axis. 




498 


ON LIGHT. 


[ 531 — 

The optic angle is the angle BAC (fig. 399), formed between the 
principal optic axes of the two eyes when they are directed towards the 
same point. This angle is smaller in proportion as the objects are more 
distant. 



The visual angle is the angle AOB (fig. 400), under which an object is 
seen; that is to say, the angle formed by the secondary axes drawn from 
the optic centre of the crystalline to the opposite extremities of the object. 
For the same distance, this angle decreases with the magnitude of the 
object, and for the same object it decreases as the distance increases, as is 



the case when the object passes from AB to A'B'. It follows, therefore, 
that objects appear smaller in proportion as they are more distant; for 
as the secondary axes, AO, BO, cross in the centre of the crystalline, the 
size of the image projected on the retina depends on the size of the visual 
angle, AOB. 

531. Estimation of the distance and size of objects.— The esti¬ 
mation of distance and of size depends on numerous circumstances ; these 
are—the visual angle, the optic angle, the comparison with objects whose 
size is familiar to us, the diminution of the precision of the image by the 
interposition of a more or less vaporous medium. 

When the size of an object is known, as the figure of a man, the height 
of a tree, or of a house, the distance is estimated by the magnitude of the 
visual angle under which it is seen. If its size is unknown, it is judged 
relatively to that of objects which surround it. 

A colonnade, an avenue of trees, the gas-lights on the side of a road 
appear to diminish in size in proportion as their distance increases, 
because the visual angle decreases ; but the habit of seeing the columns, 
trees, etc., in their proper height, leads our judgment to rectify the im- 










DISTANCE OF DISTINCT VISION. 


499 


- 533 ] 

pression produced by vision. Similarly, although very distant mountains 
are seen under a very small angle, and occupy but a small space in the 
field of view, our familiarity with the effects of aerial perspective enables 
us to form a correct idea of their real magnitude. 

The optic angle is also an essential element in appreciating distance. 
This angle increasing or diminishing according as objects approach or 
recede, we move our eyes so as to make their optic axes converge towards 
the object which we are looking at, and thus obtain an idea of its distance. 
Nevertheless, it is only by long custom that we can establish a relation 
between our distance from the objects and the corresponding motion of the 
yes. It is a curious fact that persons bom blind, and whose sight has 
been restored by the operation for cataract, imagine at first that all objects 
are at the'same distance. 

532. Distance of distinct vision. —The distance of distinct vision is, 
as already stated, the distance at which objects must be placed so as to 
be seen with the greatest distinctness. It varies in different individuals, 
and in the same individual it is often different in the two eyes. For small 
objects, such as print, it is from 10 to 12 inches in normal cases. 

In order to obtain an approximate measurement of the least distance of 
distinct vision, two small parallel slits are made in a card at a distance of 
0'03 of an inch. These apertures are held close before the eye, and when 
a fine slit in another card is held very near this aperture, the slit is seen 
double, because the rays of light which have traversed both apertures do 
not intersect each other on the retina, but behind it. But, if the latter 
card is gradually removed, the distance is ultimately reached at which 
both images coincide and form one distinct image. Stampfer has con¬ 
structed an optometer on this principle. 

Persons who see only at a very short distance are called myoptic, or 
short-sighted , and those who see only at a long distance are presbyoptic, or 
long-sighted . 

533. Adaptation of the eye to all distances. —The eye has a re¬ 
markable property which is not met with to the same extent in any optical 
instrument. It is, that, although images have a tendency to be formed so 
much the more in front of the retina as the objects are more distant, they 
are really formed on the retina; for the eye sees clearly at various dis¬ 
tances besides that of distinct vision. But, although we can see at very 
unequal distances, we cannot do so simultaneously, which indicates some 
modifications in the system of the eye, or, at all events, the necessity of 
fixing our attention on the object which we wish to see. If, for example, 
we look at two objects, one of which is at the distance of a yard from the 
eye, and the other at two yards, when we fix our attention on the first, 
the second becomes dim, and if on the second, the first in turn becomes 
indistinct. Hence, it is concluded that when the eye is adapted to see at 


ON LIGHT. 


500 


[ 534 - 


one distance, it is not in a condition to see at another, hut that it can 
adapt itself either to the one or to the other. 

Several hypotheses have been proposed to explain how it is that the 
eye can see distinctly at various distances. M. Mile thinks that the 
luminous rays undergo a diffraction or inflexion on the edge of the iris, 
which produces very different focal distances. Relying on the unequal 
refrangibility of the crystalline, which decreases from the centre to the 
circumference, and observing that a series of foci would result, of which 
the nearest are formed by rays which traverse the crystalline nearest its 
centre, M. Pouillet assumes that, as the pupil opens to a greater or less 
extent, distant objects are seen by rays passing near the edge of the crys¬ 
talline, and less remote objects by rays passing near the centre. Contrac¬ 
tions and dilatations of the pupillary aperture are, in fact, connected with 
the accommodation of the eye to distance; but they are also connected with 
variations in the intensity of light, and for the same distance the aperture 
of the pupil may vary greatly. 

Rohaut, Olbers, and others have suggested that the diameter of the 
eye from the back to the front is changed by the muscles which move it, 
so as to bring the retina nearer or farther from the crystalline, at the same 
time that the image itself is nearer or farther; we know, in fact, that in 
convergent lenses (475) the image is nearer in proportion as the object is 
more distant. 

Hunter and Young attributed to the crystalline a contractile property, 
in virtue of which it takes a more or less convex form, so as always to 
cause the rays to converge upon the retina. Kepler, Camper, and others 
assumed, that by the action of the ciliary processes, the crystalline is 
moved nearer to or farther from the retina. 

It has lastly been supposed that distinctness of vision at various dis¬ 
tances may arise from the fact that the differences in the focal distance 
in the crystalline, in proportion as objects become more distant, are so 
small that the image retains sufficient distinctness. This is confirmed by 
the experiments of Magendie and by those of He Haldat. The former 
observed, with the eye of an albino, that the precision of the images did 
not vary for objects placed at very unequal distances j and De Haldat has 
found that, if a crystalline be placed as an object-glass in the shutter of a 
dark room, equally distinct images of external objects maybe obtained on 
aground glass screen, whether the objects be at a distance of 10 or 12 
inches, or of 20 to 30 yards. This property of the crystalline in the inert 
state appears contrary to the laws of refraction; it is doubtless to be at¬ 
tributed to its structure, which is totally different from that of ordinary 
lenses. He Haldat has offered no explanation of these phenomena; the 
following theory is due to Sturm. 

534. Sturm’s theory of vision.— In order to explain the adaptability 


BINOCULAR VISION. 


501 


- 535 ] 

of the eye to various distances, Sturm observes that, as it has been shown 
by Young, Chossat, and others, that the curvatures of the different media 
of the eye are not spherical, this organ cannot be regarded exactly as a 
system of homogeneous spherical lenses superposed on the same axis, and 
that the crystalline especially cannot be compared to an ordinary spherical 
lens. The eye must be considered as formed of many unequally refract¬ 
ing media, bounded by surfaces which not only are not spherical, but 
which do not even form a system symmetrical round a common axis. 
This being the case, Sturm, premising certain considerations relative to 
surfaces known in mathematics under the name of skew surfaces, investi¬ 
gates the form which a very thin pencil of rays would take, which is suc¬ 
cessively refracted in several unequally refracting media. Considering 
the case in which the pencil traverses a diaphragm of very small aper¬ 
ture, whose plane is perpendicular to the axis of the beam, and supposing 
the beam to emanate from a point situate on the axis, Sturm finds by cal¬ 
culation that the successive intersections of the rays form a caustic surface 
(457), which cuts the axis of the beam in two points, and that between 
these two points the beam is more condensed than elsewhere, but beyond 
it is more and more divergent. Sturm has called these two points, which 
we designate by the letters F and /, the foci of the beam, and the distance 
which separates them is the focal interval. 

Applying these theoretical considerations to- vision, Sturm advances a 
theory which may be stated thus: The place in which light can act upon 
the retina is not a single point, but a linear focus, F f, in all the extent of 
which the luminous beam, which penetrates into the pupil, is so condensed 
as to give rise to the sensation of vision. Consequently, when external 
objects approach or recede, it is enough for distinct vision that the retina 
be always comprised between the two foci, F and f or coincide with one 
of them. 

585. Binocular vision.— A single eye sees most distinctly any point 
situated on its optical axis, and less distinctly other points also, towards 
which it is not directly looking, but which still are within its circle of 
vision. 

It is able to judge of the direction of any such point, but unable by 
itself to estimate its distance. Of the distance of an object it may indeed 
learn to judge by such criteria as loss of colour, indistinctness of outline, 
decrease in magnitude, etc.; but if the object is near, the single eye is 
not infallible, even with these aids. 

When the two eyes are directed upon a single point, we then gain the 
power of judging of its distance as compared with that of any other 
point, and this we seem to gain by the sense of greater or less effort 
required in causing the optical axis to converge upon the one point or 
upon the other. Now a solid object may be regarded as composed of 


502 


ON LIGHT. 


[ 536 - 

points which are at different distances from the eye. Hence, in looking 
at such an object, the axes of the two eyes are rapidly and insensibly 
varying their angle of convergence, and we as rapidly are gaining 
experience of the difference in distance of the various points of which 
the object is composed, or, in other words, an assurance of its solidity. 
Such kind of assurance is necessarily unattainable in monocular vision. 

536. The principle of the stereoscope. —Let any solid object, such 
as a small box, be supposed to be held at some short distance before the 
two eyes. On whatever point of it they are fixed, they will see that 
point the most distinctly, and other points more or less clearly. But it 
is evident that, as the two eyes see from different points of view, there 
will be formed in the right eye a picture of the object different from that 
formed in the left; and it is by the apparent union of these two dissimilar 
pictures that we see the object in relief. If, therefore, we delineate the 
object, first as seen by the right eye, and then as seen by the left, and 
afterwards present these dissimilar pictures again to the eyes, taking care 
to present to each eye that picture which was drawn from its point of 
view, there would seem to be no reason why we should not see a 
representation of the object as we saw the object itself, in relief. Ex¬ 
periment confirms the supposition. If the object held before the eyes 
were a truncated pyramid, r and l, fig. 401, would represent its principal 



lines, as seen by the right and left eyes respectively. If a card be held 
between the figures, and they are steadily looked at, r by the right eye, 
and l simultaneously by the left, for a few seconds, there will be seen a 
single picture having the unmistakeable appearance of relief. Even 
without a card interposed, the eye, by a little practice, may soon be 
taught so to combine the two as to form this solid picture. Three 
pictures will in that case be seen, the central being solid, and the two 
outside ones plain. Fig. 402 will explain this. Let r and l be any two 
corresponding points, say the points marked by a large dot in the figures 
drawn above; R and L the positions of the right and left eyes; then the 















STEREOSCOPE. 


503 


-537] 

right eye sees the point r in the direction Ho, and the left eye the point 
l in the direction Lo, and accordingly, each by itself judging only by the 
direction, they together see these two points 
as one, and imagine it to be situated at o. 

But the right eye, though looking in the 
direction Rr, also receives an image of l on 
another part of the retina, and the left eye 
in the same way an image of r, and thus 
three images are seen. A card, however, 
placed in the position marked by the dotted 
line, will of course cut off the two side 
pictures. To assist the eye in combining 
such pairs of dissimilar pictures, both 
mirrors and lenses have been made use of, 
and the instruments in which either of 
these are adapted to this end are called 
stereoscopes. 

537. The reflecting stereoscope.— 

In the reflecting stereoscope plane mirrors 
are used to change the apparent position of the pictures, so that they 
are both seen in the same direction, and their combination by the 
eye is thus rendered easy and almost inevitable. If ab ab (fig. 403) 
are two plane mirrors inclined to one another at an angle of 90°, the two 
arrows, xy, would both be seen by the eyes situated at R and L in the 
position marked by the dotted arrow. If, instead of the arrows, we now 




Fig. 403. Fig. 404. 

substitute such a pair of dissimilar pictures as we have spoken of above, 
of the same solid object, it is evident that, if the margins of the pictures 
coincide, othercorresponding points of the pictures will not. The eyes, 
however, almost without effort, soon bring such points into coincidence, 












504 ON LIGHT. [ 538 - 

and in so doing make them appear to recede or advance, as they are 
farther apart or nearer together than any two corresponding points 
(the right-hand comer, for instance) of the margins, when the pictures 
are placed side by side, as in the diagram, fig. 403. It will be plain, also, 
on considering the position for the arrows in fig. 403, that, to adapt such 
pictures as those in fig. 401 to use in a reflecting stereoscope, one of them 
must be reversed, or drawn as it would be seen through the paper if held 
up to the light. 

538. The refracting: stereoscope. —Since the rays passing through 
a convex lens are bent always towards the thicker part of the lens, any 
segment of such a lens may be readily adapted to change the apparent 
position of any object seen through it. Thus, if ac ac (fig. 404) are two 
segments cut from a double convex lens, and placed with their edges 
together, the arrows x y would be both seen in the position of the dotted 
arrow by the eyes at R and L. 

If we substitute for the arrows two dissimilar pictures of the same 
solid object, or the same landscape, we shall then, if a diaphragm, ab , be 
placed between the lenses to prevent the pictures being seen crosswise by 
the eyes, see but one picture, and that apparently in the centre, and 
magnified. As before, if the margins are brought by the power of the 
lenses to coincide, other corresponding points will not be coincident until 
combined by an almost insensible effort of the eyes. Any pair of cor¬ 
responding points which are farther apart than any other pair, will then 
be seen farther back in the picture, just as any point in the background 
of a landscape would be found (if we came to compare two pictures of 
the landscape, one drawn by the right eye, and the other by the left) to 
be represented by two points farther apart from one another than two 
others which represented a point in the foreground. 

To any one curious in such experiments, it will be instructive to notice 
that there is also a second point on this side of 
the paper, at which, if a person look steadily, 
the diagrams in fig. 405 will combine, and form 
quite a different stereoscopic picture. Instead 
of a solid pyramid, a hollow pyramidal box 
will then be seen. The point may easily be 
found by experiment. Here again two exter¬ 
nal images will also be seen. If we wish to 
shut these out, and see only their central 
stereoscopic combination, we must use a dia¬ 
phragm of paper held parallel to the plane of 
the picture with a square hole in it. This 
paper screen must be so adjusted that it may 
conceal the right-hand^figure from the left eye, and the left-hand figure 


l r 




PERSISTENCE OF IMAGES. 


505 


- 539 ] 

from tlie right eye, while the central stereoscopic picture may be seen 
through the hole. It will be plain from the diagram that o is the point 
to which the eyes must be directed, and at which they will imagine the 
point to be situated, which is formed by the combination of the two points 
r and l. The dotted line shows the position of the screen. A stereoscope 
with or without lenses may easily be constructed, which will thus give 
us, with the ordinary stereoscopic slides, a reversed picture. For instance, 
if the subject be a landscape, the foreground will retire and the back¬ 
ground come forward. 

When the two retinas view simultaneously two different colours, the 
impression produced is that of a single mixed tint. The power, however, of 
combining the two tints into a single one varies in different individuals, and 
in some is extremely weak. If two white discs at the base of the stereo¬ 
scope be illuminated by two pencils of complementary colours, and if 
each coloured disc be looked at with one eye, a single white one is seen, 
showing that the sensation of white light may arise from two comple¬ 
mentary and simultaneous chromatic impressions on each of the two 
retinas. 

539. Persistence of impression on the retina. —When an 
ignited piece of charcoal is rapidly rotated, we cannot distinguish it; the 
appearance of a circle of fire is produced; similarly rain, in falling in 
drops, appears in the air like a series of liquid threads. In a rapidly 
rotating toothed wheel the individual teeth cannot be seen. But if, 
during darkness, the wheel be suddenly illuminated, as by the electric 
spark, the individual parts may be clearly made out. These various ap¬ 
pearances are due to the fact that the impression of these images on 
the retina remains for some time after the object which has produced 
them has disappeared or become displaced. The duration of the per¬ 
sistence varies with the sensitiveness of the retina and the intensity of 
light. The following experiment is a further illustration of this property. 
A series of equal sections are traced on a disc of glass, and they are alter¬ 
nately blackened; in the centre there is a pivot, on which a second disc 
is fixed of the same dimensions as the first, but completely blackened, 
with the exception of a single sector; then placing the apparatus between 
a window and the eye, the second disc is made to rotate. If the move¬ 
ment is slow, all the transparent sectors are seen, but only one at a time; 
by a more rapid rotation we see simultaneously two, three, or a greater 
number. 

M. Plateau has investigated the duration of the impression by nume¬ 
rous similar methods, and has found that it is on the average half a second. 
Among many curious instances of these phenomena, the following is one 
of the most remarkable. If after having looked at a brightly illuminated 
window the eyes are suddenly closed, the image remains for a few instants, 

z 




506 


ON LIGHT. 


[ 540 - 

tliat is, a sash work is seen consisting of luminous panes surrounded by 
dark frames: after a few seconds the colours become interchanged, the 
same framework is now seen, but the frames are now bright, and the 
glasses are perfectly black ; this new appearance may again revert to its 
original appearance. 

The impression of colours remains as well as that of the form of ob¬ 
jects ; for if circles divided into sectors are painted in different colours, 
they become confounded, and give the sensation of the colour which 
would result from their mixture. Blue and yellow give green; yellow 
and red, orange; blue and red, violet; the seven colours of the spectrum 
give white, as shown in Newton’s disc (fig. 354). 

A great number of pieces of apparatus are founded on the persistence 
of sensation on the retina. Such are the thaumatrope , the phenakistoscope , 
Faraday's wheel , the kaleidophone. 

540. Accidental images,— A coloured object being placed upon a 
black ground, if it is steadily looked at for some time, the eye is soon 
tired, and the intensity of the colour enfeebled; if now the eyes are 
directed towards a white sheet, or to the ceiling, an image will be seen 
of the same shape as the object, but of a complementary colour (487) ; 
that is, such a one as united to that of the object would form white. 
For a green object the image will be red j if the object is yellow the 
image will be violet. 

Accidental colours are of longer duration in proportion as the object 
has been more brilliantly illuminated, and the object has been longer 
looked at. When a lighted candle has been looked at for some time, 
and the eyes are turned towards a dark part of the room, the appearance 
of the flame remains, but it gradually changes colour; it is first yellow, 
then it passes through orange to red, from red through violet to greenish 
blue, which is gradually feebler until it disappears. If the eye which 
has been looking at the light be turned towards a white wall, the colours 
follow almost the opposite direction: there is first a dark picture on a 
white ground, which gradually changes into blue, is then successivelv 
green and yellow, and ultimately cannot be distinguished from a white 
ground. 

The reason of this phenomenon is, doubtless, to be sought in the fac 
that the subsequent action of light on the retina is not of equal duratioi 
for all colours, and that the decrease in the intensity of the subsequent 
action does not follow the same law for all colours. 

541. Irradiation.— This is a phenomenon in virtue of which white 
objects or those of a very bright colour, when seen on a dark ground, 
appear larger than they really are. With a black body on a bright 
ground, the converse is the case. Irradiation arises from the fact that 
the impression produced on the retina extends beyond the outline of the 


IRRADIATION. 


507 


- 542 ] 

image. It bears the same relation to the space occupied by the image 
that the duration of the impression does to the time during which the 
image is seen. 

The effect of irradiation is very perceptible in the apparent magnitude 
of stars, which may thus appear much larger than they really are ; also 
in the appearance of the moon when two or three days old, the brightly 
illuminated crescent seeming to extend beyond the darker portion of the 
disc, and hold it in its grasp. 

Plateau, who has investigated this subject, finds that irradiation differs 
very much in different people, and even in the same person it differs on 
different days. He has also found that irradiation increases with the 
lustre of the object, and the length of time during which it is viewed. 
It manifests itself at all distances, diverging lenses increase it, condensing 
lenses diminish it. 

Accidental haloes are the colours which, instead of succeeding the im¬ 
pression of an object like accidental colours, appear round the object itself 
when it is looked at fixedly. The impression of the halo is the opposite 
to that of the object; if the object is bright the halo is dark, and vice 
versa. These appearances are best produced in the following manner. A 
white surface, such as a sheet of paper, is illuminated by coloured light, 
and a narrow opaque body held so as to cut off some of the coloured rays. 
In this manner a narrow shadow is obtained which is illuminated by the 
surrounding white daylight, and appears complementary to the coloured 
ground. If red glass is used, the shadow appears green, and blue when 
a yellow glass is used. 

The contrast of colours is a reciprocal action exerted between two 
adjacent colours, and in virtue of which to each one is added the com¬ 
plementary colour of the other. This contrast was observed by M. 
Chevreul, who has made it the subject of profound study. It is by the 
reciprocal influence of coloured shadows that the contrast of colour is 
explained. 

M. Chevreul has found that when red and yellow colours are adjacent, 
red acquires a violet and orange a yellow tint. If the experiment is made 
with red and blue, the former acquires a yellow, and the latter a green 
tint: with yellow and blue, yellow passes to orange, and blue towards 
indigo; and so on for a vast number of combinations. The importance 
of this phenomenon in its application to the manufacture of cloths, carpets, 
etc., may be readily conceived. 

542. The eye is not achromatic. —It had long been supposed that the 
human eye was perfectly achromatic, but this is clearly impossible, as all 
the refractions are made the same way, viz. towards the axis; moreover, 
the experiments of Wollaston, of Young, of Fraunhofer, and of Muller, 
have shown that it was not true in any absolute sense. 

z 2 


508 


ON LIGHT. 


T543- 

Fraunhofer showed that in a telescope with two lenses, a very fine 
wire placed inside the instrument in the focus of the object-glass is seen 
distinctly through the eye-piece, when the telescope is illuminated with 
red light; but it is invisible by violet light even when the eyepiece is in 
the same position. In order to see the wire again, the distance of the lenses 
must be diminished to a far greater extent than would correspond to the 
degree of refrangibility of violet light in glass. In this case, therefore, 
the effect must be due to a chromatic aberration in the eye. 

Muller, on looking at a white disc on a dark ground, found that the 
image is sharp when the eye is accommodated to the distance of the disc, 
that is, when the image forms on the retina; but he found that if the 
image is formed in front of or behind the retina, the disc appears sur¬ 
rounded by a very narrow blue edge. 

If a finger be held up in front of one eye (the other being closed) in 
such a manner as to allow the light to enter only one-half of the pupil, 
and, of course, obliquely, and the eye be then directed to any well- 
defined line of light, such as a slit in the shutter of a darkened room, or 
a strip of white paper on a black ground, this line of light will appear as 
a complete spectrum. 

Muller concluded from these experiments that the eye is sensibly 
achromatic as long as the image is received at the focal distance, or 
when it is accommodated to the distance of the object. The cause of this 
apparent achromatism cannot be exactly stated. It has generally been 
attributed to the tenuity of the luminous beams which pass through the 
pupillary aperture, and that these unequally refrangible rays, meeting 
the surfaces of the media of the eye almost at the normal incidence, are 
very little refracted, from which it follows that the chromatic aberration 
is imperceptible (496). 

As to the spherical aberration, we have already seen how this is cor¬ 
rected by the iris (525). The iris is in point of fact a diaphragm, which 
arrests the marginal rays, and only allows those to pass which are near 
the axis. 

543. Short sight and long sight: myopy and presbytism. —The 

most usual affections of the eye are myopy and presbytism, or short sight 
and bug sight. Short sight is the habitual accommodation of the eyes for 
a distance less than that of ordinary vision, so that persons affected in this 
way only see very near objects distinctly. The usual cause of short sight 
is a too great convexity of the cornea or of the crystalline; the eye being 
then too convergent, the focus, in place of forming on the retina, is formed 
in front, so that the image is indistinct. It may be remedied by means of 
diverging glasses, which in making the rays deviate from their common 
axis throw the focus farther back, and cause the image to be formed on 
the retina. 

The habitual contemplation of small objects, as when children are too 


SPECTACLES. 


509 


- 544 ] 

much accustomed, in reading and writing, to place the paper close to their 
eyes, or working with a microscope, may produce short sight. It is com¬ 
mon in the case of young people, but diminishes with age. 

Long sight is the contrary of short sight: the eye can see distant objects 
very well, but cannot distinguish those which are very near. The cause 
of long sight is that the eye is not sufficiently convergent, and hence 
the image of objects is formed beyond the retina: but if the objects are 
removed farther off, the image approaches the retina, and when they are 
at a suitable distance is exactly formed upon it, so that the object is 
clearly seen. 

Long sight is corrected by means of converging lenses. These glasses 
bring the rays together before their entrance into the eye, and, therefore, 
if the converging power is properly chosen, the image will be formed 
exactly on the retina. 

It is not many years since double convex lenses were alone used for 
long-sighted persons, and double concave for short-sighted persons. Wol¬ 
laston first proposed to replace these glasses by concavo-convex lenses, C 
and F (fig. 331), so placed that their curvature is in the same direction 
as that of the eye. By means of these glasses a much wider range is 
attained, and hence they have been called periscopic glasses. 

544. Eye-glasses. Spectacles. —The glasses commonly used by 
short or long sighted persons are known under the general name of eye¬ 
glasses or spectacles. Generally speaking, numbers are engraved on these 
glasses which express their focal length in inches. 

The number which a short or long sighted person ought to use may be 
calculated, knowing the distance of distinct vision. The formula 

.(i) 

a—p 

serves for long-sighted persons, where f being the number which ought 
to be taken, p is the distance of distinct vision in ordinary cases (about 
12 inches), and d the distance of distinct vision for the person affected by 
long sight. 

The above formula is obtained from the equation - — ^-= \ by sub- 

PPT 

stituting d for p'. In this case the formula (6) of article 482 is used, 
and not formula (5), because the image seen by spectacles being on the 
same side of the object in reference to the lens, the sign of p' ought to 
be the opposite of that of p , as in the case of virtual images from the 
paragraph already cited. 

For short-sighted persons,/is calculated by the formula - —^= —~ 
(482), which belongs to concave lenses, and which, replacing p f by cl, gives 






510 


ON LIGHT. 


[ 545 - 

To calculate, for instance, tlie number of a glass which a person ought 
to use in whom the distance of distinct vision is 36, knowing that the dis¬ 
tance of ordinary distinct vision is 12 inches. Makings =12 and d= 36 

in the above formula (1), we get f— X - 1 ^ = 18. 

545. Diplopy. — Diplopy is an affection of the eye which f causes 
objects to be seen double, that is, that two images are seen instead of one. 
Usually the two images are almost entirely superposed, and one of them 
is much more distinct than the other. Diplopy may be caused by the 
co-operation of two unequal eyes, but it may also affect a single eye. 
The latter case is, doubtless, due to some defect of conformation in the 
crystalline or other parts of the eye which produces a bifurcation of the 
luminous ray, and thus two images are formed on the retina instead of 
one. A single eye may also be affected with triplopy, but in this case the 
third image is exceedingly weak. 

546. Achromatopsy : Daltonism. — Achromatopsy , or colour disease , 
is a curious affection which renders us incapable of distinguishing 
colours, or at any rate certain colours. In some cases the insensibility 
is complete, while in others some colours can be very well distinguished. 
Persons affected in this manner can distinguish the outlines of bodies 
without difficulty, and they can also discriminate between light and 
shade, but they are unable to distinguish the different tints. 

D’Hombres-Firmas cites an instance of a person affected with achro¬ 
matopsy, who had painted in a room a landscape of which the ground, 
trees, houses, and men were all painted blue, and when asked why he 
had not given each its proper colour, he replied that he wished to 
assimilate the colour of his drawing to that of his furniture; now this 
was red. 

Achromatopsy is also sometimes called Daltonism, because Dalton, who 
has carefully described it, was so affected. 

547. Ophthalmoscope. —This instrument, as its name indicates, is 
designed for the examination of the eye, and was invented in 1851 by Prof. 
Helmholz. It consists:—1. Of a concave spherical reflector of glass or 
metal, M (figs. 406, 407), in the middle of which is a small hole about 
a sixth of an inch in diameter. The focal length of the reflector is from 
8 to 10 inches. 2. Of a converging achromatic lens, o, which is held in 
front of the eye of the patient. 3. Of several lenses, some convergent, 
others divergent, any one of which can be fixed in a frame behind the 
mirror so as to correct any given imperfection in the observer’s sight. If 
the mirror is of silvered glass, it is not necessary that it be pierced at 
the centre; it is sufficient that the silvering at the centre be removed. 

To make use of the ophthalmoscope, the patient is placed in a darkened 
room, and a lamp furnished with a screen put beside him, E. The screen 



OPHTHALMOSCOPE. 


511 


- 547 ] 

serves to shade the light from his head, and keep it in darkness. The 
observer A, holding in one hand the reflector, employs it to concentrate 
the light of the lamp near the eye B of the patient, and with his 
other hand holds the achromatic lens o in front of the eye. By this ar¬ 



rangement the hack of the eye is lighted up, and its structure can he 
clearly discerned. 

Fig. 407 shows how the image of the hack of the eye is produced, 
which the observer A sees on looking through the hole in the reflector. 
Let ab he the part of the retina on which the light is concentrated, 
pencils of rays proceeding from ab would form an inverted and aerial 
image of ab at a'b'. These pencils, however, on leaving the eye, pass 
through the lens o, and thus the image a"b /f is in fact formed, inverted, 
hut distinct, and in a position fit for vision. 



The great quantity of light concentrated hy the ophthalmoscope is 
apt ^o irritate painfully the eye of the patient. There are therefore in¬ 
terposed between the lamp and the reflector coloured glasses, to cut ofl 
the irritating rays, viz., the red, yellow, and violet rays. The glasses 
generally employed are stained green or cobalt-blue. 


























512 


ON LIGHT. 


[ 548 - 


CHAPTER VII. 

SOURCES OF LIGHT. PHOSPHORESCENCE. 

548. Various sources of light.— The various sources of light are 
the sun, the stars, heat, chemical combination, phosphorescence, elec¬ 
tricity, and meteoric phenomena. The last two sources will be treated 
under the articles Electricity and Meteorology. 

The origin of the light emitted by the sun and by the stars is un¬ 
known; it is assumed that the ignited envelope by which the sun is 
surrounded is gaseous, because the light of the sun, like that emitted 
from all gaseous bodies, gives no trace of polarisation in the polarising 
telescope (Chapter VIII.). 

As regards the light developed by heat, Pouillet has observed that 
bodies begin to be luminous in the dark at a temperature of 500° to 
600° ; above that the light is brighter in proportion as the temperature is 
higher. 

The luminous effects witnessed in many chemical combinations are 
due to the high temperatures produced. This is the case with the 
artificial lights used for illuminations; for as we have already seen, 
luminous flames are nothing more than gaseous matters containing 
solids heated to the point of incandescence. 

549. Phosphorescence: its sources. — Phosphorescence is the pro¬ 
perty which a large number of substances possess of emitting light when 
placed under certain conditions. 

M. Becquerel, who has studied this subject in a very comprehensive 
manner, and has arrived at some extremely remarkable results, refers 
the phenomena to five causes. 

i. Spontaneous phosphorescence in certain vegetables and animals; 
for instance, it is very intense in the glow-worm and in the lampyre, 
and the brightness of their light appears to depend on their will. In 
tropical climates the sea is often covered with a bright phosphorescent 
light due to some extremely small zoophytes. These animalculse emit 
a luminous matter so subtle that MM. Quoy and Gaimard, during a 
voyage under the equator, having placed two in a tumbler of water, the 
liquid immediately became luminous throughout its entire mass. 

ii. Phosphorescence by elevation of temperature. This is best seen in 
certain species of diamonds and in fluorspar, which, when heated to 300° 
or 400°, suddenly become luminous, emitting a bluish light. 

iii. Phosphorescence by mechanical effects , such as friction, percussion, 
cleavage, etc.; for example, when two crystals of quartz are rubbed 
against each other in darkness, or when a lump of sugar is broken. 


PHOSPHORESCENCE. 


513 


- 550 ] 


Phosphorescence by electricity , like that which results from the 
friction of mercury against the glass in a harometic tube, and especially 
from the electric sparks proceeding either from an ordinary electrical 
machine, or from a RuhmkorfPs coil. 

y. Phosphorescence by insolation or exposure to the sun. A large number 
of substances, after having been exposed to the action of solar light, or of 
the diffused light of the atmosphere, emit in darkness a phosphorescence, 
the colour and intensity of which depend on the nature and physical con¬ 
dition of these substances. It is this kind of phosphorescence which has 
been studied by M. Becquerel, an abstract of whose researches is given in 
the next paragraph. 

550. Phosphorescence by insolation.— This was first observed in 
1604 in Bolognese phosphorus (sulphide of barium), but M. Ed. Becquerel 
has also discovered it in a great number of substances. The sulphides 
of calcium and strontium are those which present it in the highest 
degree. When well prepared, after being exposed to the light, they are 
luminous for several hours in darkness. But as this phosphorescence 
takes place in vacuo as well as in a gaseous medium, it cannot be attri¬ 
buted to a chemical action, but rather to a temporary modification 
which the body undergoes from the action of light. 

After the substances above named, the best phosphorescents are the 
following, in the order in which they are placed : a large number of dia¬ 
monds (especially yellow), and most specimens of fluorspar; then 
arragonite, calcareous concretions, chalk, apatite, heavy spar, dried 
nitrate of calcium, and dried chloride of calcium, cyanide of calcium, a 
large number of strontium or barium compounds, magnesium and its car¬ 
bonate, etc. Besides these a large number of organic substances 
also become phosphorescent by insolation; for instance, dry paper, silk, 
cane-sugar, milk-sugar, amber, the teeth, etc. 

Becquerel finds that the different spectral rays are not equally well 
fitted to render substances phosphorescent. The maximum effect takes 
place in the violet rays, or even a little beyond ; while the light emitted 
by phosphorescent bodies generally corresponds to rays of a smaller re- 
frangibility than those of the light received by them, and giving rise to 
the action. 

The tint which phosphorescent bodies assume is very variable, and 
even in the same body it changes with the manner in which it is pre¬ 
pared. In strontium compounds green and blue tints predominate; and 
orange, yellow, and green tints in the sulphides of barium. 

The duration of phosphorescence varies also in different bodies. In the 
sulphides of calcium and strontium phosphorescence lasts as much as 
thirty hours ; with other substances it does not exceed a few seconds or 
even a fraction of a second. 

z 3 


514 


ON LIGHT. 


[ 550 - 

Phosphoroscope . In experimenting with bodies whose phosphorescence 
lasts a few minutes or even a few seconds, it is simply necessary to expose 
them to solar or diffused light for a short time, and then place them in 
darkness: their luminosity is very apparent, especially if care has pre¬ 
viously been taken to close the eyes for a few instants. But in the case 



Fig. 408. 

of bodies whose phosphorescence lasts only a very short time, this 
method is inadequate. M. Becquerel has invented a very ingenious ap¬ 
paratus, the phosphoroscope , by which bodies can be viewed immediately 
after being exposed to light: the interval which separates the insolation 
and observation can be made as small as possible, and measured with 
great precision. 










































PHOSPHORESCENCE. 


515 


- 550 ] 

This apparatus, which is constructed by M. Duboscq, consists of a 
closed cylindrical box, AB (fig. 408), of blackened metal; on the ends 
there are two apertures opposite each other which have the form of a 
circular sector. Only one of these, o, is seen in the figure. The box 
is fixed, but it is traversed in the centre by a movable axis, to which are 
fixed two circular screens, MM and PP, of blackened metal (fig. 409). 
Each of these screens is perforated by four apertures of the same shape 
as those in the box; but while the latter correspond to each other, the 
apertures of the screens alternate, so that the open parts of the one cor¬ 
respond to the closed parts of the other. The two screens, as already 
mentioned, are placed in the box, and fixed to the axis, which by means 
of a train of wheels, worked by a handle, can be made to turn with any 
velocity. 

In order to investigate the phosphorescence of any body by means of 
this instrument, the body is placed on a stirrup interposed between the 
two rotating screens. The light cannot pass at the same time through 
the opposite apertures of the sides A and B, because one of the closed 
parts of the screen MM, or of the screen PP, is always between them. 
So that when a body, a, is illuminated by light from the other side of 
the apparatus, it could not be seen by an observer looking at the aperture 
o, for then it would be masked by the screen PP. Accordingly, when an 
observer saw the body a, it would not be illuminated, as the light would 
be intercepted by the closed parts of the screen MM. The body a would 
alternately appear and disappear; it would disappear during the time of 
its being illuminated, and appear when it was no longer so. The time 
which elapses between the appearance and disappearance depends on 
the velocity of rotation of the screens. Suppose, for instance, that they 
made 150 turns in a second ; as one revolution of the screens is effected 
in of a second, there would be four appearances and four disappear¬ 
ances during that time. Hence the length of time elapsing between the 
time of illumination and of observation would be § of ^ of a second 
or 0 0008 of a second. 

Observations with the phosphoroscope are made in a dark chamber, 
the observer being on that side on which is the wheelwork. A ray of 
solar or of electric light is allowed to fall upon the substance «, and 
the screens being made to rotate more or less rapidly, the body a 
appears luminous by transparence in a continuous manner, when the in¬ 
terval between insolation and observation is less than the duration of the 
phosphorescence of the body. By experiments of this kind, Becquerel 
has found that substances which usually are not phosphorescent become 
so in the phosphoroscope; such, for instance, is Iceland spar. Uranium 
compounds present the most brilliant appearance in this apparatus; they 
emit a very bright luminosity when the observer can see them (H)03 or 


516 


ON LIGHT. 


[ 551 - 

0‘004 of a second after insolation. But a large number of bodies present 
no effect in tbe phosphoroscope j for instance, quartz, sulphur, phosphorus, 
metals, and liquids. 


CHAPTER VIII. 

DOUBLE REFRACTION. INTERFERENCE. POLARISATION. 

551. The undulatory theory of light. —It has been already stated 
(429) that the phenomenon of light is, with good reason, ascribed to 
undulations propagated through an exceedingly rare medium called the 
luminiferous ether, which is supposed to pervade all space, and to exist 
between the molecules of the ordinary forms of matter. In a word, it is 
held that light is due to the undulations of the ether, just as sound is 
due to undulations propagated through the air. In the latter case the 
undulations cause the drum of the ear to vibrate and produce the sensa¬ 
tion of sound. In the former case the undulations cause points of the 
retina to vibrate and produce the sensation of light. The two cases 
differ in this, that in the case of sound there is independent evidence of 
the existence and vibration of the medium (air) which propagates the 
undulation, whereas in the case of light the existence of the medium 
and its vibrations are assumed, because that supposition connects and 
explains in the most complete manner a long series of very various phe¬ 
nomena. There is, however, no independent evidence of the existence of 
the luminiferous ether. 

The analogy between the phenomena of sound and light is very close ; 
thus, the intensity of a sound is greater as the amplitude of the vibration 
of each particle of the air is greater, and the intensity of light is greater 
as the amplitude of the vibration of each particle of the ether is greater. 
Again, a sound is more acute as the length of each undulation producing 
the sound is less, or, which comes to the same thing, according as the 
number of vibrations per minute is greater. In like manner, the colour 
of light is different according to the length of the undulation producing 
the light; a red light is due to a comparatively long undulation, and 
corresponds to a deep sound, while a violet light is due to a short undu¬ 
lation, and corresponds to an acute sound. 

Although the length of the undulations cannot be observed directly, 
yet they can be inferred from certain phenomena with great exactness. 
The following table gives the length of the undulations corresponding 
to the light at the principal dark lines of the spectrum. The lengths are 
given in decimals of an inch. 




- 551 ] 


UNDULATORY THEORY OF LIGHT. 


517 


Dark 

Line. 

B 

C 

D 

E 

F 

G 

H 


Length of 
Undulation. 
0-0000271 
0-0000258 
0-0000244 
0-0000207 
0-0000191 
0-0000169 
00000155 


It will be remarked that the limits are very narrow, within which the 
lengths of the undulations of the ether must be comprised, if they are to 
be capable of producing the sensation of light. In this respect light is in 
marked contrast to sound. For the limits are very wide within which 
the lengths of the undulations of the air may be comprised when they 
produce the sensation of sound (215). 

The undulatory theory readily explains the colours of different bodies. 
According to that theory, certain bodies have the property of exciting 
undulations of different lengths, and thus producing light of given colours. 
White light or daylight results from the coexistence of undulations of all 
possible lengths. 

The colour of a body is due to the power it has of extinguishing cer¬ 
tain vibrations, and reflecting others j and the body appears of the colour 
produced by the coexistence of the reflected vibrations. A body appears 
white when it reflects all different vibrations in the proportion in which 
they are present in the spectrum : it appears black when it reflects light 
in such small quantities as not to affect the eye. A red body is one 
which has the property of reflecting in predominant strength those 
vibrations which produce the sensation of red. This is seen in the fact 
that, when a piece of red paper is held against the daylight, and the re¬ 
flected light is caught on a white wall, this also appears red. A piece of 
red paper in the red part of the spectrum appears of a brighter red, and 
a piece of blue paper held in the blue part appears of a brighter blue; 
while a red paper placed in the violet or blue part appears almost black. 
In the last case the red paper can only reflect red rays, while it extinguishes 
the blue rays, and as the blue of the spectrum is almost free from red, so 
little is reflected that the paper appears black. 

The undulatory theory likewise explains the colours of transparent 
bodies. Thus, a vibrating motion on reaching a body sets it in vibration. So 
also the vibrations of the luminiferous ether are communicated to the ether 
in a body, and setting it in motion produce light of different colours. When 
this motion is transmitted through any body, it is said to be transparent 
or translucent , according to the different degrees of strength with which 
this transmission is effected. In the opposite case it is said to be opaque. 









518 


ON LIGHT. 


[ 552 - 

Wlien light falls upon a transparent body, the body appears colourless 
if all the vibrations are transmitted in the proportion in which they exist 
in the spectrum. But if some of the vibrations are checked or ex¬ 
tinguished, the emergent light will be of the colour produced by the 
coexistence of the unchecked vibrations. Thus, when a piece of blue 
glass is held before the eye, the vibrations producing red and yellow are 
extinguished, and the colour is due to the emergent vibrations which 
produce blue light. 

The undulatory theory also accounts for the reflection and refraction 
of light, as well as other phenomena which are yet to be described. The 
explanation of the refraction of light is of so much importance that we 
shall devote to it the following article. 

552. Physical explanation of single refraction. —The explanation 
of this phenomenon by means of the undulatory theory of light presupposes 
that of the mode of propagation of a plane wave. Now, if a disturbance 
originated at any ‘point of the ether, it would be propagated as a spherical 
wave in all directions round that point with a uniform velocity. If, 
instead of a single point, we consider the front of a plane wave, it is 
evident that disturbances originate simultaneously at all points of that 
front, and that spherical waves proceed from each point with the same 
uniform velocity. Consequently all these spheres will at any subsequent 
instant be touched by a plane parallel to the original plane. The dis¬ 
turbances propagated from the points in the first position of the wave 
will mutually destroy each other except in the tangent plane \ conse¬ 
quently the wave advances as a plane wave, its successive positions 
being the successive positions of the tangent plane. If the wave moves 
in the medium with a velocity v , it will describe a space vt in a time t. 

Now let us conceive a plane wave moving through vacuum to meet 
at an angle I, the plane surface of an ordinary refracting medium, and 
suppose its velocity of propagation in vacuo to be v, and in the medium 
to be v'. It is obvious, that, if the wave begins to enter at a point A, part 
of the wave will advance within the medium, and part without; these 
parts being inclined to each other at a certain angle, and at any subsequent 
time, t, the perpendicular distances of these two parts from A will be vt 
and v't. Consequently, if R is the angle which the part of the wave 
within the medium makes with the surface of the medium, we shall 
have 

Sin I: sin R :: vt : v't :: v i v 

But a succession of parallel plane waves will give rise to a pencil of 
parallel rays at right angles to the waves ; consequently, with respect to 
any one of these rays, I and R are the angles of incidence and refraction. 
Therefore the ratio of the sines of those angles is constant and equals 
v : v which is the distinctive law of single refraction. 


DOUBLE REFRACTION. 


519 


- 554 ] 

Moreover, if n is the refractive index of the substance, v v' equals n, 
that is v equals v'/x. Now, under all circumstances, n is greater than 1, 
and therefore v is greater than v', a result which coincides with that ob¬ 
tained from experiment (436). 

DOUBLE REFRACTION. 

553. Double refraction. —It has been already stated (460) that a 
large number of crystals possess the property of double refraction, in 
virtue of which a single incident ray in passing through any one of them 
is divided into two, or undergoes bifurcation. Whence it follows that, 
when an object is seen through one of these crystals, it appears double. 
The fact of the existence of double refraction in Iceland spar was first 
stated by Bartholin in 1669, but the law of double refraction was first 
enunciated exactly by Huyghens in his treatise on light written in 1678, 
and published in 1690. 

Crystals which possess this peculiarity are said to be double refracting. 
It is found to a greater or less extent in all crystals which do not belong 
to the cubical system. Bodies which crystallise in this system, and those, 
which, like glass, are destitute of crystallisation, have no double refrac¬ 
tion. The property can, however, be imparted to them when they are 
unequally compressed, or when they are cooled quickly after having been 
heated, in which state glass is said to be unannealed. Of all substances, 
that which possesses it most remarkably is Iceland spar or carbonate of 
calcium. In many substances the power of double refraction can hardly 
be proved to exist directly by the bifurcation of an incident ray; but its 
existence is shown indirectly by their being able to ‘depolarise 1 light. 

Fresnel has explained double refraction by assuming that the ether in 
double refracting bodies is not equally elastic in all directions; from 
which it follows that the vibrations in certain directions at right angles 
to each other are transmitted with unequal velocities; these directions 
being dependent on the constitution of the crystal. This hypothesis is 
confirmed by the property which glass acquires of becoming double 
refracting by being unannealed and by pressure. 

554. Uniaxial crystals.— In all double refracting crystals there is 
one direction, and in some a second direction possessing the following 
property. When a point is looked at through the crystal in this parti¬ 
cular direction, it does not appear double. The lines fixing these directions 
are called optic axes ; and sometimes, though not very properly, axes of 
double refraction. A crystal is called uniaxial when it has one optic axis, 
that is to say, when there is one direction within the crystal along which 
a ray of light can proceed without bifurcation. When a crystal has two 
such axes, it is called a biaxial crystal. 


520 


ON LIGHT. 


[ 555 - 

The uniaxial crystals most frequently used in optical instruments are 
Iceland spar, quartz, and tourmaline. Iceland spar crystallises in rhom- 

bohedra, whose faces form with each 
other angles of 105° 5' or 74° 55'. It 
has eight solid angles (see fig. 410). 
Of these two, situated at the extremi¬ 
ties of one of the diagonals, are seve¬ 
rally contained by three obtuse angles. 
A line drawn within one of these two 
angles in such a manner as to be equally 
inclined to the three edges containing 
the angle is called the axis of the 
crystal. If all the edges of the crystal were equal, the axis of the crystal 
would coincide with the diagonal, ah. 

Brewster has shown that in all uniaxial crystals the optic axis coin¬ 
cides with the axis of crystallisation. 

The principal plane with reference to a point of any face of a crystal, 
whether natural or artificial, is a plane drawn through the point at right 
angles to the face and parallel to the optic axis. If in fig. 410 we sup¬ 
pose the edges of the rhombohedron to be equal, the diagonal plane 
abed contains the optic axis ( ab ), and is at right angles to the faces aedf 
and chbg ; consequently it is parallel to the principal plane at any point 
of either of those two faces. For this reason acbd is often called the 
principal plane with respect to those faces. 

555. Ordinary and extraordinary ray. —Of the two rays into which 
an incident ray is divided on entering a uniaxial crystal, one is called 
the ordinary and the other the extraordinary ray. The ordinary ray 
follows the laws of single refraction, that is with respect to that ray the 
sine of the angle of incidence bears a constant ratio to the sine of the 
angle of refraction, and the plane of incidence coincides with the plane of 
refraction. Except in particular positions the extraordinary ray follows 
neither of these laws. The images corresponding to the ordinary and 
extraordinary rays are called the ordinary and extraordinary images 
respectively. 

If a transparent specimen of Iceland spar be placed over a dot of ink, 
on a sheet of white paper, the two images will be seen. One of them, 
the ordinary image, will seem slightly nearer to the eye than the other, 
the extraordinary image. Suppose the 'spectator to view the dot in a 
direction at right angles to the paper, then, if the crystal, with the face 
still on the paper, be turned round, the ordinary image will continue 
fixed, and the extraordinary image will describe a circle round it, the 
line joining them being always in the direction of the shorter diagonal 
of the face of the crystal, supposing its edges to be of equal length. In 



Fig. 410. 



DOUBLE REFRACTION. 


- 557 ] 


52J 


this case it is found that the angle between the ordinary and extra¬ 
ordinary ray is 6° 12'. 

556. The laws of double refraction in a uniaxial crystal. —These 
phenomena are found to obey the following laws:— 

i. Whatever be the plane of incidence, the ordinary ray always obeys 
the two general laws of single refraction (461). The refractive index for 
the ordinary ray is called the ordinary refractive index. 

ii. In every section perpendicular to the optic axis the extraordinary 
ray also follows the laws of single refraction. Consequently in this plane 
the extraordinary ray has a constant refractive index, which is called the 
extraordinary refractive index. 

iii. In every principal section the extraordinary ray follows the second 
law only of single refraction, that is, the planes of incidence and refrac¬ 
tion coincide, but the ratio of the sines of the angles of incidence and 
refraction is not constant. 

iv. The velocities of light along the rays are unequal. It can be 
shown that the difference between the squares of the reciprocals of the 
velocities along the ordinary and extraordinary rays is proportional to the 
square of the sine of the angle between the latter ray and the axis of 
the crystal. 

There is an important difference between the velocity of the ray and 
the velocity of the corresponding plane wave. If the velocities of the 
plane waves corresponding to the ordinary and extraordinary rays are 
considered, the difference between the squares of these velocities is 
proportional to the square of the sine of the angle between the axis 
of the crystal and the normal to that plane wave which corresponds 
to the extraordinary ray. The normal and the ray do not generally 
coincide. 

Huyghens gave a very remarkable geometrical construction, by means 
of which the directions of the refracted rays can be determined when the 
directions of the incident ray and of the axis are known relatively to the 
face of the crystal. This construction was not generally accepted by 
physicists until Wollaston and subsequently Malus showed its truth by 
numerous exact measurements. 

557. Positive and negative uniaxial crystal. —The term extra¬ 
ordinary refractive index has been defined in the last article. For the 
same crystal its magnitude always differs from that of the ordinary refrac¬ 
tive index, for example, in Iceland spar the ordinary refractive index is 
1*654, while the extraordinary refractive index is 1*483. In this case the 
ordinary index exceeds the extraordinary index. When this is the case, 
the crystal is said to be negative. On the other hand, when the extraor¬ 
dinary index exceeds the ordinary index, the crystal is said to be positive. 
The list on the following page gives the names of some of the principal 
uniaxial crystals:— 


522 


ON LIGHT. 


[ 558 - 


Negative Uniaxial Crystals. 


Iceland spar 

Emerald 

Spathose iron 

Apatite 

Tourmaline 

Pyromorphite 

Sapphire 

Ferrocyanide of potassium 

Ruby 

Nitrate of sodium 

Positive Uniaxial 

Crystals. 

Zircon 

Ice 

Quartz 

Titanite 

Apophyllite 

Boracite 


558. Double refraction in biaxial crystals. —A large number of 
crystals, including all those belonging to the trimetric , the monoclinic , and 
the triclinic systems, possess two optic axes , in other words, in each of these 
crystals there are two directions along which a ray of light passes with¬ 
out bifurcation. A line bisecting the acute angle between the optic axes 
is called the medial line; one that bisects the obtuse angle is called the 
supplementary line. It has been found that the medial and supplemen¬ 
tary lines and a third line at right angles to both are closely related to 
the fundamental form of the crystal to which the optic axes belong. 
The acute angle between the optic axes is different in different crystals. 
The following table gives the magnitude of this angle in the case of cer¬ 


tain crystals:— 

Nitre.5° 20' Brazilian topaz . . 49° 50' 

Strontianite. 6 56 Sugar.50 0 

Arragonite.18 18 Selenite.60 0 

Anhydrite. 28 7 Kyanite.81 48 

Heavy spar. 37 42 Epidote.84 19 

Mica. 45 0 Sulphate of iron . . 90 0 


When a ray of light enters a biaxial crystal, and passes in any direction 
not coinciding with an optic axis, it undergoes bifurcation j in this case, 
however, neither ray conforms to the laws of single refraction, but both 
are extraordinary rays. To this general statement the following excep¬ 
tion must be made. In a section of a crystal at right angles to the medial 
line one ray follows the laws of ordinary refraction, and in a section at 
right angles to the supplementary line the other ray follows the laws of 
ordinary refraction. 


INTERFERENCE AND DIFFRACTION. 

559. Interference of light.— The name interference is given to the 
mutual action which two luminous rays exert upon each other when they 
are emitted from two neighbouring sources, and meet each other under a 













INTERFERENCE OF LIGHT. 


523 


- 559 ] 

very small angle. This action may be observed by means of the following 
experiment. In the shutter of a dark room two very small apertures 
are made, of the same diameter, at a very slight distance from each 
other. The apertures are closed by pieces of coloured glass, red for 
example, by which two pencils of homogeneous light are obtained. These 
two pencils form two divergent luminous cones, which meet at a certain 
distance; they are received on a white screen a little beyond the place at 
which they meet, and in the segment common to the two discs which form 
upon this screen some very well defined alternations of red and black 
bands are seen. If one of the two apertures be closed, the fringes dis¬ 
appear, and are replaced by an almost uniform red tint. From the fact 
that the dark fringes disappear when one of the beams is intercepted, it 
is concluded that they arise from the interference of the two pencils which 
cross obliquely. 

This experiment was first made by Grimaldi, but was modified by 
Young. Grimaldi had drawn from it the conclusion that light added to 
light produced darkness. The full importance of this principle remained 
for a long time unrecognised, until these inquiries were resumed by 
Young and Fresnel, of whom the latter, by a modification of Grimaldi’s 
experiment, rendered it an experimentum cruets of the truth of the un- 
dulatory hypothesis. 



In Grimaldi’s experiment diffraction (560) takes place; for the luminous 
rays pass by the edge of the aperture. In Fresnel’s experiment the two 
pencils interfere without the possibility of diffraction. 

Two plane mirrors M and N (fig. 411), of metal are arranged close to 
each other, so as to form a very obtuse angle, MON, which must indeed 
be very little less than 180°. 

A pencil of red light, which passes into the dark chamber, is brought to 
a point by means of a lens, L, in front of the mirrors, and falls partly on 
one and partly on the other. After reflection, the luminous rays which 

















524 


ON LIGHT. 


[ 559 - 

fall on OM proceed as if they originated in the image formed by OM of 
the luminous point at the focus of L. In like manner, those which fall 
on ON proceed as if they originated in the image of the luminous point 
formed by ON. A little consideration will show that these two images 
are very near to one another. Now suppose the reflected rays to fall on 
a screen placed nearly at right angles to their direction, and therefore at 
right angles to the plane of the paper. Then two pencils of rays fall on 
the screen proceeding as if from two neighbouring points. Consequently 
every point of the screen which receives light from both pencils is illu¬ 
minated by two rays, viz. one from the image formed by OM, and one from 
the image formed by ON. Now the combined action of these two pencils 
is to form a series of parallel bands alternately light and dark. This is the 
fundamental phenomenon of interference, and that it results from the joint 
action of the two pencils is plain, since, if the light which falls upon either 
of the mirrors be cut off, the dark bands disappear. 

This remarkable fact is explained in the most satisfactory manner by 
the undulatory theory of light. The explanation exactly resembles that 
already given of the formation of nodes and loops by the combined action 
of two aerial waves (230); the only difference being that in that case 
the vibrating particles were supposed to be particles of air, whereas, in 
the present case, the vibrating particles are supposed to be those of the 
luminiferous ether. Consider any point A on the screen, and first let us 
suppose the distances of A from the two images above named to be equal. 
Then the undulations which reach A will always be in the same phase , and 
the particle of ether at A will vibrate as if the light came from one source; 
the amplitude of the vibration, however, will be increased in exactly the 
same manner as happens at a loop or ventral point; consequently at A 
the intensity of the light will be increased. And the same will be true 
for all points on the screen, such that the difference between their dis¬ 
tances from the two images equals the length of one , two, three , etc., 
undulations. If, on the other hand, the distances of A from the two 
images differ by the length of half an undulation then the two waves 
would reach A in exactly opposite phases. Consequently, whatever ve¬ 
locity would be communicated at any instant to a particle of ether by the 
one undulation, an exactly equal and opposite velocity would be commu¬ 
nicated by the other undulation, and the particle would be permanently 
at rest, or there would be darkness at that point; this result being pro¬ 
duced in a manner precisely resembling the formation of a nodal point 
already explained. The same will be true for all positions of A, such 
that the differences between its distances from the two images equal three 
halves, or five halves, or seven halves, etc., of an undulation. Accord¬ 
ingly, there will be on the screen a succession of alternations of light and 
dark points, or rather lines—for what is true of points in the plane of the 


DIFFRACTION OF LIGHT. 


525 


- 560 ] 

paper (fig. 411) will be equally true of points on the screen which is 
supposed to be at right angles to the plane of the paper. Between the 
light and dark lines the intensity of the light will vary, increasing gra¬ 
dually from darkness to its greatest intensity, and then decreasing to the 
second dark line, and so on. 

If instead of red light any other coloured light were used, for example 
violet light, an exactly similar phenomenon would be produced, but the 
distance from one dark line to another would be different. If white light 
were used, each separate colour tends to produce a different set of dark 
lines. Now these sets being superimposed on each other, and not coin¬ 
ciding, the dark lines due to one colour are illuminated by other colours, 
and instead of dark lines a succession of coloured bands is produced. 
The number of coloured bands produced by white light is much smaller 
than the number of dark lines produced by a homogeneous light; since 
at a small distance from the middle band the various colours are com¬ 
pletely blended, and a uniform white light produced. 

560. Diffraction and fringes. —Diffraction is a modification which 
light undergoes when it passes the edge of a body, or when it traverses 
a small aperture; a modification in virtue of which the luminous rays 
appear to become bent, and to penetrate into the shadow. 

This phenomenon may be observed in the following manner: A beam 
of solar light is allowed to pass through a very small aperture in the 



Fig. 412. 


shutter of a dark room, where it is received on a condensing lens, L (fig. 
412),with a short focal length. A red glass is placed in the aperture 
so as only to allow red light to pass. An opaque screen, e, with a sharp 
edge, is placed behind the lens beyond its focus, and intercepts one por¬ 
tion of the luminous cone, while the other is projected on the screen b, 
of which B represents a front view. The following phenomena are now 
seen: Within the geometrical shadow, the limit of which is represented 
by the line ab, a faint light is seen, which gradually fades in proportion 
as it is farther from the limits of the shadow. In that part of the screen 
which, being above the line ab , might be expected to be uniformly illu¬ 
minated, a series of alternate dark and light bands or fringes are seen 
parallel to the line of shadow, which gradually become more indistinct 
and ultimately disappear. The limits between the light and dark fringes 















ON LIGHT. 


526 


[ 561 - 


are not quite sharp lines ; there are parts of maximum and minimum 
intensity which gradually fade off into each other. 

All the colours of the spectrum give rise to the same phenomenon, hut 
the fringes are broader in proportion as the light is less refrangible. 
Thus, with red light they are broader than with green, and with green 
than with violet. Hence, with white light, which is composed of 
different colours, the dark spaces of one tint overlap the light spaces of 
another, and thus a series of prismatic colours will be produced. 

If, instead of placing the edge of an opaque body between the light 
and the screen, a very narrow body be interposed, such as a hair or a 
fine metallic wire, the phenomena will be different. Outside the space 
corresponding to the geometrical shadow, there is a series of fringes, as 
in the former case. But within the shadow also there is a series of 
alternate light and dark bands. They are called interior fringes, and 
are much narrower and more numerous than the external fringes. 

When a small opaque circular disc is interposed, its shadow on the 
screen shows in the middle a bright spot surrounded by a series of 
coloured concentric rings ; the bright spot is of various colours according 
to the relative positions of the disc and screen. The haloes some¬ 
times seen round the sun and moon belong to this class of pheno¬ 
mena. They are due, as Fraunhofer has shown, to the diffraction of 
light by small globules of fog in the atmosphere. Fraunhofer has even 
given a method of estimating the mean diameter of these globules from 
the dimensions of the haloes. A beautiful phenomenon of the same kind 
is produced by looking at a flame through lycopodium powder strewed 
on glass. 

561. Gratings. —Phenomena of diffraction of another class are pro¬ 
duced by allowing the pencil of light from the luminous point to 
traverse an aperture in an opaque screen. The diffracted light may 
be received on a sheet of white paper, but the images are much better 
seen through a small telescope placed behind the aperture. If the aper¬ 
ture is very small, the telescope may be dispensed -,.ith, and the figure 
may be viewed by placing the aperture before the eye.' 

Some of the simpler apertures, such as straight lines, triangles, squares 
or circles, may be cut out of tinfoil pasted on glass. Gratings may be 
obtained either by a series of fine equidistant wires, or by careful ruling 
on a piece of smoked glass ; and apertures of any form may be produced 
with great accuracy by taking on glass a collodion picture of a sheet of 
paper on which the required forms are drawn in black. 

Looking through any of these apertures, we see the luminous point 
surrounded with coloured spectra of very various forms, and of great 
beauty. 

The beautiful colours seen on looking through a bird’s feather at a 


-5611 


GRATINGS. 


527 


distant source of light, and the colours of striated surfaces, such as 
mother-of-pearl, are due to a similar cause. 

The whole of these phenomena are in exact accordance with the 
undulatory theory, but the explanation is in many cases difficult. 

The case of gratings is more simple and important than the others, 
and therefore shall be considered in detail. 

If a series of fine equidistant lines ruled on glass, or a series of fine 
equidistant wires, be placed before the eye or before a telescope, and a 
distant point or line of light be viewed through the grating thus formed, 
we see on each side of the bright point or line a series of equidistant 
spectra, all having their violet ends directed inwards. 

To explain these appearances, let us suppose the telescope removed, 
and the spectra received on a distant screen. 


C 

-p 

p 

- -0 

p 

-p 

D 

Fig. 413. 



In figure 413 let 0 represent the luminous point, AB the grating, and 
CD the distant screen. 

We conceive of the effect on the screen of the light transmitted 
through the grating in the following manner. The ether in the trans¬ 
parent intervals of the grating becomes simultaneously disturbed and 
kept in vibration by the light from 0. The disturbance of each point 
in those intervals becomes the origin of a spherical wave, as in art. 552, 
and the effect produced at any point of the screen is the sum of the effects 
due to the action of the waves thus proceeding from all the transparent 
intervals. Now, at the point o, which is equidistant from all parts of 
the grating, all these waves will arrive in the same phase, and will, 
therefore, reinforce each other, and give a bright point. 

At other points, pp, on each side of o, whose distance from successive 
intervals of the grating differ by one wave length, or any whole number 



528 


ON LIGHT. 


[ 562 - 

of wave lengths, the vibrations will also arrive in the same phase, and 
produce brightness. But at intermediate points the vibrations will arrive 
from different points of the grating in all phases, and will, therefore, 
neutralise each other and give rise to darkness. 

The fact that the spectra on each side of the central one are coloured 
arises from the wave lengths being different for different colours; and 
the measurement of the distances between the spectra corresponding to 
different colours affords the most accurate method of determining these 
wave lengths. 

562. Colours of thin plates. Newton’s rings.— All transparent 
bodies, solids, liquids, or gases, when in sufficiently fine laminae, appear 
coloured with very bright tints, especially by reflection. Crystals which 
cleave easily, and can be attained in very thin plates, such as mica and 
selenite, show this phenomenon, which is also well seen in soap bubbles. 
A drop of oil spread rapidly over a large sheet of water exhibits all the 
colours of the spectra in a constant order. A soap bubble appears white 
at first, but in proportion as it is blown out, brilliant iridescent colours 
appear, especially at the top, where it is thinnest. These colours are ar¬ 
ranged in horizontal zones around the summit, which appears black when 
there is not thickness enough to reflect light, and the bubble then sud¬ 
denly bursts. 

Newton, who first studied the phenomena of the coloured rings in 
soap bubbles, wishing to investigate the relation between the thickness 
of the thin plate, the colour of the rings, and their extent, produced 



them by means of a layer of air interposed between two glasses, one plane 
and the other convex, and with a very long focus. The two surfaces 
being cleaned and exposed in ordinary light in front of a window, so 
as to reflect light, there is seen at the point of contact a black spot 
surrounded by six or seven coloured rings, the tints of which become 
gradually less strong. If the glasses are viewed by transmitted light, 
the centre of the rings is white, and each of the colours is exactly 
complementary of that of the rings by reflection. 

With homogeneous light, red for example, the rings are successively 
black and red ; the diameters of corresponding rings are less as the colour 
is more refrangible, but with white light the rings are of the different 
colours of the spectrum, which arises from the fact that, as the rings of 





POLARISATION OF LIGHT. 


529 


- 564 ] 

the different simple colours have different diameters, they are not exactly 
superposed, but are more or less separated. 

If the focal length of the lens is from three to four yards, the rings 
can be seen with the naked eye; but if the length is less, the rings 
must be looked at with a lens. 

563. Explanation of Newton’s rings.— Newton’s rings, and all 
phenomena of thin plates, are simple cases of interference. 

In fig. 414, let MNOP represent a thin plate of a transparent body, 
on which a pencil of parallel rays of homo¬ 
geneous light, ab, impinges; this will be 
partially reflected in the direction be , and 
partially refracted towards d. But the re¬ 
fracted ray will undergo a second reflection 
at the surface, OP; the reflected ray will 
emerge at e in the same direction as the pencil 
of light reflected at the first surface ; and con¬ 
sequently the two pencils be and ef will 
destroy or augment each other’s effect accord¬ 
ing as they are in the same or different 
phases. We shall thus have an effect pro¬ 
duced similar to that of the fringes. 

It is usual to speak of the successive rings as the first, second, third, 
etc. By the first ring is understood that of least diameter. Newton de¬ 
termined by calculation the thickness of the layer of air at the points 
where the successive rings were formed, and found that the thicknesses 
corresponding to the successive dark rings are proportional to the numbers 
0, 2, 4, 6,., while for the bright rings the thicknesses were pro¬ 
portional to 1, 3, 5.He found that for the first bright ring the 

thickness was Yriooo °f an inch, when the light used was the brightest 
part of the spectrum, that is the part on the confines of the orange and yel¬ 
low rays. He further found that for rings of the same order the dia¬ 
meter is greater as the refrangibility of the light producing it is less. 



Fig. 414. 


POLARISATION OF LIGHT. 

564. Polarisation by double refraction.— It has been already seen 
that, when a ray of light passes through a crystal of Iceland spar, it 
becomes divided into two rays of equal intensity, viz. the ordinary ray, 
and the extraordinary ray. These rays are found to possess other pecu¬ 
liarities, which are expressed by saying that they are polarised, namely, the 
ordinary ray in a principal plane, and the extraordinary ray in a plane at 
right angles to a principal plane. The phenomena which are thus desig¬ 
nated may be described as follows :—Suppose a ray of light which has 

A A 





530 


ON LIGHT. 


[ 565 - 

undergone ordinary refraction in a crystal of Iceland spar to be allowed 
to pass through a second crystal, it will generally be divided into two 
rays, namely, one ordinary, and the other extraordinary, but of unequal 
intensities. If the second crystal be turned round until the two principal 
planes coincide, that is, until the crystals are in similar or in opposite 
positions, then the extraordinary ray disappears, and the ordinary ray is 
at its greatest intensity; if the second crystal is turned further round, 
the extraordinary ray reappears, and increases in intensity as the angle 
increases, while the ordinary ray diminishes in intensity until the 
principal planes are at right angles to each other, when the extraordinary 
ray is at its greatest intensity, and the ordinary ray vanishes. These are 
the phenomena produced when the ray which experienced ordinary re¬ 
fraction in the first crystal passes through the second. If the ray which 
has experienced extraordinary refraction in the first crystal is allowed to 
pass through the second crystal, the phenomena are similar to those above 
described, but when the principal planes 'coincide, an extraordinary ray 
alone emerges from the second crystal, and when the planes are at right 
angles, an ordinary ray alone emerges. 

These phenomena can also be described thus : Let 0 and E denote the 
ordinary and. extraordinary rays produced by the first crystal. When 0 
enters the second crystal, it generally gives rise to two rays, an ordinary 
(0o), and an extraordinary (Oe), of unequal intensities. When E enters 
the second crystal, it likewise gives rise to two rays, viz. an ordinary (Eo), ; 
and an extraordinary (Ee), of unequal intensities; the intensities varying I 
with the angle between the principal planes of the crystals. When the j 
principal planes coincide, only two rays, viz. 0o and Ee, emerge from 
the second crystal, and when the planes are at right angles, only two 
rays, viz. Oe and Eo, emerge from the second crystal. Since 0 gives rise 
to an ordinary ray when the principal planes are parallel, and E gives 
rise to an ordinary ray when they are at right angles, it is manifest that 0 
is related to the principal plane in the same manner that E is related 
to a plane at right angles to a principal plane. 

This phenomenon, which is produced by all double refracting crystals, 
was observed by Huyghens in Iceland spar, and in consequence of a 
suggestion of Newton’s was afterwards called polarisation. It remained, 
however, an isolated fact until the discovery of polarisation by reflec- 
tion recalled the attention of physicists to the subject. The latter dis¬ 
covery was made by Malus in 1808. 

565. Polarisation by reflection.— When a ray of light, ad (fig. 415),' 
falls on a polished unsilvered glass surface, fghi, inclined to it at an 
angle of 35° 25', it is reflected, and the reflected ray is polarised in the! 
plane of reflection. If it were transmitted through a crystal of Iceland 
spar, it would be transmitted without bifurcation, and undergo an ordinary 
refraction, when the principal plane coincides with the plane of reflection; 



POLARISATION OF LIGHT. 


-566] 


531 


it would also be transmitted without bifurcation, but undergo extraordi¬ 
nary refraction, when the principal plane is 
at right angles to the plane of reflection ; 
in other positions of the crystal it would 
give rise to an ordinary and extraordinary 
ray of different intensities, according to 
the angle between the plane of reflection 
and the principal plane of the crystal. 

The peculiar property which the light has 
acquired by reflection at the surface fghi 
can also be exhibited as follows. Let 
the polarised ray be be received at c on a 
second surface of unsilvered glass, at the 
same angle, viz. 35° 25'. If the surfaces are 
parallel, the ray is reflected; but if the a 
second plate is caused to turn round cb f 
the intensity of the reflected ray con- Pig, 415 , 

tinually diminishes, and when the glass 

surfaces are at right angles to each other, no light is reflected. By 
continuing to turn the upper mirror, the intensity of the reflected ray 
gradually increases, and attains a maximum value when the surfaces are 
again parallel. 

The above statement will serve to describe the phenomenon of pola¬ 
risation by reflection so far as the principles are concerned; the appa¬ 
ratus best adapted for exhibiting the phenomenon will be described 
further on. 

566. Angle of polarisation. —The polarising angle of a substance is 
the angle which the incident ray must make with the normal to a plane 
polished surface of that substance in order that the polarisation be com¬ 
plete. For glass this angle is 54° 35', and if in the preceding experiment 
the lower mirror were inclined at any other angle than this, the light 
would not be completely polarised in any position ; this would be shown 
by its being partially reflected from the upper surface in all positions. 
Such light is said to be partially polarised. The polarising angle for 
water is 52° 45'; for quartz, 57° 32'; for diamond, 68 °; and it is 56° 30' 
for obsidian, a kind of volcanic glass which is often used in these 
experiments. 

Light which is reflected from the surface of water, from a slate roof, 
from a polished table, is all more or less polarised. The ordinary light of 
the atmosphere is frequently polarised, especially in the earlier and later 
periods of the day, when the solar rays fall obliquely on the atmosphere. 
Almost all reflecting surfaces may be used as polarising mirrors. Metallic 
surfaces form, however, an important exception. 

a a 2 



532 ON LIGHT. [ 567 - 

Brewster has discovered the following remarkably simple law in refer¬ 
ence to the polarising angle. 

The polarising angle of a substance is that angle of incidence for which the 
reflected polarised ray is at right angles to the 
refracted ray. 

■ Thus, in fig. 416, if si is the incident, ir 
the refracted, and if the reflected ray, the 
polarisation is most complete when fi is at 
right angles to ir. 

The plane of polarisation is the plane of 
reflection in which light becomes polarised; 
it coincides with the plane of incidence, 
and, therefore, contains the polarising 
angle. 

567. Polarisation by single refrac¬ 
tion. —When an unpolarised luminous ray falls upon a glass plate 
placed at the polarising angle, one part is reflected ; the other part? 
in passing through the glass, becomes refracted, and the transmitted 
light is now found to be partially polarised. If the light which has 
passed through one plate, and whose polarisation is very feeble, be 
transmitted through a second plate parallel to the first, the effects 
become more marked, and by ten or twelve plates are tolerably com¬ 
plete. A bundle of such plates, for which the best material is the 
glass used for covering microscopic objects, fitted in a tube at the 
polarising angle, is frequently used for examining or producing polarised 
light. 

If a ray of light fall at any angle on a transparent medium, the same 
holds good with a slight modification. In fact, part of the light is reflected 
and part refracted, and both are found to be partially polarised, equal 
quantities in each being polarised, and their planes of polarisation being at 
right angles to each other. It is, of course, to be understood that the po¬ 
larised portion of the reflected light is polarised in the plane of reflection, 
which is likewise the plane of refraction. 

568. Polarising instruments. —Every instrument for investigating 
the properties of polarised light consists essentially of two parts, one for 
polarising the light, the other for ascertaining or exhibiting the fact of 
light having undergone polarisation. The former part is called the pola- 
riser, the latter the analyser. Thus in art. 564 the crystal producing the 
first refraction is the polariser, that producing the second refraction is the 
analyser. In art. 565, the mirror at which the first reflection takes place 
is the polariser, that at which the second reflection takes place is the 
analyser. Some of the most convenient means of producing polarised light 
will now be described, and it will be remarked that any instrument that 



Fig. 416. 



POLARISATION OF LIGHT. 


533 


- 569 ] 

can be used as a polariser can also be used as an analyser. The experi¬ 
menter has therefore considerable liberty of selection. 

569. TCorremberg’s apparatus.— The most simple, but complete, 
instrument for polarising light is that invented by M. Norremberg. 
It may be used for repeating most of the experiments on polarised 
light. 



Fig. 417. 


It consists of two brasss rods b and d (fig. 417), which support an un¬ 
silvered mirror, n, of ordinary glass, moveable about a horizontal axis. 
A small graduated circle indicates the angle of inclination of the mirror. 
Between the feet of the two columns there is a silvered glass, p, which 
is fixed and horizontal. At the upper end of the columns there is a gra¬ 
duated plate, i, in which a circular disc, o, rotates. This disc, in which 
there is a square aperture, supports a mirror of black glass, m, which is 
inclined to the vertical at the polarising angle. An annular disc, k, can be 
fixed at different heights on the columns by means of a screw. A second 











534 on light. [ 570 - 

ring', a, may be moved around the axis. It supports a black screen, in the 
centre of which there is a circular aperture. 

When the mirror n makes with the vertical an angle of 35° 25', which 
is the complement of the polarising angle for glass, the luminous rays, 
Sw, which meet the mirror at this angle, become polarised, and are re¬ 
flected in the direction np towards the mirror p, which sends them in the 
direction pnr. After having passed through the glass n, the polarised ray 
falls upon the blackened glass m under an angle of 35° 25', because the 
mirror makes exactly the same angle with the vertical. But if the disc o , 
to which the mirror m is fixed, be turned horizontally, the intensity of 
the light reflected from the upper mirror gradually diminishes, and totally 
disappears when it has been moved through 90°. This position is that 
represented in the diagram : the plane of incidence on the upper mirror is 
then perpendicular to the plane of incidence, S np, on the mirror n. When 
the upper mirror is again turned, the intensity of the light increases until 
it has passed through 180°, when it again reaches a maximum. The mir¬ 
rors m and n are then parallel. The same phenomena are repeated as the 
mirror m continues to be turned in the same direction, until it again comes 
into its original position. The intensity of the reflected being greatest 
when the mirrors are parallel, and being reduced to zero when they are at 
right angles. If the mirror w is at a greater or less angle than 35° 25', 
a certain quantity of light is reflected in all positions of the plane of inci¬ 
dence. 

570. Tourmaline. —The primary form of this crystal is a regular 
hexagonal prism. Tourmaline, as already stated, is a negative uniaxial 
crystal, and its optic axis coincides with the axis of the prism. For op¬ 
tical purposes a plate is cut from it parallel to the axis. When a ray of 
light passes through such a plate, an ordinary ray and an extraordinary 
ray are produced, polarised in planes at right angles to each other, viz. the 
former in a plane at right angles to the plate parallel to the axis, and the 
latter in a plane at right angles to the axis. The crystal possesses, how¬ 
ever, the remarkable property of rapidly absorbing the ordinary ray; con¬ 
sequently, when a plate of certain thickness is used, the extraordinary ray * 
alone emerges, in other words, a beam of common light emerges from the 
plate of tourmaline polarised in a plane at right angles to the axis of the 
crystal. If the light thus transmitted be viewed through another 
similar plate held in a parallel position, little change will be observed, 
excepting that the intensity of the transmitted light will be about equal 
to that which passes through a plate of double the thickness j but if the 
second tourmaline be slowly turned, the light will become feebler, and 
will ultimately disappear when the axes of the two plates are at right 
angles. 

The objections to the use of the tourmaline are that it is not very trans- 


POLARISATION OF LIGHT. 


535 


- 572 ] 

parent, and that plates of considerable thickness must be used if the pola¬ 
risation is to be complete. For unless the ordinary ray is completely ab¬ 
sorbed, the emergent light will be only partially polarised. 

Mr. Herapath has lately discovered that sulphate of iodoquinine has 
the property of polarising light in a remarkable degree. Unfortunately, 
it is very fragile and difficult to obtain in large crystals. 

571. Double refracting prisms of Iceland spar. —When a ray of 
light passes through an ordinary rhombohedron of Iceland spar, the 
ordinary and extraordinary rays emerge parallel to the original ray, 
consequently the separation of the rays is proportional to the thickness 
of the prism. But if the crystal is cut so that its faces are inclined to 
each other, the deviations of the ordinary and extraordinary rays 
will be different, they will not emerge parallel, and their separation will 
be greater as their distance from the prism increases. The light, how¬ 
ever, in passing through the prism becomes decomposed, and the rays will 
be coloured. It is therefore necessary to achromatise the prism, which 
is done by combining it with a prism of glass with its 
refracting angle turned in the contrary direction (fig. 419). 

In order to obtain the greatest amount of divergence, the 
refracting edges of the prism should be cut parallel to the 
optic axis, and this is always done. 

Let us suppose that a ray of polarised light passes 
along the axis of the cylinder (fig. 419), and let us 
suppose that the cylinder is caused to turn slowly 
round its axis ; then the resulting phenomena are exactly 
like those already described (564). Generally there will be an ordinary 
and extraordinary ray produced, whose relative intensities will vary as 
the tube is turned. But in two opposite positions the ordinary ray 
alone will emerge, and in two others at right angles to the former the 
extraordinary ray will alone emerge. When the ordinary ray alone 
emerges, the principal plane of the crystal, that is, a plane at right 
angles to its face, and parallel to its refracting edge, coincides with the 
original plane of polarisation of the ray. Consequently, by means of the 
prism, it can be ascertained both that the ray is polarised, and likewise 
the plane in which it is polarised. 

572. Nicol’s prism.— The Nicol’s prism is one of the most valuable 
means of polarising light, for it is perfectly colourless, it polarises light 
completely, and it transmits only one beam of polarised light, the other 
being entirely suppressed. 

It is constructed out of a rhombohedron of Iceland spar, about an inch 
in height and ^ of an inch in breadth. This is bisected in the plane which 
passes through the obtuse angles, as shown in fig. 421, that is along the 
plane acbd (fig. 410). The two halves are then again joined in the same 
order by means of Canada balsam. 



Fig. 419. 







536 


ON LIGHT. 


[ 573 - 

The principle of the Nicol’s prism is this: the refractive index of 
Canada balsam 1-549 is less than the ordinary index of Iceland spar 
1-654, but greater than its extraordinary index 1-483. Hence, when 
a luminous ray, SC, fig. 421, enters the prism, the ordinary ray under¬ 
goes total reflection on the surface ob , and takes the direction QdO, by 



which it is refracted out of the crystal; while the extraordinary ray, Ce, 
emerges alone. Since the Nicole prism allows only the extraordinary 
ray to pass, it may be used, like a tourmaline, as an analyser or as a 
polariser. 

573. Physical theory of polarised light. —The explanation of the 
dark bands produced by the interference of light is stated in art. 559 to 
resemble exactly that of the formation of nodes and loops given in 
art. 230. 

It might hence be supposed that the vibrations producing the light 
are similar to those producing sound. But this is by no means the 
case. In fact, if art. 564 be examined, it will be found that no assump¬ 
tion is there made as to the direction in which the vibrating particles 
move, and accordingly that explanation is equally true whether the 
particles vibrate in the direction AB, BA, or at right angles to AB. As 
a matter of fact the former is the case with the vibrations producing 
sound, the latter with the vibrations producing light. In other words, 
the vibrations producing sound take place in the direction of propaga¬ 
tion, the vibrations producing light are transversal to the direction of 
propagation. 

This assumption as to the direction of the vibration of the particles 
of ether producing light is rendered necessary, and is justified by the 
phenomena of polarisation. 

When a ray of light is polarised, all the particles of ether in that ray 
vibrate in straight lines parallel to a certain direction in the front of the 
wave corresponding to the ray. 

When a ray of light enters a double refracting medium, such as 
Iceland spar, it becomes divided into two, as we have already seen. Now 
it can be shown to be in strict accordance with mechanical principles that, 
if a medium possesses unequal elasticity in different directions, a plane 
wave produced by transversal vibrations entering that medium will give 







- 574 ] COLOURS PRODUCED BY INTERFERENCE OF POLARISED LIGHT. 537 

rise to two plane waves moving with different velocities within the 
medium, and the vibrations of the particles in front of these waves will 
be in directions parallel respectively to two lines at right angles to each 
other. If, as is assumed in the undulatory theory of light, the ether 
exists in a double refracting crystal in such a state of unequal elasticity 
then the two plane waves will be formed as above described, and these 
having different velocities will give rise to two rays of unequal refrangi- 
bility (compare art. 652). This is the physical account of the phe¬ 
nomenon of double refraction. It will be remarked that the vibrations 
corresponding to the two rays are transversal, rectilinear, and in direc¬ 
tions perpendicular to each other in the rays respectively. Accordingly 
the same theory accounts for the fact that the two rays are both polarised, 
and in planes at right angles to each other. 

It is a point still unsettled whether, when a ray of light is polarised 
with respect to a given plane, the vibrations take place in directions 
within or perpendicular to that plane. Fresnel was of the latter opinion. 
It is, however, convenient in some cases to regard the plane of polarisa¬ 
tion as that in which the vibrations take place. 

COLOURS PRODUCED BY THE INTERFERENCE OF POLARISED LIGHT. 

574. Laws of tlie interference of polarised rays. —After the dis¬ 
covery of polarisation, Fresnel and Arago tried whether polarised rays 
presented the same phenomena of interference as ordinary rays. They 
were thus led to the discovery of the following laws in reference to the 
interference of polarised light, and, at the same time, of the brilliant 
phenomena of coloration, .which will be presently described. 

I. When two rays polarised in the same plane interfere with each other, 
they will produce by their interference fringes of the very same kind as 
if they were common light. 

II. When two rays of light are polarised at right angles to each other, 
they produce no coloured fringes in the same circumstances under which 
two rays of common light would produce them. When the rays are po¬ 
larised in planes inclined to each other at any other angles, they produce 
fringes of intermediate brightness, and if the angle is made to change, the 
fringes gradually decrease in brightness from 0° to 90°, and are totally 
obliterated at the latter angle. 

III. Two rays originally polarised in planes at right angles to each 
other may be subsequently brought into the same plane of polarisation 
without acquiring the power of forming fringes by their interference. 

IV. Two rays polarised at right angles to each other, and afterwards 
brought into the same plane of polarisation, produce fringes by their 
interference like rays of common light, provided they originated in a 
pencil the whole of which was originally polarised in any one plane. 

a a 3 


538 


ON LIGHT. 


[575- 

V. In the phenomena of interference produced by rays that have suf¬ 
fered double refraction, a difference of half an undulation must he allowed, 
as one of the pencils is retarded by that quantity from some unknown 
cause. 

575. Effect produced by causing: a pencil of polarised rays 
to traverse a double refracting crystal. —The following important 
experiment may be made most conveniently by Norremberg’s apparatus 
(tig. 417). At g (fig. 418), there is aNicol’s prism. A plate of a double 
refracting crystal cut parallel to its axis is placed on the disc at e. In 
the first place, however, suppose the plate of the crystal to be removed. 
Then, since the Nicol’s prism allows only the extraordinary ray to pass, 
when it is turned so that its principal plane coincides with the plane of 
reflection, no light will be transmitted (572). Place the plate of doubly 
refracting crystal, which is supposed to be of moderate thickness, in the 
path of the reflected ray at e. Light is now transmitted through the 
Nicol’s prism. On turning the plate, the intensity of the transmitted 
light varies; it reaches its maximum when the principal plane of the 
plate is inclined at an angle of 45° to the plane of reflection, and dis¬ 
appears when these planes either coincide with or are at right angles to 
each other. The light in this case is white. The interposed plate may 
be called the depolarising plate. The same or equivalent phenomena 
are produced when any other analyser is used. Thus, suppose the double 
refracting prism to be used. Suppose the depolarising plate to be re¬ 
moved. Then, generally, two rays are transmitted, but if the principal 
plane of the analyser is turned into the plane of primitive polarisation, 
the ordinary ray only is transmitted, and then, when turned through 90°, 
the extraordinary ray only is transmitted. Let the analyser be turned into 
the former position, then, when the depolarising plate is interposed, both 
ordinary and extraordinary rays are seen, and when the depolarising plate 
is slowly turned round, the ordinary and extraordinary rays are seen to 
vary in intensity, the latter vanishing when the principal plane of the po¬ 
larising plate either coincides with or is at right angles to the plane of 
primitive polarisation. 

576. Effect produced when the plate of crystal is very thin.— 

In order to exhibit this, take a thin film of selenite or mica between the 
twentieth and sixtieth of an inch thick, and interpose it as in the last 
article. If the thickness of the film is uniform, the light now transmitted 
through the analyser will be no longer white, but of a uniform tint; the 
colour of the tint being different for different thicknesses, for instance, 
red, or green, or blue, or yellow, according to the thickness; the intensity 
of the colour depending on the inclination of the principal plane of the 
film to the plane of reflection, being greatest when the angle of inclina¬ 
tion is 45°. Let us now suppose the crystalline film to be fixed in that 


- 577 ] COLOURS PRODUCED BY INTERFERENCE OF POLARISED LIGHT. 539 

position in which the light is brightest, and suppose its colour to be red. 
Let the analyser (the Nicol’s prism) be turned round, the colour will grow 
fainter, and when it has been turned through 45°, the colour disappears, 
and no light is transmitted j on turning it farther, the complementary 
colour, green, makes its appearance, and increases in intensity until the 
analyser has been turned through 90°$ after which the intensity dimi¬ 
nishes until an angle of 135° is attained, when the light again vanishes, 
and on increasing the angle, it changes again into red. Whatever be the 
colour proper to the plate, the same series of phenomena will be observed, 
the colour passing into its complementary when the analyser is turned. 
That the colours are really complementary is proved by using a double 
refracting prism as analyser. In this case two rays are transmitted, each 
of which goes through the same changes of colour and intensity as the 
single ray described above, but whatever be the colour and intensity of 
the one ray in a given position, the other ray will have the same when 
the analyser has been turned through an angle of 90°. Consequently 
these two rays give simultaneously the appearances which are succes¬ 
sively presented in the above case by the same ray at an interval of 90°. 
If now the two rays are allowed to overlap they produce white light j 
thereby proving their colours to be complementary. 

Instead of using plates of different thickness to produce different tints, 
the same plate may be employed inclined at different angles to the pola¬ 
rised ray. This causes the ray to traverse the film obliquely, and, in fact, 
amounts to an alteration in its thickness. 

With the same substance, but with plates of increasing thickness, the 
tints follow the laws of the colours of Newton’s rings (562). The thick¬ 
ness of the depolarising plate must, however, be different from that ol 
the layer of air in the case of Newton’s rings to produce corresponding 
colours. Thus corresponding colours are produced by a plate of mica and 
a layer of air when the thickness of the former is about 400 times that 
of the latter. In the case of selenite the thickness is about 230 times ; 
and in the case of carbonate of calcium, about 13 times that of the corre¬ 
sponding layer of air. 

577. Theory of the phenomena of depolarisation. —The phe¬ 
nomena described in the last articles admit of complete explanation by 
the undulatory theory, but not without the aid of abstruse mathematical 
calculations. What follows will show the nature of the explanation. Let 
us suppose, for convenience, that in the case of a polarised ray the 
particles of ether vibrate in the plane of polarisation (see art. 573), 
and that the analyser is a double refracting prism, with its principal 
plane in the plane of primitive polarisation; then the vibrations being 
wholly in that plane have no resolved part in a plane at right angles to 
it, and, consequently, no extraordinary ray passes through the analyser; 


540 


ON LIGHT. 


[ 578 - 

in other words, only an ordinary ray passes. Now take the depolarising 
plate cut parallel to the axis, and let it he interposed in such a manner 
that its principal plane makes any angle (0) with the plane of primitive 
polarisation. The effect of this will he to cause the vibrations of the 
primitive ray to he resolved in the principal plane, and at right angles to 
the principal plane, thereby giving rise to an ordinary ray (0), and an 
extraordinary ray (E), which, however, do not become separated on ac¬ 
count of the thinness of the depolarising plate. They will not form a 
single plane polarised ray on leaving the plate, since they are unequally 
retarded in passing through it, and consequently leave it in different phases. 
Since neither of the planes of polarisation of 0 and E coincides with the 
principal plane of the analyser, the vibrations composing them will again 
be resolved by the analyser into vibrations in and at right angles to the 
principal plane, viz. 0 gives rise to Oo and Oe , and E gives rise to Eo and 
Eo. But the vibrations composing Oo and Eo being in the same plane give 
rise to a single ordinary ray, Io, and in like manner Oe and Ee give rise to 
a single extraordinary ray, Ie. Thus the interposition of the depolarising 
plate restores the extraordinary ray. 

Suppose the angle 0 to be either 0° or 90°. In either case the vibrations 
are transmitted through the depolarising plate without resolution, conse¬ 
quently they remain wholly in the plane of primitive polarisation, and on 
entering the analyser cannot give rise to an extraordinary ray. 

If the Nicol’s prism is used as an analyser, the ordinary ray is suppressed 
by mechanical means. Consequently only Ie will pass through the prism, 
and that for all values of 0 except 0° and 90°. 

A little consideration will show that the joint intensities of all the rays 
existing at any stage of the above transformations must continue constant, 
but that the intensities of the individual rays will depend on the magni¬ 
tude of 0, and when this circumstance is examined in detail, it explains 
the fact that Ie increases in intensity as 0 increases from 0° to 45°, and 
then decreases in intensity as 0 increases from 45° to 90°. 

In regard to the colour of the rays, it is to be observed that the for¬ 
mulae for the intensities of Io and le contain a term depending on the 
length of the wave and the thickness of the plate. Consequently, when 
white light is used, the relative intensities of its component colours are 
changed, and, therefore, Io and le will each have a prevailing tint, which 
will be different for different thicknesses of the plate. The tints will, 
however, be complementary, since, the joint intensities of Io and Ie being 
the same as that of the original ray, they will, when superimposed, 
restore all the components of that ray in their original intensities, and 
therefore produce white light. 

578. Coloured rings produced by polarised light in traversing 
double refracting films. — In the experiments with Norremberg’s 


- 578 ] COLOURS PRODUCED BY INTERFERENCE OF POLARISED LIGHT. 541 


apparatus, which have just been described (575), a pencil of parallel 
rays traverses the film of crystal perpendicularly to its faces, and as all 
parts of the film act in the same manner, there is everywhere the 
same tint. But when the incident rays traverse the plate under dif¬ 
ferent obliquities, which comes to the same thing as if they traversed 
plates differing in thickness, coloured rings are formed similar to 
Newton’s rings. 

The best method of observing these new phenomena is by means of the 
tourmaline pincette. This is a small instrument consisting of two tourma¬ 
lines, cut parallel to the axis, each of them being fitted in a copper disc. 
These two discs, which are perforated in the centre, and blackened, are 




Fig. 422. 


mounted in two rings of silvered copper, which is coiled, as shown in the 
figure, so as to form a spring, and press together the tourmalines. The 
tourmalines turn with the disc, and may be so arranged that their axes 
are either perpendicular or parallel. 

The crystal to be experimented upon being fixed in the centre of a cork 
disc is placed between the two tourmalines, and the pincette is held be¬ 
fore the eye so as to view diffused light. The tourmaline farthest from the 
eye acts as polariser, and the other as analyser. If the crystal thus viewed 
is uniaxial, and cut perpendicularly to the axis, and a homogeneous light, 
red for instance, is looked at, a series of alternately dark and red rings 
are seen. With another simple colour, similar rings are obtained, but 
their diameter decreases with the refrangibility of the colour. On the 
other hand, the diameters of the rings diminish when the thickness of the 
plates increases, and beyond a certain thickness no more rings are pro¬ 
duced. If, instead of illuminating the rings by homogeneous light, white 
light be used, as the rings of the different colours produced have not the 
same diameter, they are partially superposed, and produce very brilliant 
variegated colours. 

The position of the crystal has no influence on the rings, but this is 
not the case with the relative position of the two tourmalines. For 
instance, in experimenting on Iceland spar cut perpendicular to the axis, 
and from 1 to 20 millimeters in thickness, when the axis of the tour¬ 
malines is perpendicular, a beautiful series of rings is seen brilliantly 
coloured, and traversed by a black cross, as shown in fig. 423. If the 
axes of the tourmalines are parallel, the rings have tints complementary 


ON LIGHT. 


542 


[ 579 - 


to those they had at first, and there is a white cross (fig. 424) instead of a 
black one. 

In order to understand the formation of these rings when polarised 
light traverses double refracting films, it must first be premised that 
these films are traversed by a converging conical pencil, whose summit 
is the eye of the observer. Hence it follows that the virtual thickness of 
the film which the rays traverse increases with their divergence; but 
for rays of the same obliquity this thickness is the same: hence there 
result different degrees of retardation of the ordinary with respect to the 



Fig. 423. 


Fig. 424. 


Fig. 425. 





extraordinary ray at different points of the plate, and consequently dif¬ 
ferent colours are produced at different distances from the axis, but the 
same colours will be produced at the same distance from the axis, and 
consequently the colours are arranged in circles round the axis. The 
arms of the black cross are parallel to the optic axis of each of the tour¬ 
malines, and are due to an absorption of the polarised light in these direc¬ 
tions. When the tourmalines are parallel the vibrations are transmitted, 
and hence the white cross. 

Analogous effects are produced with all uniaxial crystals ; for instance, 
tourmaline, emerald, sapphire, beryl, mica, pyromorphite, and ferrocya- 
nide of potassium. 


Fig. 426. Fig. 427. Fig. 428. 

579. Rings in biaxial crystals. —In biaxial crystals, coloured rings 
are also produced, but their form is more complicated. The coloured 


- 580 ] COLOURS PRODUCED BY INTERFERENCE OF POLARISED LIGHT. 543 

bands, instead of being circular and concentric, have the form of curves, 
with two centres, the centre of each system corresponding to an axis 
of the crystal. Figs. 426, 427, and 428 represent the curves seen when a 
plate of nitre, cut perpendicularly to the axis, is placed between the two 
tourmalines, the plane containing the axis of the nitre being in the plane 
of primitive polarisation. When the axis of the two tourmalines are at 
right angles to each other the fig. 426 is obtained. On turning the cry¬ 
stal without altering the tourmalines, tho fig. 427 is seen, which changes 
into fig. 428 when the crystal has been turned 45°. If the axes of the 
tourmalines are parallel, the same coloured curves are obtained, but the 
colours are complementary, and the black cross changes into white. The 
angle of the optic axis in the case of nitre is only 5° 20', and hence the 
whole system can be seen at once. But when the angle exceeds 20° to 
25°, the two systems of curves cannot be simultaneously seen. There is 
then only one dark bar instead of the cross, and the bands are not oval 
but circular. Fig. 425 represents the phenomenon as seen with arra- 
gonite. 

Herschel, who has carefully measured the rings produced by biaxial 
crystals, refers them to the kind of curve known in geometry as the 
lemniscate, in strict accordance with the results of the undulatory theory 
of light. 

The observation of the system of rings which plates of crystals give 
in polarised light presents a means of distinguishing between optical 
uniaxial and optical biaxial crystals, even in cases in which no conclu¬ 
sion can be drawn as to the system in which a mineral crystallises 
from mere morphological reasons. In this way, the optical investiga¬ 
tion becomes a valuable aid in mineralogy, as, for example, in the case of 
mica, of which there are two mineralogical species, the uniaxial and the 
biaxial. 

All the phenomena which have been described are only obtained by 
means of polarised light. Hence a double refracting film, with either a 
Nicol’s prism or a tourmaline as analyser, may be used to distinguish be¬ 
tween polarised and unpolarised light, that is, as a polariscope. 

580. Colours produced by compressed or by unannealed glass.— 
Ordinary glass is not endowed with the power of double refraction. It 
acquires this property, however, if by any cause its elasticity becomes 
more modified in one direction than in another. In order to effect this, 
it may be strongly compressed in a given direction, or it may be curved, 
or tempered, that is to say, cooled after having been heated. If the 
glass is then traversed by a beam of polarised light, effects of colour are 
obtained which are entirely analogous to those described in the case of 
doubly refracting crystals. They are, however, susceptible of far 
greater variety, according as the plates of glass have a circular, square, 


ON LIGHT. 


544 


[ 581 - 


rectangular, or triangular shape, and according to the degree of tension of 
their particles. 

When the polariser is a mirror of black glass, on which the light of the 
sky is incident, and the analyser is a Nicol’s prism, through which the 
glass plates traversed by polarised light are viewed, figs. 429, 430, 432, 
represent the appearances presented successively, when a square plate 
of compressed glass is turned in its own plane; figs. 431 and 434 re- 
Fig. 429. Fig. 430. Fig. 431. 






Fig. 432. Fig. 433. Fig. 434. 

present the appearances produced by a circular plate under the same 
circumstances ; and fig. 433, that produced when one rectangular plate is 
superposed on another. This figure also varies when the system of plates 
is turned. 

Compressed and curved glasses present phenomena of the same kind, 
which also vary under the same conditions. 


ELLIPTICAL, CIRCULAR, AND ROTATORY POLARISATION. 

581. Definition of elliptical and circular polarisation.— In the 

cases hitherto considered the particles of ether composing a polarised ray 
vibrate in parallel straight lines; to distinguish this case from those we 
are now to consider such light is frequently called plane polarised light. 
It sometimes happens that the particles of ether describe ellipses round 
their positions of rest, the planes of the ellipses being perpendicular to the 
direction of the ray. If the axes of these ellipses are equal and parallel, 
the ray is said to be elUpticaUy polarised. In this case the particles which, 



- 582 ] ELLIPTICAL AND CIRCULAR POLARISATION. 545 

when at rest, occupied a straight line, are, when in motion, arranged in a 
helix round the line of their original position as an axis, the helix chang¬ 
ing from instant to instant. If the axes of the ellipses are equal, they 
become circles, and the light is said to be circularly polarised. If the 
minor axes become zero, the ellipses coincide -with their major axes, and 
the light becomes plane polarised. Consequently plane polarised light and 
circularly polarised light are particular cases of elliptically polarised light. 

582. Theory of the origin of elliptical and circular polarisa¬ 
tion.— Let us in the first place consider a simple pendulum (51) vibrat¬ 
ing in any plane the arc of vibration being small. Suppose that, when 
in its lowest position, it received a blow in a direction at right angles to 
the direction of its motion, such as would make it vibrate in an arc at 
right angles to its arc of primitive vibration, it follows from the law of 
the composition of velocities (48) that the joint effect will be to make it 
vibrate in an arc inclined at a certain angle to the arc of primitive vibra¬ 
tion, the magnitude of the angle depending on the magnitude of the blow. 
If the blow communicated a velocity equal to that with which the body 
is already moving, the angle would be 45°. Next suppose the blow to 
communicate an equal velocity, but to be struck when the body is at its 
highest point, this will cause the particle to describe a circle, and to 
move as a conical pendulum (53). If the blow is struck under any 
other circumstances, the particle will describe an ellipse. Now as the 
two blows would produce separately two simple vibrations in direc¬ 
tions at right angles to each other, we may state the result arrived at 
as follows:—If two rectilinear vibrations are superinduced on the 
same particle in directions at right angles to each other, then:—1. If 
they are in the same or opposite phases, they make the point describe a 
rectilinear vibration in a direction inclined at a certain angle to either of 
the original vibrations. 2. But if their phases differ by 90° or a quarter 
of a vibration, the particle will describe a circle, provided the vibrations are 
equal. 3. Under other circumstances the particle will describe an ellipse. 

To apply this to the case of polarised light. Suppose two rays of 
light polarised in perpendicular planes to coincide, each would separately 
cause the same particles to vibrate in perpendicular directions. Con¬ 
sequently,—1. If the vibrations are in the same or opposite phases, the 
light resulting from the two rays is plane-polarised. 2. If the rays are 
of equal intensity, and their phases differ by 90°, the resulting light is 
circularly polarised. 3. Under other circumstances the light is ellipti¬ 
cally polarised. 

As an example, if reference is made to arts. 575 and 576, it will be seen 
that the rays denoted by O and E are superimposed in the manner above 
described. Consequently the light which leaves the depolarising plate is 
elliptically polarised. If, however, the principal plane of the depolarising 


546 ON LIGHT. [ 583 - 

plate is turned so as to make an angle of 45° with the plane of primitive 
polarisation, 0 and E have equal intensities, and if further the plate is 
made of a certain thickness, so that the phases of 0 and E may differ by 
90°, or by a quarter of a vibration, the light which emerges from the 
plate is circularly polarised. This method may be employed to produce 
circularly polarised light. 

Circular or elliptical polarisation may be either right-handed or left- 
handed , or what is sometimes called dextrogyrate and Icevogyrate. If the 
observer looks along the ray in the direction of propagation, from pola- 
riser to analyser, then, if the particles move in the same direction as the 
hands of a watch, with its face to the observer, the polarisation is right- 
handed. 

583. Fresnel's rhomb.— This is a means of obtaining circularly 
polarised light. We have already seen (532) that, to obtain a ray of 
circularly polarised light, it is sufficient to 
decompose a ray of plane polarised light in 
such a manner as to produce two rays of light 
of equal intensity polarised in planes at right 
angles to each other, and differing in their 
paths by a quarter of an undulation. Fresnel 
effected this by means of a rhomb, which 
has received his name. It is made of glass; 
its acute angle is 54°, and its obtuse 126°. If 
a ray, a, fig. 435, of plane polarised light 
fall perpendicularly on the face AB, it will 
undergo two total internal reflections at an 
angle of about 54°, one at E, and the other at 
F, and will emerge perpendicularly. 

If the plane ABDC be inclined at an angle of 45° to the plane of 
polarisation, the polarised ray will be divided into two coincident rays 
with their planes of polarisation at right angles to each other, and it ap¬ 
pears that one of them loses exactly a quarter of an undulation, so that 
on emerging from the rhomb the ray is circularly polarised. If the ray 
emerging as above from Fresnel’s rhomb is examined, it will be found to 
differ from plane polarised light in this, that, when it passes through a 
double refracting prism, the ordinary and extraordinary rays are of equal 
intensity in all positions of the prism. Moreover, it differs from ordinary 
light in this, that, if it is passed through a second rhomb placed parallel 
to the first, there will be a second quarter of an undulation lost, so that 
the parts of the original plane-polarised ray will differ by half an undu¬ 
lation, and the emergent ray will be plane polarised; moreover, the plane 
of polarisation will be inclined at an angle of 45° to ABCD, but on the 
other side from the plane of primitive polarisation. 



Fig. 435. 






ROTATORY POLARISATION. 


547 


-586] 

584. Elliptical polarisation.— Our limits will not allow us to enter 
into this subject, but we may state that, in addition to the method already 
mentioned (583), elliptically polarised light is generally obtained when¬ 
ever plane polarised light suffers reflection. Polarised light reflected from 
metals becomes elliptically polarised, the degree of ellipticity depending 
on the direction of the incident ray, and of its plane of polarisation, as well 
as on the reflecting substance. When reflected from silver, the polarisa¬ 
tion is almost circular, and from galena almost plane. If elliptically 
polarised light be analysed by the Nicol-prism, it never vanishes, though 
at alternate positions it becomes fainter; it is thus distinguished from 
plane and from circular polarised light. If analysed by Iceland spar, 
neither image disappears, but they undergo changes in intensity. 

Light can also be polarised elliptically in Fresnel’s rhomb. If the angle 
between the planes of primitive polarisation and of incidence be any other 
than 45°, the emergent ray is elliptically polarised. 

585. Rotatory polarisation. —Rock crystal or quartz possesses a 
remarkable property which was long regarded as peculiar to itself among 
all crystals, though it has been since found to be shared by tartaric acids 
and its salts, together with some other crystalline bodies. This property 
is called rotatory polarisation, and may be described as follows :—Let a 
ray of homogeneous light (for example, red light) be polarised, and let the 
analyser, say a Nicol-prism, be turned till the light does not pass 
through it. Take a thin section of a quartz crystal cut at right angles 
to its axis, and place it between the polariser and the analyser with its 
plane at right angles to the ray. The light will now pass through the 
analyser. The phenomenon is not the same as that previously described 
(575), for, if the rock crystal is turned round its axis, no effect is pro¬ 
duced, and if the analyser is turned, the ray is found to be plane polarised, 
in a plane inclined at a certain angle to the plane of primitive polarisa¬ 
tion. If the light is red, and the plate 1 millimetre thick, this angle is 
about 17°. In some specimens of quartz the plane of polarisation is 
turned to the right hand, in others to the left hand. Specimens of the 
former kind are said to be right-handed, those of the latter kind left- 
handed. This difference corresponds to a difference in crystallographic 
structure. The property possessed by rock crystal of turning the plane 
of polarisation through a certain angle was thoroughly investigated by 
M. Biot, who amongst other results arrived at this:—For a given colour the 
angle through which the plane of polarisation is turned is proportional to 
the thickness of the quartz. 

586. Physical explanation of rotatory polarisation. —The ex¬ 
planation of the phenomenon described in the last article is as follows:— 
When a ray of polarised light passes along the axis of the quartz crystal, 
it is divided into two rays of circularly polarised light of equal intensity, 


548 ON LIGHT. [ 587 - 

which pass through the crystal with different velocities. In one the cir¬ 
cular polarisation is right-handed, in the other left-handed (582). The 
existence of these rays was proved by Fresnel, who succeeded in separa¬ 
ting them. On emerging from the crystal, they are compounded into a 
plane polarised ray, hut since they move with unequal velocities within 
the crystal, they emerge in different phases, and consequently the plane 
of polarisation will not coincide with the plane of primitive polarisation. 
This can be readily shown by reasoning similar to that employed in art. 
582. The same reasoning will also show that the plane of polarisation 
will be turned to the right or left according as the right-handed or left- 
handed ray moves with the greater velocity. Moreover, the amount of the 
rotation will depend on the amount of the retardation of the ray whose 
velocity is least, that is to say, it will depend on the thickness of the plate 
of quartz. In this manner the phenomena of rotatory polarisation can be 
completely accounted for. 

587. Coloration produced by rotatory polarisation.— The rota¬ 
tion is different with different colours; its magnitude depends on the 
refrangibility, and is greatest with the most refrangible rays. In the 
case of red light a plate 1 millimetre in thickness will rotate the plane 
17°, while a plate of the same thickness will rotate it 44° in the case of 
violet light. Hence with white light there will, in each position of the 
analysing Nicol, be a greater or less quantity of each colour transmitted. 
In the case of a right-handed crystal, when the Nicol is turned to the 
right, the colours will successively appear from the less refrangible to the 
more so, that is, in the order of the spectrum from red to violet; with a 
left-handed crystal in the reverse order. Obviously in turning the Nicol 
to the left, the reverse of these results will take place. 

When a quartz plate cut perpendicularly to the axis and traversed by 
a ray of polarised light is looked' at through a 
doubly refracting prism, two brilliantly coloured 
images are seen, of which the tints are comple¬ 
mentary; for their images are partially superposed, 
and in this position there is white light (fig. 436). 
AVhen the prism is turned from left to right, the 
two images change colours, and assume succes¬ 
sively all the colours of the spectrum. 

This will be understood from what has been said about the different 
rotation for different colours. Quartz rotates the plane of polarisation 
for red 17° for each millimetre, and for violet 44° ; hence from the great 
difference of these two angles, when the polarised light which has 
traversed the quartz plate emerges, the various simple colours which it 
contains are polarised in different planes. Consequently, when the rays 
thus transmitted by the quartz pass through a double refracting prism, 



ROTATORY POWER OF LIQUIDS. 


549 


- 588 ] 


they are each decomposed into two others polarised at right angles to 
each other : the various simple colours are not divided in the same pro¬ 
portion between the ordinary and extraordinary rays furnished hy the 
prism ; the two images are, therefore, coloured ; hut, since these which 
are wanting in the one occur in the other, the colours of the images are 
perfectly complementary. 

These phenomena of coloration may he well seen hy means of Nor- 
remberg’s apparatus (fig. 417). A quartz plate, s, cut at right angles to 
the axis and fixed in a cork disc, is placed on the screen, e ; the mirror n 
(fig. 417) being then so inclined that a ray of polarised light passes 
through the quartz ; the latter is viewed through a refracting prism, g ; 
when this tube is turned, the complementary images furnished hy the 
passage of polarised light through the quartz are seen. 

588. Rotatory power of liquids. —Biot has found that a great num¬ 
ber of liquids and solutions possess the property of rotatory polarisation. 
He has further observed that the deviation of the plane of polari¬ 
sation can reveal differences in the composition of bodies where none 
is exhibited by chemical analysis. For instance, uncrystallisable grape- 
sugar deflects the plane of polarisation to the left, while cane-sugar de¬ 
flects it to the right, although the chemical composition of the two 
sugars is the same. 

The rotatory power of liquids is far less than that of quartz. In concen¬ 
trated syrup of cane-sugar, which possesses the rotatory power in the 
highest degree, the power is — that of quartz, so that it is necessary to 
operate upon columns of liquids of considerable length, 8 inches for 
example. 

Fig. 437 represents the apparatus devised by Biot for measuring the 
rotatory power of liquids. On a copper groove, g , fixed to a support, r, is 
a brass tube 20 centimetres long, in which is contained the liquid experi¬ 
mented upon. This tube, which is tinned inside, is closed at each end by 
glass plates fastened by screw collars. Atm is a mirror of black glass, 
inclined at the polarising angle to the axis of the tubes bd and a, so that 
the ray reflected by the mirror m, in the direction bda, is polarised. In 
the centre of the graduated circle h, inside the tube a, and at right angles 
to the axis bda , is a double refracting achromatic prism, which can be 
turned about the axis of the apparatus by means of a button, m. The 
latter is fixed to a limb, c, on which is a vernier, to indicate the number 
of degrees turned through. Lastly, from the position of the mirror m, 
the plane of polarisation, Soc?, of the reflected ray is vertical, and the zero 
of the graduation on the circle, h, is on this plane. 

Before placing the tube d in the groove g, the extraordinary image fur¬ 
nished by the double refracting prism disappears whenever the limb c cor¬ 
responds to the zero of the graduation, because then the double refracting 


550 


ON LIGHT. 



Fig. 437. 

tion takes place to the right; and if with the same solution tubes of 
different lengths are taken, the rotation is found to increase proportionally 
to the length, in conformity with art. 585 : further, with the same 
tube, but with solutions of various strength, the rotation increases with 
the quantity of sugar dissolved, so that the quantitative analysis of a 
solution may be made by means of its angle of deviation. 

In this experiment homogeneous light must be used; for, as the 
various tints of the spectra have different rotatory powers, white light 
is decomposed in traversing an active liquid, and the extraordinary 


[588- 


prism is so turned that its principal section coincides with the plane of 
polarisation (573). This is the case also when the tube d is full of water or 
any other inactive liquid, like alcohol, ether, etc., which shows that the 
plane of polarisation has not been turned. But if the tube be filled with 
a solution of cane-sugar or any other active liquid, the extraordinary image 
reappears, and to extinguish it the limb must be turned to a certain 
extent either to the right or to the left of zero, according as the liquid 
is right-handed or left-handed, showing that the polarising plane has 
been turned by the same angle. With solution of cane-sugar the rota- 











soleil’s saccharimeter. 


451 


-589] 

image does not disappear completely in any position of the double re¬ 
fracting prism, it simply changes the tint. The transition tint (589) 
may, however, be observed. To avoid this inconvenience, a piece of red 
glass is placed in the tube between the eye and the double refracting 
prism, which only allows red light to pass. The extraordinary image 
disappears in that case, whenever the principal section of the prism 
coincides with the plane of polarisation of the red ray. 

589. Soleil’s saccharimeter. —M. Soleil has constructed an apparatus, 
based upon the rotatory power of liquids, for analysing saccharine sub¬ 
stances, to which the name saccharimeter is applied. 



Fig. 438. 


Figure 438 represents the saccharimeter fixed horizontally on its foot, 
and fig. 439 gives a longitudinal section with the modifications which 
have been introduced by M. Duboscq. 

The principle of this instrument is not the amplitude of the rotation 
of the plane of polarisation as in Biot’s apparatus, but that of compen¬ 
sation ; that is to say, a second active substance is used acting in the 
opposite direction to that analysed, and whose thickness can be altered 
until the contrary actions of the two substances completely neutralise 
each other. Instead of measuring the deviation of the plane of polarisa- 























ON LIGHT. 


552 


[589- 


tion, the thickness is measured which the plate of quartz must have in 
order to obtain perfect compensation. 

The apparatus consists of three parts—a tube containing the liquid to 
be analysed, a polariser, and an analyser. 

The tube m , containing the liquid, is made of copper, tinned on the 
inside, and closed at both ends by two glass plates. It rests on a sup¬ 
port, k, terminated at both ends by tubes r and a, in which are the 
crystals used as analysers and polarisers, and which are represented in 
section (fig. 439). 

In front of the aperture, S (fig. 439), is placed an ordinary moderator 
lamp. The light emitted by this lamp in the direction of the axis first 
meets a double refracting prism, r, which serves as polariser (570). The 
ordinary image alone meets the eye, the extraordinary image being pro¬ 
jected out of the field of vision in consequence of the amplitude of the 


Fig. 439. 



angle which the ordinary makes with the extraordinary ray. The double 
refracting prism is in such a position that the plane of polarisation is 
vertical, and passes through the axis of the apparatus. 

Emerging from the double refracting prism, the polarised ray meets a 
plate of quartz with double rotation ; that is, this plate rotates the plane 
both to the right and to the left. This is effected by constructing the 
plate of two quartz plates of opposite rotation placed one on the other, 
as shown in figure 442, so that the line of separation is vertical and in 
the same plane as the axis of the apparatus. These plates cut perpen¬ 
dicularly to the axis, have a thickness of 3*75 millimetres, corresponding 
to a rotation of 90°, and give a rose-violet tint called the tint of passage 
or transition-tint. As the quartz, whether right-handed or left-handed, 
turns always to the same extent for the same thickness, it follows that 
the two quartz, a and b, turn the plane of polarisation equally, one to the 



















soleil’s saccharimeter. 


-589] 


553 


right and the other to the left. Hence, looked at through a double 
refracting prism, they present exactly the same tint. 

Having traversed the quartz, q, the polarised ray passes into the liquid 
in the tube m, and then meets a single plate of quartz, i, of any thick¬ 
ness, the use of which will he seen presently. The compensator n> 
which destroys the rotation of the column of liquid m, consists of 
two quartz plates, with the same rotation either to the right or the left, 
hut opposite to that of the plate i. These two quartz plates, a section of 
which is represented in fig. 412, are obtained by cutting obliquely a 
quartz plate with parallel sides, so as to form two prisms of the same 
angle, N, N ; superposing then these two prisms, as shown in the figure, 
a single plate is obtained with parallel faces, which can be varied at will. 
This is effected by fixing each prism to a slide, so as to move it in either 
direction without disturbing the parallelism. This motion is effected by 
means of a double rackwork and pinion motion turned by a milled head, 
b (figs. 433, 439). 

When these plates move in the direction indicated by the arrows 
(fig. 440), it is clear that the sum of their thicknesses increases, and that 
it diminishes when the plates are moved in the contrary direction. A 
scale and a vernier follow the plates in their motion, and measure the 
thickness of the compensator. This scale, represented with its vernier 
in figure 441, has two divisions with a common zero, one from left to 
right for right-handed liquids, and another from right to left for left- 
handed. 

When the vernier is at zero of the scale, the sum of the thicknesses of 
the plates NN' is exactly equal to that of plate i, and as the rotation of 
the latter is opposed to that of the compensator, the effect is zero. But 
by moving the plates of the compensator in one or the other direction, 
either the compensator or the quartz, i, preponderates, and there is a 
rotation from left to right. 

Behind the compensator is a double refracting prism, c (fig. 439), serv¬ 
ing as analyser to observe the polarised ray which has traversed the 
liquid and the various quartz plates. In order to understand more 
easily the obj ect of the prism c, we will neglect for a moment the crystals 
and the lenses on the right of the drawing. If at first the zero of the 
vernier, o, coincides with that of the scale, and if the liquid in the tube 
is inactive, the actions of the compensator, and of the plate i, neutralise 
each other; and the liquid having no action, the two halves of the plate 
q } seen through the prism <?, give exactly the same tint as has been 
observed above. But if the tube filled with inactive liquid be replaced 
by one full of solution of sugar, the rotatory power of this solution is 
added to that of one of the halves (a or b) of the plate q (viz. that half 
which tends to turn the plane of polarisation in the same direction as the 

B B 


554 


ON LIGHT. 


[589- 

solution), and subtracted from that of the other. Hence the two halves 
of the plate q no longer show the same tint; the half a , for instance, is 
red, while the half b is blue. The prisms of the compensator are then 
moved, by turning the milled head b , either to the right or to the left, 
until the difference of action of the compensator and of the plate i com¬ 
pensates the rotatory power of the solution, which takes place when the 
two halves of the plate O, with double rotation, revert to their original 
tint. 

The direction of the deviation and the thickness of the compensator 
are measured by the relative displacement of the scale e , and of the 
vernier, r. Ten of the divisions on the scale correspond to a difference of 
1 millimeter in the thickness of the compensator; and as the vernier 
gives itself tenths of these divisions, it therefore measures differences of 
~ in the thickness of the compensator. 

When once the tints of the two halves of the plate are exactly the same, 
and therefore the same as before interposing the solution of sugar, the 
division on the scale corresponding to the vernier is read off, and the cor¬ 
responding number gives the strength of the solution. This depends on the 
principle that 16*471 grains of pure and well-dried sugar-candy being dis¬ 
solved in water, and the solution diluted to the volume of 100 cubic centi¬ 
metres, and observed in a tube of 20 centimetres in length, the deviation 
produced is the same as that effected by a quartz a millimetre thick. In 
making the analysis of raw sugar, a normal weight of 16*471 grains of 
sugar is taken, dissolved in water, and the solution made up to 100 cubic 
centimetres, with which a tube 20 centimetres in length is filled, and the 
number indicated by the vernier read off, when the primitive tint has been 
obtained. This number being 42, for example, it is concluded that the 
amount of crystallisable sugar in the solution is 42 per cent, of that which 
the solution of sugar-candy contained, and, therefore, 16*471 grains x 
or 6*918 grains. This result is only valid when the sugar is not mixed 
with uncrystallisable sugar or some other left-handed substance. In that 
case the crystallisable sugar, which is right-handed, must be, by means 
of hydrochloric acid, converted into uncrystallisable sugar, which is left- 
handed : and a new determination is made which together with the first 
gives the quantity of crystallisable sugar. 

The arrangement of crystals and lenses, o, g,f and a, placed behind the 
prism c, forms what M. Soleil calls the producer of sensible tints. For the 
most delicate tint, that by which a very feeble difference in the colora¬ 
tion of the two halves of the rotation plate can be distinguished is not the 
same for all eyes; for most people it is of a violet blue tint like flax- 
blossom, and it is important either to produce this tint or some other 
equally sensible to the eye of the observer. This is effected by placing 
in front of the prism c, at first a quartz plate, o, cut perpendicular to the 


POLARISATION OF HEAT. 


555 


- 591 ] 

axis, then a small Galilean telescope consisting 1 of a double convex glass, 
ff, and a double concave glass, f y which can be approximated or removed 
from each other according to the distance of distinct vision of each observer. 
Lastly, there is a double refracting prism, c, acting as polariser in reference 
to the quartz, and the prism a as analyser; and hence, when the latter is 
turned either right or left, the light which has traversed the prism c, and 
the plate o, changes its tint, and finally gives that which is the most 
delicate for the experimenter. 

590. Analysis of diabetic urine. —In the disease diabetes , the urine 
contains a large quantity of fermentescible sugar called diabetic sugar, 
which in the natural condition of the urine turns the plane of polarisation 
to the right. To estimate the quantity of this sugar, the urine is first 
clarified by heating it with acetate of lead and filtering; the tube is filled 
with the clear liquid thus obtained; and the milled head, b, turned, 
until by means of the double rotating plate the same tint is obtained as 
before the interposition of the urine. Experiment has shown that 100 
parts of the saccharimetric scale represent the displacement which the 
quartz compensators must have when there are 225*6 grains of sugar in a 
litre; hence each division of the scale represents 2*256 of sugar. Ac¬ 
cordingly, to obtain the quantity of sugar in a given urine, the number 
indicated by the vernier at the moment at which the primitive tint 
reappears must be multiplied by 2*256. 

591. Polarisation of heat. —The rays of heat, like those of light, 
may become polarised by reflection and by refraction. The experiments 
on this subject are difficult of execution ; they were first made by Malus 
and Berard, in 1810; after the death of Malus they were continued by 
the latter philosopher. 

In his experiments, the calorific rays reflected from one mirror were 
received upon a second, just as in Norremberg’s apparatus; from the 
second they fell upon a small metallic reflector, which concentrated them 
upon the bulb of a differential thermometer. Berard observed that heat 
was not reflected when the plane of reflection of the second mirror was 
at right angles to that of the first. As this phenomenon is the same as 
that presented by light under the same circumstances, Berard concluded 
that heat became polarised in being reflected. 

The double refraction of heat may be shown by concentrating the sun’s 
rays by means of a heliostat on a prism of Iceland spar, and in¬ 
vestigating the resultant pencil by means of a thermopile, which must 
have a sharp narrow edge. In this case also there is an ordinary and an 
extraordinary ray, which follow the same laws as those of light. In the 
optic axis of the calcspar, heat is not doubly refracted. A Nicol’s prism 
can be used for the polarisation of heat as well as for that of light: a 
polarised ray does not traverse the second Nicol if the plane of its principal 

n b 2 


556 


ON LIGHT. 


[ 591 - 

section is perpendicular to tlie vibrations of the ray. The phenomena 
of the polarisation of heat may also he studied by means of plates of tour¬ 
maline and of mica. The angle of polarisation is virtually the same for 
heat as for light. In all these experiments the prisms must be very near 
each other. 

The diffraction, and therefore the interference, of rays of heat has 
recently been established by the experiments of Knoblauch and others. 
And Forbes, who has repeated Fresnel’s experiment with a rhombohedron 
of rock salt, has found that heat by two total internal reflections is 
circularly polarised just as is the case with light. 


- 593 ] 


PROPERTIES OF MAGNETS. 


557 


BOOK VIII. 

ON MAGNETISM. 


CHAPTER I. 

PROPERTIES OF MAGNETS. 

592. Natural and artificial magnets. — Magnets are substances 
which have the property of attracting iron, and the term magne¬ 
tism is applied to the cause of this attraction, and to the resulting 
phenomena. 

This property was known to the ancients; it exists in the highest 
degree in an ore of iron which is known in chemistry as the magnetic 
oxide of iron. Its composition is represented by the formula Fej 0 4 . 
This magnetic oxide of iron, or loadstone, as it is called, was first found 
at Magnesia, in Asia Minor, and has derived its name from this circum¬ 
stance. It is very abundant in nature; it is met with in the older 
geological formations, especially in Sweden and Norway, where it is 
worked as an iron ore, and furnishes the best quality of iron. 

When a bar or needle of steel is rubbed with a magnet, it acquires 
magnetic properties. Such bars are called artificial magnets; they are 
more powerful than natural magnets, and as they are also more con¬ 
venient, they will be exclusively referred to in describing the phenomena 
of magnetism ; the best modes of preparing them will be explained in a 
subsequent article. 

593. Poles and neutral line. —When a small particle of soft iron is 
suspended by a thread, and a magnet is approached to it, the iron is 
attracted towards the magnet, and some force is required for its removal. 
The force of the attraction varies in different parts of the magnet: it is 
strongest at the two ends, and is totally wanting in the middle. 

This variation may also be seen very clearly when a magnetic bar is 
placed in iron filings; these become arranged round the ends of the bar 
in feathery tufts, which decrease towards the middle of the bar, where 
there are none. That part of the surface of the bar where there is no 
visible magnetic force is called the neutral line j and the points near the 




558 ON MAGNETISM. [ 594 - 

ends of the bars where the attraction is greatest are called the poles. 
Every magnet, whether natural or artificial, has two poles, and a neutral 
line: sometimes, however, in magnetising bars and needles, poles are 
produced lying between the extreme points. These intermediate points 
are called consequent poles. 

We shall presently see that a freely suspended magnet always sets 
with one pole pointing towards the north, and the other towards the 



Fig. 443. 

south. The end pointing towards the north is called in this country the 
north pole, and the other end is the south pole. The end of the magnetic 
needle pointing to the north is also sometimes called the marked end of 
the needle. 

594. Mutual action of two poles. —The two poles of a magnet 

appear identical when they are 
brought in contact with iron filings, 
but this identity is only apparent. 
For when a small magnetic needle, 
ab (fig. 444), is suspended by a fine 
thread, and the north pole, A, of 
another needle is brought near its 
north pole, o, a repulsion takes 
place. If, on the contrary, A is 
brought near the south pole, b , of 
the moveable needle, the latter is 
strongly attracted. Hence these 
two poles, a and b, are not identi¬ 
cal, for one is repelled and the 
other attracted by the same pole of 
the magnet, A. It may be shown 
in the same manner that the two 
poles of the latter are also different, by successively presenting them to 
the same pole, a, of the moveable needle. In one case there is 
repulsion, in the other attraction. Hence the following law may be 
enunciated: 

Poles of the same name repel , and poles of contrary name attract one 
another. 











PROPERTIES OF MAGNETS. 


559 


-596] 

The opposite actions of the north and south poles may be shown by 
the following experiment:—A piece of iron, a key for example, is supported 
by a magnetised bar. A second magnetised bar of the same dimensions 
is then moved along the first, so that their poles are contrary (fig. 445). 
The key remains suspended so long as the two poles are at some distance , 



but when they are sufficiently near, the key drops just as if the bar 
which supported it had lost its magnetism. This, however, is not the 
case, for the key would be again supported if the first magnet were pre¬ 
sented to it after the removal of the second bar. 

The attraction which a magnet exerts upon iron is reciprocal, which is 
indeed a general principle of all attractions. It is easily verified by pre¬ 
senting a mass of iron to a moveable magnet, when the latter is attracted. 

595. Hypothesis of two mag-netic fluids.— In order to explain 
the phenomena which have been described, the existence of two hypo¬ 
thetical magnetic fluids has been assumed, each of which acts repulsively 
on itself, but attracts the other fluid. The fluid predominating at the 
north pole of the magnet is called the north or boreal fluid, and that at the 
south pole, the south or austral fluid. Sometimes the terms positive and 
negative are employed, corresponding to the north and south fluids. 

It is assumed that, before magnetisation, these fluids are combined 
round each molecule, and mutually neutralise each other; they can 
be separated by the influence of a force greater than that of their mutual 
attraction, and can arrange themselves round the molecules to which 
they are attached, but cannot be removed from them. 

The hypothesis of the two fluids is very convenient in explaining 
magnetic phenomena, and will be adhered to in what follows. But it 
must not be regarded as anything more than an hypothesis, and it will 
afterwards be shown that magnetic phenomena appear to result from 
electrical currents, circulating in magnetic bodies; a mode of view which 
connects the theory of magnetism with that of electricity. 

596. Precise definition of poles.— By the aid of the preceding 
hypothesis we are enabled to obtain a clearer idea of the distribution of 
the magnetism in a magnetised bar, and to account for the circumstance 




560 


ON MAGNETISM. 


[ 597 - 


that there is no free magnetism in the middle of the bar, and that it is 
strongest at the poles. If AB (fig. 446) represent a magnet, then the 
alternate black and white spaces may be taken to represent the position 
of the magnetic fluids in a series of particles after magnetisation; in 


s n s n s 


TW^JWEJWTJWCJmZJm2\ 
1HDHDHDHDHDHDI 

] HDHDHDHDHD BO 

1HDHDHD 

Fig. 446. 



accordance with what has been said, the white spaces representing the 
south fluid all point in one direction, and the north fluid in the oppo¬ 
site direction. The last half of the terminal molecule at one end would 
have north polarity, and at the other south polarity. Let N represent 
the north pole of a magnetic needle placed near the magnet AB; then 
the south fluid, .<?, in the terminal molecule would tend to attract N, 
and the north fluid n would tend to repel it; but as the molecule of 
south fluid s is nearer N than the molecule of north fluid n, the attrac¬ 
tion between s and N would be greater than the repulsion between n and 
N. Similarly the attraction between s' and N would be greater than the 
repulsion between n' and N, and so on with the following s" and n" etc. 
And all these forces would giye a resultant tending to attract N, whose 
point of application would have a certain fixed position, which would be 
the south pole of AB. In like manner it might be shown that the 
resultant of the forces acting at the other end of the bar would form a 
north pole, and would hence repel the north pole of the needle, but 
would attract its south pole. 

That such a series of polarised particles really acts like an ordinary 
magnet may be shown by partly filling a glass tube with steel filings, 
and passing the pole of a strong magnet five or six times along the 
outside in one constant direction, taking care not to shake the °tube. 
The individual filings will thus be magnetised, and the whole column 
of them presented to a magnetic needle will attract and repel its poles 
just like an ordinary bar magnet, exhibiting a north pole at one end, 
a south pole at the other, and no polarity in the middle; but on shaking 
the tube, or turning out the filings, and putting them in again so as to 
destroy the regularity, every trace of polarity will disappear. 

It appears hence that the polarity at each end of a magnet is caused 
by the fact that the resultant action on a magnetic body is strongest 
near the ends, and does not arise from an accumulation of the magnetic 
fluids at the ends. 

597. Experiment with broken magmets.— That the magnetic 





PROPERTIES OF MAGNETS. 


561 


-598] 

fluids are present in all parts of the bar, and not simply accumulated at 
the ends, is also evident from the following experiment. A steel knit¬ 
ting-needle is magnetised by friction with one of the poles of a magnet, 
and then the existence of the two poles and of the neutral line having 
been ascertained by means of iron filings, it is broken in the middle. 
But now, on presenting successively the two halves to a magnet, each 
will be found to possess two opposite poles and a neutral line, and in 
fact is a perfect magnet. If these new magnets are broken in turn in 
two halves, each will be a complete magnet with its two pole§ and 
neutral line, and so on, as far as the division can be continued. It is, 
therefore, concluded by analogy that the smallest parts of a magnet, 
the ultimate molecules, contain the two fluids. 

This experiment proves also that the magnetic fluids are not neutralised, 
but are simply latent; for if they had been neutralised, they would not 
have been set at liberty by the separation of the two particles. This pro¬ 
perty which we attribute to the two magnetisms, of becoming latent 
without being previously neutralised, is illustrated in the experiment 
with the two magnets and a key described in article 594. 

598. Magnetic induction.— When a magnetic substance is placed in 
contact with a magnet, the two fluids of the former become separated; and 
so long as the contact remains, it is a complete magnet, having its two 
poles and its neutral line. For instance, if a small cylinder of soft iron, 
ab (fig. 447), be placed in contact with one of the poles of a magnet, the 
cylinder can in turn support a second cylinder; this in turn a third, and 
so on, to as many as seven or eight, according to the power of the magnet. 



Each of these little cylinders is a magnet; it it be the north pole of tbe 
magnet to which the cylinders are attached, the part a will have south, 
and b north magnetism; b will in like manner develope in the nearest end 
of the next cylinder south magnetism, and so on. But these cylinders 
are only magnets so long as the influence of a magnetised bar continues. 
For, if the first cylinder be removed from the magnet, the other cylinders 
immediately drop, and retain no trace of magnetism. The separation of 
the two fluids is only momentary, which proves that the magnet yields 
nothing to the iron. Nickel also becomes magnetised under the influence 
of a strong magnet. 


b b 3 





562 


ON MAGNETISM. 


[ 599 - 

This action, in virtue of which a magnet can develope magnetism in 
iron, is called magnetic induction or influence, and it can take place without 
actual contact between the magnet and the iron, as is seen in the follow¬ 
ing experiment. A bar of soft iron is held with one end near a magnetic 
needle. If now the north pole of a magnet be approached to the iron 
without touching it, the needle will be attracted or repelled, according as 
its south or north pole is near the bar. For the north pole of the magnet 
will develope south magnetism in the end of the bar nearest it, and, 
therefore, north magnetism at the other end, which would thus attract 
the south, but repel the north end of the needle. Obviously, if the other 
end of the magnet were brought near the iron, the opposite effects would 
be produced on the needle. 

Magnetic induction explains the formation of the tufts of iron filings 
which become attached to the poles of magnets. The parts in contact 
with the magnet are converted into magnets; these act inductively on the 
adjacent parts, these again on the following ones, and so on, producing a 
filamentary arrangement of the filings. 

599. Coercive force. —We have seen from the above experiments 
that soft iron becomes instantaneously magnetised under the influence 
of a magnet, but that this magnetism is not permanent, and ceases 
when the magnet is removed. Steel likewise becomes magnetised by 
contact with a magnet, but the operation is effected with difficulty, 
and the more so as the steel is more highly tempered. Placed in 
contact with a magnet a steel bar acquires magnetic properties very 
slowly, and to make the magnetism complete, the steel must be 
rubbed with one of the poles. But this magnetism, once evoked in 
steel, is permanent, and does not disappear when the inducing force is 
removed. 

These different effects in soft iron and steel are ascribed to a coercive 
force, which, in a magnetic substance, offers a resistance to the separation 
of the two fluids, but which also prevents their recombination when once 
separated. In steel this coercive force is very great, in soft iron it is very 
small or even quite absent. By oxidation, pressure, or torsion, a certain 
amount of coercive force may be imparted to soft iron, as will be explained 
under magnetisation. 

600. Difference between magnets and magnetic substances.— 

Magnetic substances are substances which, like iron, steel, nickel, are 
attracted by the magnet. They contain the two fluids, but in a state of 
neutralisation. Compounds containing iron are usually magnetic, and the 
more so in proportion as they contain a larger quantity of iron. Some, 
however, like iron pyrites, are not attracted by the magnet. 

A magnetic substance is readily distinguished from a magnet. The 
former has no poles; if successively presented to the two ends of a mag- 


TERRESTRIAL MAGNETISM. 


563 


- 601 ] 

netic needle, ah (fig. 444), it will attract both ends equally, while a magnet 
would attract the one, but repel the other. Magnetic substances also have 
no action on each other, while magnets attract or repel each other, ac¬ 
cording as unlike or like poles are presented. 

Iron is not the only substance which possesses magnetic properties; 
nickel has considerable magnetic power, but far less than that of iron; 
cobalt is less magnetic than nickel; while to even a slighter extent 
chromium and manganese are magnetic. It is remarkable, however, 
that magnets cannot be formed with these substances. They are attracted 
by a magnet, but contrary and permanent poles cannot be imparted to 
them. 

In speaking of electricity, we shall see that powerful magnets exert a 
peculiar influence on all substances. 


CHAPTER II. 


TERRESTRIAL MAGNETISM. COMPASSES. 


601. Directive action of the earth on magnets. —When a mag¬ 
netised needle is suspended by a thread, as represented in fig. 444 
or when placed on a pivot on which it can move freely (fig. 448), it 
ultimately sets in a position which is more or less north and south. 
If removed from this position, it always 

returns to it after a certain number of F 

oscillations. 

Analogous observations have been 
made in different parts of the globe, 
from which the earth has been com¬ 
pared to an immense magnet, whose 
poles are very near the terrestrial poles, 
and whose neutral line virtually coin¬ 
cides with the equator. 

The polarity in the northern hemi¬ 
sphere is called the northern or boreal 
polarity, and that in the southern 
hemisphere the southern or austral 
polarity. In French works the end of the needle pointing north is 
called the austral or southern pole, and that pointing to the south, the 
boreal or northern pole; a designation based on this hypothesis of a 
terrestrial magnet, and on the law that unlike magnetisms attract each 
Other. In practice it will be found more convenient to use the English 
names, and call that end of the magnet which points to the north the 









5G4 


ON MAGNETISM. 


[ 602 - 

north pole, and that which points to the south the south pole. That end 
of the needle pointing north is in England sometimes spoken of as the 
marked end of the needle. 

602. Terrestrial magnetic couple.— From what has been stated, 
it is clear that the magnetic action of the earth on a magnetised needle 
may be compared to a couple, that is, to a system of two equal forces, 
parallel, but acting in contrary directions. 

For let ah (fig. 449) be a moveable magnetic needle making an angle with 
the magnetic meridian MM' (603). The earth’s north pole acts at¬ 
tractively on the marked pole, a, and repulsively on the other pole, b, and 


77 



two contrary forces are produced, an, and bn', which are equal and parallel; 
for the terrestrial pole is so distant, and the needle so small, as to justify 
the assumption that the two directions an and bn' are parallel, and that the 
two poles are equidistant from the earth’s north pole. But the earth’s 
south pole acts similarly on the poles of the needle, and produces two other 
forces, as and bs', which are also equal and parallel, but the two forces 
an and as may be reduced to a single resultant «N (33), and the forces 
bn' and bs' to a resultant bS ; these two forces aN and bS are equal, parallel, 
and act in opposite directions, and they constitute the terrestrial magnetic 
couple ; it is this couple which makes the needle set ultimately in the mag¬ 
netic meridian, a position in which the two forces N and S are in equili¬ 
brium. 

The force which determines the direction of the needle thus is 
neither attractive nor repulsive, but simply directive. If a small 
magnet be placed on a cork floating in water, it will at first oscillate, 
and then gradually move into a line which is virtually north and south. 
But if the surface of the water be quite smooth, the needle will not 
move either towards the north or towards the south.. 

If, however, a magnet be approached to the floating needle, attraction 
or repulsion ensues, according as one or the other of the poles is pre¬ 
sented. The reason of the different actions exerted by the earth and 
by a magnet on a floating needle is as follows. When the north pole, 
for instance, of the magnet is presented to the south pole of the needle, 
the latter i3 attracted ; it is, however, repelled by the south pole of the 
baagnet. Now, the force of magnetic attraction or repulsion decreases 




TERRESTRIAL MAGNETISM. 


565 


- 604 ] 

with the distance, and as the distance between the south pole of the 
needle and the north pole of the magnet is less than the distance 
between the south pole of the needle and the south pole of the magnet, 
the attraction predominates over the repulsion, and the needle moves 
towards the magnet. But the earth’s magnetic north pole is so distant 
from the floating needle that its length may be considered infinitely 
small in comparison, and one pole of the needle is just as strongly 
repelled as the other is attracted. 

603. Magnetic meridian, declination. —The geographical meridian 
of a place is the imaginary plane passing through this place and through 
the two terrestrial poles, and the meridian is the outline of this plane upon 
the surface of the globe. Similarly the magnetic meridian of a place is 
the vertical plane passing at this place through the two poles of a move- 
able magnetic needle in equilibrium about a vertical axis. 

In general the magnetic meridian does not coincide with the geo¬ 
graphical meridian, and the angle which the magnetic makes with the 
geographical meridian, or, what is the same thing, the angle which the 
direction of the needle makes with the meridian, is called the declination 
or variation of the magnetic needle. The declination is said to be east or 
west , according as the north pole of the needle is to the east or west of 
the geographical meridian. 

604. Variations in declination. —The declination of the magnetic 
needle, which varies in different places, is at present west in Europe 
and in Africa, but east in Asia, and in North and South America. 
It shows further considerable variations even in the same place; 
these variations are of two kinds; some are regular, and are either 
secular, annual, or diurnal; others, which are irregular, are called 
perturbations. 

Secular variations. —In the same place, the declination varies in the 
course of time, and the needle appears to make oscillations to the east 
and west of the meridian, the duration of which is several centuries. 
The declination has been known at Paris since 1580, and the following 
table represents the variations which it has undergone:— 


Year. Declination. Year. Declination. 

1580 ..... 11° 30' E. 1825 . 22° 22' W. 

1663 ..... 0 1830 . 22° 12' W. 

1700 . 8° 10' W. 1835 . 22° 4'W. 

1780 . 19° 55' W. 1850 . 20°30'W. 

1785 . 22° W. 1855 . 19°57'W. 

1805 . 22° 5'W. 1860 . 19°32'W. 

1814.22°34'W. 1865 . 18° 44' W. 


This table shows that since 1580 the declination has varied at Paris 
as much as 34°, and that the greatest declination was attained in 1814, 
since which time the needle has gradually tended towards the east. 













566 


ON MAGNETISM. 


[ 605 - 

At London, the needle showed in 1580 an east declination of 11° 36'; 
in 1663 it was at zero; from that time it gradually tended towards the 
west, and reached its maximum declination of 24° 41' in 1818; since then 
it has steadily diminished; it was 22° 30' in 1850, and is now (1868) 20° 
10' W. 

At Yarmouth and Dover the variation is about 40' less than at London; 
at Hull and Southampton about 20' greater; at Newcastle and Swansea 
about 1° 15', and at Liverpool 1° 30', at Edinburgh 2° 5', and at Glasgow 
and Dublin about 2° 25', greater than at London. 

In certain parts of the earth the magnetic coincides with the geo¬ 
graphical meridian. These points are connected by an irregularly curved 
imaginary line, called a line of no variation , or agonic line. Such a line 
cuts the east of South America, and, passing east of the West Indies, 
enters North America, near Philadelphia, and traverses Hudson’s Bay; 
thence it passes through the North Pole, entering the Old World east of 
the White Sea, traverses the Caspian, cuts the east of Arabia, turns then 
towards Australia, and passes through the South Pole, to join itself 
again. 

Isogonic lines are lines connecting those places on the earth's surface in 
which the declination is the same. The first of the kind was constructed 
in 1700 by Halley; as the elements of the earth’s magnetism are 
continually changing, the course of such a line can only be determined 
for a certain time. One of the newest has been constructed by Captain 
Evans for the year 1857, and is given in the British Association Keport 
for 1861. 

605. Annual variations.— Cassini first discovered in 1780 that the 
declination is subject to small annual variations. At Paris and London 
it is greatest about the vernal equinox, diminishes from that time to the 
summer solstice, and increases again during the nine following months. 
It does not exceed from 15' to 18', and it varies somewhat at different 
epochs. 

The diurnal variations were first discovered by Graham in 1722; they 
can only be observed by means of long needles and very delicate instru¬ 
ments. In this country the north pole moves every day from east to 
west from sunrise until one or two o’clock, it then tends towards the 
east, and at about ten o’clock regains its original position. During the 
night the needle is almost stationary. Thus the westerly declination is 
greatest during the warmest part of the day. 

At Paris the mean amplitude of the diurnal variation from April to 
September is from 13' to 15', and for the other months from 8' to 10'. 
On some days it amounts to 25', and on others does not exceed 5'. The 
greatest variation is not always at the same time. The amplitude of the 
daily variations decreases from the poles towards the equator, where 


COMPASSES. 


5G7 


-607] 

it is very feeble. Thus in the island of Rewak it never exceeds 
3' to 4'. 

606. Accidental variations or perturbations. —The declination is 
accidentally disturbed in its daily variations by many causes, such as 
earthquakes, the aurora borealis, and volcanic eruptions. The effect of 
the aurora is felt at great distances. Auroras which are only visible in 
the north of Europe act on the needle even in these latitudes, where 
accidental variations of 20' have been observed. In polar regions the 
needle frequently oscillates several degrees ; its irregularity on the day 
before the aurora borealis is a presage of the occurrence of this phe¬ 
nomenon. 


Fig. 450. 



Another remarkable phenomenon is the miscellaneous occurrence of 
magnetic perturbations in very distant countries. Thus Sabine mentions 
a magnetic disturbance which was felt simultaneously at Toronto, the 
Cape, Prague, and Van Diemen’s Land. Such simultaneous perturbations 
have received the name of magnetic storms. 

(507. Declination compass. —The declination compass is an instru- 







568 


ON MAGNETISM. 


[ 608 - 

ment by which the magnetic declination of any place may be measured 
when its astronomical meridian is known. It consists of a brass box, AB 
(fig. 450), in the bottom of which is a graduated circle, M. In the centre 
is a pivot, on which oscillates a very light lozenge-shaped magnetic needle, 
ab. To the box are attached two uprights supporting a horizontal axis, 
X, on which is fixed an astronomical telescope, L, moveable in a vertical 
plane. The box rests on a foot, P, about which it can turn in a hoiizontal 
plane, taking with it the telescope. A fixed circle, QR, which is called 
the azimuthal circle , serves to measure the number of degrees through 
which the telescope has been turned, by means of a vernier, V, fixed to 
the box. The inclination of the telescope, in reference to the horizon, 
may be measured by another vernier, K, which moves with the axis of the 
telescope, and is read off on a fixed graduated arc, x. 

When the astronomical meridian is known, the first thing in deter¬ 
mining the declination is to range the compass horizontally by means of 
the screws, SS, and the level, n. The box, AB, is then turned until the 
telescope is in the plane of the astronomical meridian. The angle made 
by the magnetic needle with the diameter, N, which corresponds with 
the zero of the scale, and is exactly in the plane of the telescope, is then 
read off on the graduated limb, and this is east or west, according as the 
pole, a , of the needle stops at the east or west of the diameter, N. 

608. IVXetbod of reversion. —These applications of the compass are 
only correct when the magnetic axis of the needle, that is, the right line 
passing through the two poles, coincides with its axis of figure, or the 
line connecting its two ends. This is not usually the case, and a correc¬ 
tion must therefore be made, which is done by the method of reversion. 
For this purpose the needle is not fixed in the cap, but merely rests on 
it, so that it can be removed and its position reversed; thus what was 
before the lower is now the upper face. The mean between the obser¬ 
vations made in the two cases gives the true declination. 

609. Mariner’s compass. —The magnetic action of the earth has 
received a most important application in the mariner's compass. This is 
a declination compass used in guiding the course of a ship. Figure 451 
represents it enclosed in a rectangular box, placed in a larger box called 
the binnacle, and which is fixed on the deck in the after part of the vessel. 
Figure 452 represents a vertical section, and the same letters indicate the 
same parts in the two figures. 

The needle ah (fig. 452), which moves very easily on a pivot, is fixed 
to the lower part of a leaf of mica, t, on which is traced a star or rose 
with 32 branches marking the eight points or rhumbs of the wind, the 
semi-rhumbs, and the quarters. To keep the compass in a horizontal 
position, in spite of the rolling of the ship, it is supported on yimbalds. 
These are two concentric rings, one of which moves about the axis cd, 


MAGNETIC INCLINATION. 


569 


- 610 ] 

and rests in the box itself, the other moves about the axis xz , perpen¬ 
dicular to the tirst, and fitted in the ring fixed to the axis cd. 

M is a window of ground glass, by which the compass can be lighted, 
by means of a lamp placed outside the box. The bottom of the cylin¬ 
drical box, O, in which is the needle, is of glass, and gives passage to 
the light, by which the mica plate, t, is illuminated. The compass is 



. Fig. 451. Fig. 452. 


enclosed by a second glass, m, and on a pivot, i, in its centre can be fixed 
a sight vane, A, when the bearing of the land is to be taken. 

Neither the inventor of the compass nor the exact time of its invention 
is known. Guyot de Provins, a French poet of the twelfth century, first 
mentions the use of the magnet in navigation, though it is probable that 
the Chinese long before this had used it. The ancient navigators who 
were unacquainted with the compass, had only the sun or pole star as a 
guide, and were accordingly compelled to keep constantly in sight of land 
for fear of steering in a wrong direction when the sky was clouded. 

610. Inclination. Magnetic equator. —It might be supposed from 
the northerly direction which the magnetic needle takes that the force 
acting upon it is situated in a point of the horizon : this is not the case, 
for if the needle be so arranged that it can move freely in a vertical 
plane about a horizontal axis, it will be seen that, although the centre of 
gravity of the needle coincides with the centre of suspension, the north 
pole in our hemisphere dips downwards. In the other hemisphere the 
south pole is inclined downwards. 

The angle, which the magnetic needle makes with the horizon, when 
the vertical plane, in which it moves, coincides with the magnetic 
meridian, is called the inclination or dip of the needle. In any other 
plane than the magnetic meridian, the inclination increases, and is 90° 


































570 


ON MAGNETISM. 


[ 611 - 

in a plane at right angles to the magnetic meridian. For the magnetic 
inclination is the resultant of two forces, one acting in a horizontal and 
the other in a vertical plane. When the needle is moved so that it is 
at right angles to the magnetic meridian, the horizontal component can 
only act in the direction of the axis of suspension, and, therefore, cannot 
affect the needle, which is then solely influenced by the vertical com¬ 
ponent, and stands vertically. 

The value of the dip, like that of the declination, differs in different 
localities. It is greatest in the polar regions, and decreases with the 
latitude to the equator, where there is a series of points at which it is 
zero. In London at the present time (1868) the dip is 67° 57', reckoning 
from the horizontal line. In the southern hemisphere the inclination is 
again seen, but in a contrary direction, that is, the south pole of the 
needle dips below the horizontal line. 

The magnetic poles are those places in which the dipping needle stands 
vertical, that is, where the inclination is 90°. In 1830 the first of these, 
the terrestrial north pole, was found by Sir James Ross, in 96° 43' west 
longitude and 70° north latitude. The same observer found in the South 
Sea, in 76° south latitude and 168° east longitude, that the inclination 
was 88° 37'. From this and other observations, it has been calculated 
that the position of the magnetic south pole was at that time in about 
154° east longitude and 75£° south latitude. 

The line of no declination passes through these points, and the lines of 
equal declination converge towards them. 

The magnetic equator or aclinic line is the line which joins all those 
places on the earth where there is no dip, that is, all those in which the 
dipping needle is quite horizontal. It is a somewhat sinuous line, not 
differing much from a great circle inclined to the horizon at an angle of 
12°, and cutting it on two points almost exactly opposite each other, one 
in the Atlantic, and one in the Pacific. These points appear to be gradu¬ 
ally moving their position, and travelling from east to west. 

Lines connecting places in which the dipping needle makes equal 
angles are called isoclinic lines. 

The inclination is subject to secular variations, like the declination. 
At Paris, in 1671, the inclination was 75°; since then it has been con¬ 
tinually decreasing, and in 1859 was 66° 14'. In London also the dip 
has continually diminished since 1720 by about 2-6' per annum. In 
1821 it was 70° 3'; in 1838, 69° 17'; in 1854 it was 68° 31'; in 1859 it 
was 68° 21' j it is now (1868) 67° 57'. It is also subject to slight annual 
and diurnal variations j being, according to Hanstein, about 15' greater 
in summer than in winter, and 4' or 5' greater before noon than after. 

611. Inclination compass.— An inclination compass is an instrument 
for measuring the magnetic inclination or dip. It consists of a graduated 


MAGNETIC INCLINATION. 


571 


- 611 ] 

horizontal brass circle, m (fig. 453), supported on three legs, provided 
with levelling screws. Above this circle there is a plate, A, moveable 
about a vertical axis, and supporting by means of two columns a second 
graduated circle, M, which measures the inclination. The needle rests 
on a frame, r, and the diameter passing through the two zeros of the 
circle, M, can be ascertained to be perfectly horizontal by means of the 
spirit level, n. 

To observe the inclination, the magnetic meridian must first be deter¬ 
mined, which is effected by turning the plate A on the circle m, until the 
needle is vertical, which is the case when it is in a plane at right angles 



Fig. 453. 


to the magnetic meridian (610). The plate A is then turned 90° on the 
circle m, by which the vertical circle, M, is brought into the magnetic 
meridian. The angle, dca , which the magnetic needle makes with the 
horizontal diameter, is the angle of inclination. 

There are here two sources of error, which must be allowed for:— 
1. The magnetic axis of the needle may not coincide with its axis of figure: 
hence, an error which is corrected by a method of reversion analogous to 
that already described (608). 2. The centre of gravity of the needle 
may not coincide with the axis of suspension, and then the angle, dca , is 
too great or too small, according as the centre of gravity is below or 












572 


ON MAGNETISM. 


f 612 - 


above the centre of suspension; for in the first case the action of gravity 
is in the same direction as that of magnetism, and in the second is in 
the opposite direction. To correct this error the poles of the needle 
must be reversed by first demagnetising it, and then imparting a contrary 
magnetism to what it had at first. The inclination is now redetermined, 
and the mean taken of the results obtained in the two groups of operations. 

612. Astatic needle and astatic system.— An astatic needle is one 
which is uninfluenced by the earth’s magnetism. A needle moveable 
about an axis in the plane of the magnetic meridian and 
parallel to the inclination would be one of this kind; 
for the terrestrial magnetic couple acting then in the 
direction of the axis cannot impart to the needle any 
determinate direction. 

An astatic system is a combination of two needles of 
the same force joined parallel to each other with the 
poles in contrary directions, as shown in figure 454. 
If the two needles have exactly the same magnetic 
force, the opposite actions of the earth’s magnetism on 
the poles a' and b, and on the poles a and b' counter¬ 
balance each other; the system is then completely astatic, 
and sets at right angles to the magnetic meridian. 

A single magnetic needle may also be rendered astatic by placing a 
magnet near it. By repeated trials a certain position and distance can 
be found at which the action of the magnet on the needle just neutralises 
that of the earth’s magnetism, and the needle is free to obey any third 
force. 



Fig. 454. 


613. Intensity of the earth’s magnetism.— If a magnetic needle 
be moved from its position of equilibrium, it will revert to it after a series 
of oscillations, which follow laws analogous to those of the pendulum 
(71). If the magnet be removed to another place, and caused to oscillate 
during the same length of time as the first, a different number of oscilla¬ 
tions will be observed. And the intensity of the earth’s magnetism in 
the two places will be respectively proportional to the squares of the 
number of oscillations. 

If at M the number of oscillations in a minute had been 25 = n , and 
at another place, M', 24 = we should have— 


Intensity of the earth’s magnetism at M_w 2 _625 

Intensity of the earth’s magnetism at M' n 7i 576 7 


That is, if the intensity of the magnetism at the second place is taken as 
unity, that of the first is 1-085. If the magnetic condition of the needle 
had not changed in the interval between the two observations, this 
method would give the relation between the intensities at the two places. 






-613 


INTENSITY OF TERRESTRIAL MAGNETISM. 


573 


In these determinations of the intensity, it would be necessary to have 
the oscillations of the dipping needle, which are produced by the whole 
force of the earth’s magnetism. These, however, are difficult to obtain with 
accuracy, and, therefore, the oscillations of the declination 
needle are usually taken. The force which makes the decli¬ 
nation needle oscillate is only a portion of the total magnetic 
force, and is smaller in proportion as the inclination is greater. 

If the line ac (fig. 455) = M represents the total intensity, 
the angle i the inclination, then the horizontal component 
ab is M cos i. Hence, to express the intensities in the two 
places by the oscillations of the declination needle, we must 
substitute in the preceding equation the values M cos i 
and M' cos %' for M and M', and we have— 

M cos i ra' 2 

M' cos i' n /2 ‘ 

The magnetic intensity increases with the latitude. Humboldt found a 
point of minimum intensity on the magnetic equator in Northern Peru. 
This value is generally taken as the unit to which magnetic intensities 


other places are referred, as in the following table :— 

Locality. Date. Latitude 

Magnetic 

Intensity. 

St. Anthony . 

. 

. 1802 

0-0° 

1-087 

Carthagena 


. 1801 

10-25 N. 

1-294 

Naples . 


. 1805 

40-50 

1-274 

Paris 


. 1800 

48-52 

1-348 

Berlin 


. 1829 

52-51 

1-366 

Petersburg 


. 1828 

59-66 

1-410 

Spitzbergen . 


. 1823 

79-40 

1-567 


The lines connecting places of equal intensity are called isodynamic 
lines. They are not parallel to the magnetic equator, but appear to have 
about the same direction as the isothermal lines. 

According to Kuppfer, the intensity appears to diminish at greater 
heights ; a needle which made one oscillation in 24'' vibrated more slowly 
by 001" at a height of 1,000 feet: but, according to Forbes, the intensity 
is only less at a height of 3,000 feet. 

The intensity varies in the same place with the time of day; it attains 
its maximum between 4 and 5 in the afternoon, and is at its minimum 
between 10 and 11 in the morning. 

It is probable, though it has not yet been ascertained with certainty, 
that the intensity undergoes secular variations. From measurements of 
the total force made monthly at Kew between 1857 and 1862, it appeared 
that the total force experienced a very slight annual increase. 

During the last few years great attention has been devoted to the 





“ c 
Fig. 455. 







574 


ON MAGNETISM. 


[ 614 - 

observation of the magnetic elements, and observatories for this purpose 
have been fitted up in different parts of the globe. These observations 
have led to the discovery that the magnetism of the earth is in a state of 
constant fluctuation like the waves of the sea. And in studying the 
variations of the declination, etc., the mean of a great number of obser¬ 
vations must be taken, so as to eliminate the irregular disturbances, and 
bring out the general laws. 

The observations made in the English magnetic observatories have 
been reduced by Sabine, and have revealed some curious facts in refe¬ 
rence to the magnetic storms. He finds that there is a certain periodicity 
in their appearance, and that they attain their greatest frequency about 
every ten years. 

Independently of this, Schwabe, a German astronomer, who had 
studied the subject many years, has found that the spots on the sun, seen 
on looking at it through a coloured glass, vary in their number, size, and 
frequency, but attain their maximum between every ten or eleven years. 
Now Sabine has established the interesting fact that the period of their 
greatest frequency coincides with the period of greatest magnetic dis¬ 
turbance. 


CHAPTER III. 

LAWS OF MAGNETIC ATTRACTIONS AND REPULSIONS. 

614. Laws of magnetic attractions and repulsions.— Coulomb 
discovered the remarkable law in reference to magnetism, that magnetic 
attractions and repulsions are inversely as the square of the distances. He 
proved this by means of two methods:—i. that of the torsion balance, and 
ii. that of oscillation. 

615. The torsion balance. —This apparatus depends on the prin¬ 
ciple that, when a wire is twisted through a* certain space, the angle of 
torsion is proportional to the force of torsion (80). It consists (fig. 456) 
of a glass case closed by a glass top, with an aperture near the edge, to 
allow the introduction of a magnet, A. In another aperture in the 
centre of the top a glass tube fits, provided at its upper extremity with 
a micrometer. This consists of two circular pieces: d, which is fixed, 
is divided on the edge into 360°, while on e, which is moveable, there is 
a mark, c, to indicate its rotation. D and E represent the two pieces of 
the micrometer on a larger scale. On E there are two uprights con¬ 
nected by a horizontal axis, on which is a very fine silver wire supporting 




- 615 ] LAWS OF MAGNETIC ATTRACTIONS AND REPULSIONS. 


575 


a magnetic needle, ab. On the side of the case there is a graduated scale, 
which indicates the angle of the needle ab, and hence the torsion of the wire. 

When the mark c of the 
disc E is at zero of the scale, 

T), the case is so arranged 
that the wire supporting the 
needle and the zero of the 
scale in the case are in 
the magnetic meridian. The 
needle is then removed from 
its stirrup, and replaced by an 
exactly similar one of copper, 
or any unmagnetic substance $ 
the tube, and with it the 
pieces D and E, are then 
turned so that the needle 
stops at zero of the gradua¬ 
tion. The magnetic needle, 
ab, being now replaced, is 
exactly in the magnetic meri¬ 
dian, and the wire exerts no 
torsion. 

Before introducing the mag¬ 
net, A, it is necessary to investigate the action of the earth’s magnetism 
on the needle ab, when the latter is removed out of the magnetic meridian. 
This will vary with the dimensions and force of the needle, with the di¬ 
mensions and nature of the wire, and with the intensity of the earth’s 
magnetism in that place. Accordingly, the piece E is turned until ab 
makes a certain angle with the magnetic meridian. Coulomb found in 
his experiments that E had to be turned 35° in order to move the needle 
through 1°; that is, the earth’s magnetism was equal to a torsion of the 
wire corresponding to 35°. As the force of torsion is proportional to the 
angle of torsion, when the needle is deflected from the meridian by 
2, 3 . . . degrees, the directive action of the earth’s magnetism is equal 
2, 3 . . . times 35°. 

The action of the earth’s magnetism having been determined, the 
magnet A is placed in the case so that similar poles are opposite each 
other. In one experiment Coulomb found that the pole a was repelled 
through 24°. Now the force which tended to bring the needle into the 
magnetic meridian was represented by 24°+ 24 X 35 = 864, of which the 
part 24° was due to the torsion of the wire, and 24 X 35° was the equi¬ 
valent in torsion of the directive force of the earth’s magnetism. As 
the needle was in equilibrium, it is clear that the repulsive force which 



Eig. 456. 











576 


ON MAGNETISM. 


[ 616 - 

counterbalanced those forces must he equal to 864°. The disc was then 
turned until ab made an angle of 12°. To effect this, eight complete 
rotations of the disc were necessary. The total force which now tended 
to bring the needle into the magnetic meridian was composed of: 1st, 
the 12° of torsion by which the needle was distant from its starting point; 
2nd, of 8 x 360° = 2880, the torsion of the wire; and, 3rd, the force of the 
earth’s magnetism, represented by a torsion of 12 x 35°. Hence, the 
forces of torsion which balance the repulsive forces exerted at a distance 
of 24° and of 12° are— 

24° ..... 864 

12°.3312 

Now, 3312 is very nearly four times 864; hence, for half the distance 
the repulsive force is four times as great. 

616. Method of oscillations. —A magnetic needle oscillating under 
the influence of the earth’s magnetism may be considered as a pendulum, 
and the laws of pendulum motion apply to it. The method of oscillations 
consists in causing a magnetic needle to oscillate first under the influence 
of the earth’s magnetism alone, and then successively under the combined 
influence of the earth’s magnetism, and of a magnet placed at unequal 
distances. 

The following determination by Coulomb will illustrate the use of the 
method. A magnetic needle was used which made 15 oscillations in a 
minute under the influence of the earth’s magnetism alone. A magnetic 
bar about 2 feet long was then placed vertically in the plane of the mag¬ 
netic meridian, so that its north pole was downwards and its south pole 
presented to the north pole of the oscillating needle. He found that at 
a distance of 4 inches the needle made 41 oscillations in a minute, and at 
a distance of 8 inches 24 oscillations. Now, from the pendulum laws (51), 
the intensity of the forces are inversely as the squares of the times of os¬ 
cillations. Hence, if we call M the force of the earth’s magnetism, m 
the attractive force of the magnet at the distance of 4 inches, rri at the 
distance of 8 inches, we have 

M : M + m = 15 2 : 41 2 , and 
M : M + m' = 15 2 : 24 2 , 

eliminating M 

m: m'= 41 2 - 15 2 : 24 2 —15 2 = 1456 : 351 
= 4:1 nearly, 

or m : m f = 4 : 1. 

In other words, the force acting at 4 inches is quadruple that which 
acts at double the distance. 

The above results do not quite agree with the numbers required by the 
law of inverse squares. But this could only be expected to apply in the 


PROCESSES OF MAGNETISATION. 


577 


- 619 ] 

case in which the repulsive or attractive force is exerted between two 
points, and not, as is here the case, between the resultant of a system of 
points. And it is to this fact that the discrepancy between the theo¬ 
retical and observed results is due. 

In the case of the torsion balance, one pole of the magnet to be tested 
was at so great a distance that it could not appreciably modify the action 
of the other. When the distance at which two magnets act is large as 
compared with their dimensions, the total action on one another is nearly 
inversely as the third power of the distances; which, it might be shown, 
is a necessary consequence of the law that the action of the magnetic 
elements is inversely as the square of the distance. 


CHAPTER IV. 

PROCESSES OF MAGNETISATION. 

617. Magnetisation. —The various sources of magnetism are the in¬ 
fluence of powerful magnets, terrestrial magnetism, and electricity. The 
latter method will he treated of subsequently; the three principal methods 
of magnetisation by magnets are that of single touch, that of separate 
touch, and that of double touch. 

618. Method of single touch.— This consists in moving the pole of 
a powerful magnet from one end to the other of the bar to be magnetised, 
and repeating this operation several times always in the same direction. 
The neutral fluid is thus gradually decomposed throughout all the length 
of the bar, and that end of the bar which was touched last by the magnet 
is of opposite polarity to the end of the magnet by which it has been 
touched. This method only produces a feeble magnetic power, and is, 
accordingly, only used for small magnets. It has further the disadvan¬ 
tage of frequently developing consequent points. 

619. Method of separate touch.— This method, which was first used 
by Dr. Knight in 1745, consists in placing the two opposite poles of two 
magnets of equal force in the middle of the bar to be magnetised, and 
in moving each of them simultaneously towards the opposite ends of the 
bar. Each magnet is then placed in its original position, and this opera¬ 
tion repeated. After several frictions on both faces the bar is mag¬ 
netised. 

In Knight’s method the magnets are held vertically. Duhamel per¬ 
fected the method by inclining the magnets, as represented in fig. 457: 
and still more, by placing the bar to be magnetised on the opposite poles 




578 


ON MAGNETISM. 


[620- 

of two fixed magnets, the action of which coincides with that of the 
moveable magnets. The relative position of the poles of the magnets 
is indicated in the figure. 



This method produces the most regular magnets. 

620. Method of double touch.— In this method, which was invented 
by Mitchell, the two magnets are placed with their poles opposite each 
other in the middle of the bar to be magnetised. But, instead of moving 
them in opposite directions towards the two ends, as in the method of 
separate touch, they are kept at a fixed distance by means of a piece of 
wood placed between them (fig. 457), and are simultaneously moved first 
towards one end, then from this to the other end, repeating this operation 
several times, and finishing in the middle, taking care that each half of 
the bar receives the same number of frictions. 

Epinus, in 1758, perfected this method by supporting the bar to be 
magnetised, as in the method of separate touch, on the opposite poles of 
two powerful magnets, and by inclining the bars at an angle of 15° to 
20°. Powerful magnets are obtained in this way, but they have frequently 
consequent points. 

621. Magnetisation by the action of the earth.— The action of the 
earth on magnetic substances resembles that of a magnet, and hence the 
terrestrial magnetism is constantly tending to separate the two fluids which 
are in the neutral state in soft iron and in steel. But, as the coercive force 
is very considerable in the latter substance, the action of the earth is in¬ 
adequate to produce magnetisation, except when continued for a long time. 
This is not the case with perfectly soft iron. When a bar of this metal 
is held in the magnetic meridian parallel to the inclination, the neutral 
fluid is immediately decomposed, and the bar becomes endowed with 
feeble magnetic polarity. The lower extremity is a north pole, and if the 
north pole of a small magnetic needle be approached, it will be repelled. 
This magnetism is very unstable, for if the bar be turned, the poles are 
inverted, as pure soft iron is destitute of coercive force. 

While the bar is in this position, a certain amount of coercive force 
may be imparted to it by giving it several smart blows with a hammer, 
and the bar retains for a short time the magnetism which it has thus ob¬ 
tained. But the coercive force thus developed is very small, and after a 
time the magnetism disappears. 









- 622 ] 


MAGNETISATION. 


579 


If a piece of soft iron be twisted while held vertically, or, better, in the 
line of the dip, it acquires a feeble magnetism. 

It is this magnetising action of the earth which developes the magne¬ 
tism frequently observed in steel and iron instruments, such as fire irons, 
railings, lightning conductors, etc., which remain for some time in a more 
or less inclined position. They become magnetised with their north pole 
downward, just as if placed over the pole of a powerful magnet. The 
magnetism of native black oxide of iron has doubtless been produced by 
the same causes; the very different magnetic power of different specimens 
being partly attributable to the different positions of the veins of ore 
with regard to the line of dip. The ordinary irons of commerce are not 
quite pure, and possess a feeble coercive force ; hence a feeble magnetic 
polarity is generally found to be possessed by the tools in a smith’s shop. 
Cast-iron, too, has usually a great coercive force, and can be permanently 
magnetised. 

The turnings, too, of wrought iron and of steel produced by the power¬ 
ful lathes of our ironworks are found to be magnetised. 

622. Saturation. —Experiment has shown that to a certain extent 
the magnetic force which can be imparted to a bar or needle increases 
with the power of the magnets used. 

But there is a limit to the magnetic 
force which can be imparted to a bar 
or needle, and when this is attained, 
the bar is said to be saturated oi 
magnetised to saturation. A bar may 
indeed be magnetised beyond this 
point, but this is not permanent; it 
gradually diminishes until it has sunk 
to the point of saturation. 

This is readily intelligible, for the 
magnetisms once separated tend to 
reunite, and when their attractive 
force is equal to that which opposes 
their saturation, that is, the coercive 
force of the metal, equilibrium is 
attained, and the magnet is saturated. 

Hence, more magnetism ought to be 
developed in bars than they can retain, 
in order that they may decline to their 
permanent state of saturation. To 
increase the magnetism of an unsa- 

turated bar, a less feeble magnet must not be used than that by which it 
was originally magnetised. 

c c 2 



Fig. 458. 

































580 


ON MAGNETISM. 


[ 623 - 

023. Magnetic battery. —A magnetic battery or magazine consists of 
a number of magnets joined together by their similar poles. Sometimes 
they have the form of a horse-shoe, and sometimes a rectilinear form. 
The battery represented in fig. 458 consists of five superposed steel plates. 
That in fig. 459 consists of twelve plates, arranged in three layers of four 
each. The horse-shoe form is best adapted for supporting a weight, for 
then both poles are used at once. In both the bars are magnetised sepa¬ 
rately, and then fixed by screws. 

The force of a battery is not equal to the sum of the forces of each bar, 
owing to the repulsive action exerted by each bar on the adjacent ones. 
The force is increased by making the lateral plates 1 or 2 centimeters 
shorter than the one in the middle (fig. 458). 

624. Armatures. —When even a steel bar is at its limit of saturation, 
it gradually loses its magnetism. To prevent this, armatures or keepers 
are used: these are pieces of soft iron, A and B (fig. 459), which are 



Fig. 459. 


placed in contact with the poles. Acted on inductively, they become 
magnets, and react in turn on the magnetism of the bars, preserving and 
even increasing it. 

When the magnets are in the form of bars, they are arranged in pairs, 
as shown in fig. 460, with opposite poles in juxta-position, and the circuit 



Fig. 460. 


is completed by two small bars of soft iron, AB. Moveable magnetic 
needles set spontaneously towards the magnetic poles of the earth, the 
influence of which acts as a keeper. 

A horse-shoe magnet has a keeper attached to it, which is usually ar¬ 
ranged so as to support a weight. The keeper becomes magnetised under 
the influence of the two poles, and adheres with great force ; the weight 
which it can support being much more than double that which a single 
pole would hold. 

In respect to this weight, a singular and hitherto inexplicable pheno¬ 
menon has been observed. When contact is once made, and the keeper 
is charged with its maximum weight, any further addition would detach 
it; but if left in contact for a day, an additional weight may be added 









MAGNETISATION. 


581 


-626] 

without detaching it, and by slightly increasing the weight every day, 
it may ultimately be brought to support a far greater load than it would 
originally. But if contact be once broken, the weight it can now support 
does not exceed its original charge. 

In providing a natural magnet with a keeper, 
the line joining the two poles is first approxi¬ 
mately determined by means of iron filings. 

Two plates of soft iron (fig. 461), each termi¬ 
nating in a massive shoe, are then applied to the 
faces corresponding to the poles. Under the 
influence of the natural magnet, these plates 
become magnetised, and if the letters A and B 
represent the position of the poles of the natural 
magnet, the poles of the armature are a and b. 

These armatures, once magnetised, react on the 
neutral fluid of the natural magnet, decomposing 
it, and increasing its natural power. Without 
armatures natural magnets are very feeble, but 
armed they can support a weight which gradually 
increases to a certain limit, which they cannot 
exceed. 

625. Portative Force. —The portative force is the weight which a 
magnet can support, and numerous experiments have been made upon 
it by Hacker. He found that the portative force of a saturated horse-shoe 
magnet, which, by repeatedly detaching the keeper, has become constant, 
may be represented by the formula 

p = a yy; 

in which P is the portative force of the magnet, p its own weight, and 
a a coefficient, which varies with the nature of the steel and the mode of 
magnetising. It follows from this that a magnet which weighs 1000 
ounces only supports 25 times as much as one weighing 8 ounces or ~ 
as heavy, and 125 such bars would support as much as one which is as 
heavy as all together. It appears immaterial whether the section of 
the bar is quadratic or circular, and the distance of the legs is of in¬ 
considerable moment; it is important, however, that the magnet 
be suspended vertically, and that the load be exactly in the middle. 
In Hacker’s magnets the value of a was 10-33, while in Logemann’s it 
was 23. 

626. Circumstances which influence the power of magnets.— 

All bars do not attain the same state of saturation, for their coercive force 
varies. Twisting or hammering imparts to iron or steel a considerable co¬ 
ercive force. But the most powerful of these influences is the operation 
of tempering (85). Coulomb found that a steel bar tempered at dull 






582 


ON MAGNETISM. 


[626- 

redness, and magnetised to saturation, made ten oscillations in 93 seconds. 
The same bar tempered at a cherrj-red heat, and similarly magnetised to 
saturation, only took 63 seconds to make ten oscillations. 

Hence, the harder the steel the greater is its coercive force; it receives 
magnetism with much greater difficulty, but retains it more effectually. 
Very hard steel bars have, however, the disadvantage of being very brittle, 
and in the case of long thin bars, a hard tempering is apt to produce con¬ 
sequent points. Compass needles are usually tempered at the blue heat, 
that is, about 300° C., by which a high coercive force is obtained without 
great fragility. 

Increase of temperature always produces a diminution of magnetic 
force. If the changes of temperature are small, those of the atmosphere, 
for instance, the magnet is not permanently altered. Kupfer allowed a 
magnet to oscillate at different temperatures, and found a definite decrease 
in its power with increased temperature, as indicated by its slower 
oscillations. In the case of a magnet 2£ inches in length, he observed 
that with an increase of each degree of temperature the duration of 800 
oscillations was 04'' longer. If n be the number of oscillations at zero, 
and n l the number at t , then 

n t =n (1 — ct), 

where c is a constant depending in each case on the magnet used. This 
formula has an important application in the correction of the observations 
of magnetic intensity which are made at different places and at different 
temperatures, and which, in order to be comparable, must first be reduced 
to a uniform temperature. 

When a magnet has been more strongly heated, it does not regain its 
original force on cooling to its original temperature, and when it has been 
heated to redness, it is demagnetised. This was first shown by Coulomb, 
who took a saturated magnet, and progressively heated it to higher 
temperatures, and observed the number of oscillations after each heating. 
The higher the temperature to which it had been heated the slower its 
oscillations. 

A magnet heated to bright redness loses its magnetism so completely 
that it is quite indifferent, not only towards iron, but also towards 
another magnet. Incandescent iron also does not possess the property of 
being attracted by the magnet. Hence there is in the case of iron a 
magnetic limit , beyond which it is unaffected by magnetism. Such a 
magnetic limit exists in the case of other magnetic metals. With cobalt , 
for instance, it is far beyond a white heat, for at the highest temperatures 
hitherto examined it is still magnetic; the magnetic limit of chromium is 
somewhat below red heat; that of nickel at about 350° C., and of manga¬ 
nese at about 15° to 20° C. It is conceivable that some substances, which 


MAGNETISATION. 


-627] 


583 


at ordinary temperatures are unmagnetic, would become so if exposed to 
a great degree of cold. 

Epinus found that a steel bar could be powerfully magnetised by heat¬ 
ing it to redness, and allowing it to cool between the opposite poles of 
two powerful magnets. A steel bar heated to redness, and then hardened 
by sudden cooling in the vertical position, retains the magnetism imparted 
to it by the inductive action of the earth. 

627. Distribution of free magnetism.— Coulomb investigated the 
magnetic force in different parts of the magnet by the following method. 
He placed a large magnet in a vertical position in the magnetic meridian; 
he then took a small magnetic needle suspended by a thread without 
torsion, and, having ascertained the number of its oscillations under the 
influence of the earth’s magnetism alone, he presented it to different parts 
of the magnet. The oscillations were fewer as the needle was nearer the 
middle of the bar, and when they had reached that position, their number 
was the same as under the influence of the earth’s magnetism alone. He 
found that with saturated bars of more than 7 inches in length the distri¬ 
bution could always be expressed by a curve whose abscissae were the 
distances from the ends of the magnet, and whose ordinates were the 
force of magnetism at these points. 

With magnets of the above dimensions the poles are at the same 
distance from the end; Coulomb found the distance to be T6 inches in a 
bar 8 inches long. The same physicist found that, with shorter bars, the 
distance of the poles from the end is £ of the length; thus with a bar of 
three inches it would be half an inch. 

These results presume that the other dimensions of the bar are very 
small as compared with its length, that it has a regular shape, and is 
uniformly magnetised. When these conditions are not fulfilled, the 
positions of the poles can only be determined by direct trials with a 
magnetic needle. With lozenge-shaped magnets the poles are nearer the 
middle. 

Coulomb found that these lozenge-shaped bars have a greater directive 
force than rectangular bars of the same weight, thickness, and hardness. 


584 


FRICTIONAL ELECTRICITY. 


[628- 


BOOK IX. 

FRICTIONAL ELECTRICITY. 


CHAPTER I. 

FUNDAMENTAL PRINCIPLES. 

628. Electricity. Its nature. —Electricity is a powerful physical 
agent which manifests itself mainly by attractions and repulsions, but 
also by luminous and heating effects, by violent commotions, by chemical 
decompositions, and many other phenomena. Unlike gravity, it is not 
inherent in bodies, but is evoked in them by a variety of causes, among 
which are friction, pressure, chemical action, heat, and magnetism. 

Thales, six centuries before Christ, knew that when amber was rubbed 
with silk, it acquired the property of attracting light bodies; and from 
the Greek form of this word (ij\eKrpou, electron ) the term electricity has 
been derived. This is nearly all the knowledge left by the ancients; and 
it was not until towards the end of the sixteenth century that Dr. Gilbert, 
physician to Queen Elizabeth, showed that this property was not limited 
to amber, but that other bodies, such as sulphur, wax, glass, etc., also 
possessed it in a greater or less degree. 

629. Development of electricity by friction.— When a glass rod, 
or a stick of sealing wax, or shellac, is held in the hand, and rubbed with 
a piece of flannel or with the skin of a cat, the parts rubbed will be found 
to have the property of attracting light bodies, such as pieces of silk, wool, 
feathers, paper, bran, gold leaf, etc., which, after remaining a short time 
in contact, are again repelled. In order to ascertain whether bodies are 
electrified or not, instruments called electroscopes are used. The simplest 
of these, the electric pendulum (fig. 462), consists of a pith ball attached 
by means of a silk thread to a glass support. When an electrified body 
is brought near the pith ball, the latter is instantly attracted, but after 
momentary contact is again repelled (fig. 463). 

A solid body may also be electrified by friction with a liquid or with 
a gas. In the Toricellian vacuum a movement of the mercury against 




FRICTIONAL ELECTRICITY. 


585 


- 630 ] 


the sides of the glass produces a disengagement of electric light visible 
in the dark; a tube exhausted of air, hut containing a few drops of mer¬ 
cury, becomes also luminous when agitated in the dark. 

If a quantity of mercury in a dry glass be connected with a gold-leaf 



Fig. 462. 



Fig. 463. 


electroscope by a wire, and a dry glass rod immersed in it, no indications 
are observed during the immersion, but on withdrawing the rod, the 
leaves increasingly diverge, attaining their maximum when the rod 
leaves the mercury. 

Some substances, particularly metals, do not seem capable of receiving 
the electric excitement. When a rod of metal is held in the hand, and 
rubbed with silk or flannel, no electrical effects are produced in it; and 
bodies were formerly divided into ideoelectrics, or those which become 
electrical by friction, and anelectrics , or those which do not possess this 
property. These distinctions no longer obtain in any absolute sense ; it 
will presently be seen that, under appropriate-conditions, all bodies may 
be electrified by friction (631). 

With reference to the cause of the production of electricity by friction 
nothing is known. W ollaston attributed it to oxidation ; but Wilson 
and Gray have shown that electrical phenomena may be produced in 
vacuo, and Gay-Lussac proved that electricity may be developed in an 
atmosphere of carbonic acid. 

630. Conductors and non-conductors. —When a glass rod, rubbed 
at one end, is brought near an electroscope, that part only will be elec- 








586 


FRICTIONAL ELECTRICITY. 


[ 630 - 


trified which has been rubbed; the other end will produce neither 
attraction nor repulsion. The same is the case with a rod of shellac or 
of sealing wax. In these bodies electricity does not pass from one part 
to another—they do not conduct electricity. Experiment shows, that when 
a metal has received electricity in any of its parts, the electricity 
instantly spreads throughout its entire surface. Metals are hence said 
to be good conductors of electricity. 

Bodies have, accordingly, been divided into conductors and nonconductors. 
This distinction is not absolute, and we may advantageously consider bodies 
as offering a resistance to the passage of electricity which varies with 
the nature of the substance. Those bodies which offer little resistance are 
then conductors, and those which offer great resistance are nonconductors 
or insulators : electrical conductivity is thus the inverse of electrical resis¬ 
tance. We are to consider that between conductors and nonconductors 
there is a quantitative and not a qualitative difference; there is no con¬ 
ductor so good but that it offers some resistance to the passage of 
electricity, nor is there any substance which insulates so completely but 
that it allows some electricity to pass. The transition from conductors 
to nonconductors is gradual, and no line of sharp demarcation can be 
drawn between them. 

In this sense we are to understand the following table in which bodies 
are classed as conductors, semiconductors, and nonconductors; those bodies 
being conveniently designated as conductors which when applied to a 
charged electroscope discharge it almost instantaneously, semiconductors 
being those which discharge it in a short but measurable time, a few 
seconds, for instance; while nonconductors effect no discharge |n the 
course of a minute. 


Conductor's. 

Metals. 

Well-burnt charcoal. 
Graphite. 

Acids. 

Aqueous solutions. 
Water. 

Snow. 

Vegetables. 

Animals. 

Soluble salts. 

Linen. 

Cotton. 


Semiconductors. Nonconductors. 


Alcohol and ether. 
Powdered glass. 
Flour of sulphur. 
Dry wood. 

Paper. 

Ice at 0°. 


Dry oxides. 

Ice at - 25° C. 

Lime. 

Lycopodium. 

Caoutchouc. 

Air and dry gases. 

Dry paper. 

Silk. 

Diamond and precious stones. 
Glass. 

Wax. 

Sulphur. 

Besins. 

Amber. 

Shellac. 


INSULATING BODIES. 


587 


- 632 ] 

This list is arranged in the order of decreasing conductivity, or what is the 
same thing, of increasing resistance. The arrangement is not invariable 
however. Conductivity depends on many physical conditions. Glass, for 
example, which does not conduct at any ordinary temperatures, conducts 
very well at a red heat. Shellac and resin do not conduct so well when they 
are heated. Water, which is a good conductor, conducts but little in the 
state of ice at 0°, and very badly at - 25°. Powdered glass and flour of 
sulphur conduct very well, while in large masses they are nonconductors. 

631. Insulating: bodies. Common reservoir.— Bad conductors 
are called insulators , for they are used as supports for bodies in which 
electricity is to be retained. A conductor remains electrified only so 
long as it is surrounded by insulators. If this were not the case, as 
soon as the electrified body came in contact with the earth, which is a 
good conductor, the electricity would pass into the earth, and diffuse 
itself through its whole extent. On this account, the earth has been 
named the common reservoir. A body is insulated, by being placed on 
a support with glass feet, or on a resinous cake, or by being suspended 
by silk threads. No bodies, however, insulate perfectly j all electrified 
bodies lose their electricity more or less rapidly by means of the supports 
on which they rest. Glass is always somewhat hygroscopic, and the 
aqueous vapour which condenses on it, affords a passage for the elec¬ 
tricity ; the insulating power of glass is materially improved by coating 
it with shellac or copal varnish. Dry air is a good insulator, but 
when the air contains moisture, it conducts electricity, and this is the 
principal source of the loss of electricity. Hence it is necessary in 
electrical experiments, to rub the supports with cloths dried at the fire, 
and to surround electrified bodies by glass vessels, containing substances 
which attract moisture, such as chloride of calcium. 

It is from their great conductivity, that metals do not become elec¬ 
trified by friction. But if they are insulated, and then rubbed, they give 
good indications. This may be seen by the following experiment (fig. 
464). A brass tube is provided with a glass handle, by which it is held, 


Fig. 464. 

and then rubbed with silk or flannel. On approaching the metal to the 
pendulum, the pith ball will be attracted. If the metal is held in the 
hand electricity is indeed produced by friction—but it immediately passes 
through the body into the ground. 

If, too, the cap of a gold leaf electroscope be briskly flapped with a 
dry silk handkerchief, the gold leaves will diverge. 

632. Distinction of the two kinds of electricity. —If electricity 




588 


FRICTIONAL ELECTRICITY. 


[ 633 - 

be developed on a glass rod by friction with silk, and the rod be brought 
near an electrical pendulum (fig. 463), the ball will be attracted to the 
glass, and after momentary contact will be again repelled. By this con¬ 
tact the ball becomes electrified, and so long as the two bodies retain 
their electricity, repulsion follows when they are brought near each 
other. If a stick of sealing wax, electrified by friction with flannel or 
skin, be approached to another electrical pendulum, the same effects will 
be produced, the ball will fly towards the wax, and after contact will be 
repelled. Two bodies, which have been charged with electricity, repel 
one another. But the electricities, respectively developed in the pre¬ 
ceding cases, are not the same. If, after the pith ball has been touched 
with an electrified glass rod, an electrified stick of sealing wax, and then 
an electrified glass rod, be alternately approached to it, the pith ball will 
be attracted by the former and repelled by the latter. Similarly, if the 
pendulum be charged by contact with the electrified sealing wax, it will 
be repelled when this is approached to it, but attracted by the approach 
of the excited glass rod. 

On experiments of this nature, Dufay first made the observation that 
there are two different electricities : the one developed by the friction of 
x glass, the other by the friction of resin or shellac. To the first the name 
vitreous electricity is given j to the second the name resinous electricity. 

633. Theories of electricity.— Two theories have been proposed to 
account for these different effects of electricity. Franklin supposed that 
there exists a peculiar, subtle, imponderable fluid, which acts by repul¬ 
sion on its own particles, and pervades all matter. This fluid is present 
in every body in a quantity peculiar to it, and when it contains this 
quantity, it is in the natural state, or in a state of equilibrium. By 
friction, certain bodies acquire an additional quantity of the fluid, and 
are said to be positively electrified: others, by friction, lose a portion, and 
are said to be negatively electrified. The former state corresponds to 
vitreous electricity, and the latter to resinous electricity. Positive elec¬ 
tricity is represented by the sign +, and negative electricity by the sign 
— j a designation based on the algebraical principle, that when a plus 
quantity is added to an equal minus quantity zero is produced. So when 
a body containing a quantity of positive electricity is touched with a 
body possessing an equivalent quantity of negative electricity, a neutral 
or zero state is produced. 

The theory of Symmer, which is now generally admitted, explains in 
a satisfactory manner most electrical phenomena. But it is only an 
hypothesis, and must not be accepted as expressing anything absolute. 

Symmer’s theory assumes that every body contains an indefinite 
quantity of a subtle imponderable matter, which is called the electrical 
fluid. This fluid is formed by the union of two fluids—the positive, and 


- 635 ] FUNDAMENTAL PRINCIPLES OF ELECTRICITY. 589 

the negative. When they are combined they neutralise one another, and 
the body is then in the natural or neutral state. By friction, and by 
several other means, the two fluids may be separated, but one of them 
can never be excited without a simultaneous production of the other. 
There may, however, be a greater or less excess of the one or the other 
in any body, and it is then said to be electrified positively or negatively. 
As in Franklin’s theory, vitreous corresponds to positive, and resinous to 
negative electricity. This distinction is merely conventional; it is adopted 
for the sake of convenience, and there is no other reason, why resinous 
electricity should not be called positive electricity. 

Fluids of the same name repel one another, and fluids of opposite kinds 
attract each other. The fluids can circulate freely on the surface of cer¬ 
tain bodies, which are called conductors, but remain confined to certain 
parts of others, which are called nonconductors. 

As has been already said, this theory is quite hypothetical; but its 
general adoption is justified by the convenient explanation which it gives 
of electrical phenomena. 

634. Action of electrified bodies on eacb other.— Admitting the 
two-fluid hypothesis, the phenomena of attraction and repulsion may be 
enunciated in the following law, which is the basis of all the theories of 
frictional electricity: 

Two bodies charged with the same electricity repel each other; two bodies 
charged with opposite electricities attract each other. 

These attractions and repulsions take place in virtue of the action which 
the two electricities exert on themselves, and not in virtue of their action 
on the particles of matter. 

635. Law of the development of electricity by friction.— 

Whenever two bodies are rubbed together, the neutral fluid is decom¬ 
posed. The two electricities are developed at the same time and in 
equal quantities—one body takes the positive, and the other the 
negative fluid. This may be proved by the following simple experi¬ 
ment devised by Faraday:—A small flannel cap provided with a silk 
thread is fitted on the end of a stout rod of shellac, and rubbed round a 
few times. When the cap is removed by means of a silk thread, and 
presented to a pith ball pendulum charged with positive electricity, the 
latter will be repelled, proving that the flannel is charged with positive 
electricity ; while, if the shellac is presented to the pith ball, it will be 
attracted, showing that the shellac is charged with negative electricity. 
Both electricities are present in equal quantities j for if the rod be pre¬ 
sented to the electroscope before removing the cap, no action is observed. 

The electricity developed on a body by friction depends on the body 
rubbed. Thus glass becomes negatively electrified when rubbed with 
cat’s skin, but positively when rubbed with silk. In the following list the 


590 


FRICTIONAL ELECTRICITY. 


[636- 

substances are arranged in sucb an order, that each becomes positively 
electrified when rubbed with any of the bodies following, but negatively 
when rubbed with any of those which precede it: 

Cat’s skin. Glass. 

Flannel. Cotton. 

Ivory. Silk. 

Rock crystal. The hand. 

Wood. Sulphur. 

Shellac. Caoutchouc. 

Resin. Gutta percha. 

Metals. Gun cotton. 

The nature of the electricity set free by the friction depends also on 
the degree of polish, the direction of the friction, and the temperature. 
If two glass discs of different degrees of polish are rubbed against each 
other, that which is most polished is positively, and that which is least 
polished is negatively electrified. If two silk ribbons of the same kind 
are rubbed across each other, that which is transversely rubbed is nega¬ 
tively, and the other positively electrified. If two bodies of the same sub¬ 
stance, and of the same polish, but of different temperatures, are rubbed 
together, that which is most heated is negatively electrified. Generally 
speaking, the particles which are most readily displaced are negatively 
electrified. 

636. Development of electricity by pressure and cleavage.— 

Electrical excitement may be produced by other causes than friction. If 
a disc of wood covered with oiled silk, and a metal disc, both provided 
with insulating handles, be pressed together, and then suddenly separated, 
the metal disc is negatively electrified. A crystal of Iceland spar pressed 
between the fingers becomes positively electrified, and retains this state 
for some time. The same property is observed in several other minerals, 
even though conductors, provided they be insulated. If cork and caout¬ 
chouc be pressed together, the first becomes positively, and the other ne¬ 
gatively electrified. A disc of wood pressed on an orange and separated, 
carries away a good charge of electricity, if the contact be rapidly inter¬ 
rupted. But if the disc is slowly removed the quantity is smaller, for the 
two fluids recombine at the moment of their separation. For this reason 
there is no apparent effect when the two bodies pressed together are good 
conductors. 

Becquerel has also observed that cleavage is a source of electricity. If 
a plate of mica be rapidly split in the dark, a slight phosphorescence is 
perceived. Becquerel fixed glass handles to each side of the plate of mica, 
and then rapidly separated them. On presenting each of the plates thus 
separated to an electroscope, he found that one was negatively, and the 
other positively electrified. 

Laminated mica, and all badly conducting crystalline substances, 


PYROELECTRICITY. 


591 


-637] 

exhibit electrical indications by cleavage. Tbe separated plates are 
always in opposite electrical conditions, provided tbey are not good 
conductors: for if tbey were, tbe separation would not be sufficiently 
rapid to prevent tbe recombination of tbe two electricities. To the 
phenomena here described is due tbe luminous appearance seen in tbe 
dark when sugar is broken. 

637. Pyroelectricity.— Certain minerals, when warmed, acquire 
electrical properties; a phenomenon to which tbe name 'pyroelectricity is 
given. It is best studied in tourmaline, in which it was first discovered, 
from tbe fact that this mineral had tbe power of first attracting and then 
repelling hot ashes when placed among them. 

To observe this phenomenon, a crystal of tourmaline is balanced by a 
silk thread, in a glass cylinder placed on a heated metal plate. On sub¬ 
sequently investigating the electric condition of tbe ends, by approaching 
to them successively an electrified glass rod, one end will be found to be 
positively electrified, and tbe other end negatively electrified, and each 
end shows this polarity as long as the temperature rises. Tbe arrangement 
of the electricity is thus like that of tbe magnetism in a magnet. The 
points at which the intensity of free electricity is greatest are called the 
poles , and the line connecting them is the electric axis. When a 
tourmaline, while thus electrified, is broken in the middle, each of the 
pieces has its two poles. 

These polar properties depend on the change of temperature. When a 
tourmaline, which has become electrical by being warmed, is allowed to 
cool regularly, it suddenly loses electricity, and then its polarity becomes 
reversed; that is, the end which was positive now becomes negative, and 
that which was negative becomes positive, and the position of the poles 
now remains unchanged so long as the temperature sinks. Tourmaline 
only becomes pyroelectric within certain limits of temperature ; these vary 
somewhat with the length, but are usually between 10° and 150° C. 
Below and above these temperatures it behaves like any other body, and 
shows no polarity. 

The name analogous pole, is given to that end of the crystal which shows 
positive electricity when the temperature is rising, and negative electricity 
when it is sinking; antilogous pole to that end which becomes negative by 
being heated, and positive by being cooled. 

The phenomena of pyroelectricity are intimately connected with the 
crystalline form of the mineral; and is only seen in those crystals whose 
forms are hemihedral, or which are differently modified at the ends of 
their crystallographical principal axis. 

Besides tourmaline the following minerals are found to be pyroelectric; 
boracite, topaz, prehnite, silicate of zinc, scolezite, axenite. And the 
following organic bodies are pyroelectric; cane-sugar, Pasteur’s salt 
(racemate of sodium and ammonium), tartrate of potassium, &c. 


592 


FRICTIONAL ELECTRICITY. 


[ 638 - 


CHAPTER II. 

MEASUREMENT OF ELECTRICAL FORCES. 

638. Laws of electrical attractions and repulsions. —The laws 
which regulate the attractions and repulsions of electrified bodies may be 
thus stated. 

I. The repulsions or attractions betiveen two electrified bodies are in the 
inverse ratio of the squares of their distance. 

II. The distance remaining the same, the force of attraction or repulsion 
betiveen two electrified bodies is directly as the product of the quantities of 

electricity, with which they are charged. 

These laws were established by Cou¬ 
lomb, by means of the torsion balance, 
used in determining the laws of magnetic 
attractions and repulsions (617), modified 
in accordance with the requirements of the 
case. The wire, on the torsion of which 
the method depends, is so fine that a foot 
weighs only ~ of a grain. At its lower 
extremity there is a fine shellac thread, no 
(fig. 465), at one end of which is a small 
disc of copper foil, n. Instead of the ver¬ 
tical magnetic needle there is a glass rod, i, 
terminated by a gilt pith ball, m, which 
passes through the aperture r. The scale 
is fixed round the sides of the vessel, and 
during the experiment the ball m is oppo¬ 
site the zero point. The micrometer con¬ 
sists of a small graduated disc, e, moveable 
independently of the tube d, and of a 
fixed catch, a, which shows by how many 
degrees the disc is turned. In the centre 
of the disc there is a small button, to which is fixed the wire which 
supports no. 

The micrometer is moved until the zero point is opposite the catch, and 
the tube d is turned until the knob n is opposite zero of the graduated 
circle: the knob m is in the same position, and thus presses against n. 
The knob m is then removed and electrified, and replaced in the appara¬ 
tus, through the aperture r. As soon as the electrified knob m touches n, 
the latter becomes electrified, and is repelled, and after a few oscillations 










MEASUREMENT OF ELECTRICAL FORCES. 


593 


- 638 ] 

remains constant at a distance, at which the force of repulsion is equal to 
the force of torsion. In a special experiment Coulomb found the angle of 
torsion between the two to he 36°; and as the force of torsion is propor¬ 
tional to the angle of torsion, this angle represents the repulsive force 
between m and n. In order to reduce the angle to 18° it was necessary 
to turn the disc through 127°. The wire was twisted 12(3° in the 
direction of the arrow at its upper extremity, and 18° in the opposite 
direction at its lower extremity, and hence there was a total torsion of 
144°. On moving the micrometer in the same direction, until the 
angle of deviation was 8£°, 567° of torsion were necessary. Hence the 
whole torsion was 575£°. Without sensible error these angles of devia¬ 
tion may be taken at 36°, 18°, and 9°, and on comparing them with the 
corresponding angles of torsion 36°, 144°, and 576°, we see that while the 
first are as 

1 • 2 : 4? 

the latter are as 

1:4 : 16; 

that is, that for a distance 4 as great, the angle of torsion is twice as 
great, and that for a distance \ as great the repulsive force is 16 times 
as great. 

In experimenting with this apparatus, the air must be thoroughly dry, 
in order to diminish, as far as possible, loss of electricity. This is effected 
by placing in it a small dish containing chloride of calcium. 

The experiments by which the law of attraction is proved are made in 
much the same manner, but the two balls are charged with opposite 
electricities. A certain quantity of electricity is imparted to the moveable 
ball, by means of an insulated pin, and the micrometer moved until there 
is a certain angle below. A charge of electricity of the opposite kind is 
then imparted to the fixed ball. The two balls tend to move together, 
but are prevented by the torsion of the wire, and the moveable ball 
remains at a distance, at which there is equilibrium between the force of 
attraction, which draws the balls together, and that of torsion, which 
tends to separate them. The micrometer screw is then removed to 
a greater distance, by which more torsion and a greater angle between 
the two balls are produced. And it is from the relation which exists 
between the angle of deflection on the one hand, and the angle which 
expresses the force of torsion on the other, that the law of attraction has 
been deduced. 

To prove this second law let a charge be imparted to m ; n being in 
contact with it becomes charged and is repelled to a certain distance. 
The angle of deflection being noted, let the ball m be touched by an in¬ 
sulated but unelectrified ball of exactly the same size and kind; in this 
way half its charge is removed, and the angle of deflection will now be 


504 


FRICTIONAL ELECTRICITY. 


[639- 


found to be only half its original amount. In like manner if either m 
or the moveable body be now again deprived of half its electricity, the 
deflection will be a quarter of what it originally was, and so on. 

(id 

The two laws are included in the formula F where F is the 


force ; e and e f the quantities of electricity, and d the distance. 

639. Distribution of electricity. —When an insulated sphere of 
conducting material is charged with electricity, the electric fluid passes 
to the surface of the sphere, and forms an extremely thin layer. If, in 
Coulomb’s balance, the fixed ball be replaced by another electrified 
sphere, a certain repulsion will be observed. If then this sphere be 
touched with an insulated sphere identical with the first, but in the 
natural state, the first ball will be found to have lost half its electricity, 
and only half the repulsion will be observed. By repeating this ex¬ 
periment with spheres of various substances, solid and hollow, but all 
having the same superficies, the result will be the same, excepting that 
with imperfectly conducting materials, the time required for the dis¬ 
tribution will be greater. From this it is concluded that the distribution 
of electricity depends on the extent of the surface, and not on the mass, 
and, therefore, that electricity does not penetrate into the interior, but 
is confined to the surface. This conclusion is further established by the 
following experiments:— 

i. A thin hollow copper sphere provided with an aperture of about 
an inch (fig. 466), and placed on an insu¬ 
lating support, is charged in the interior 
with electricity. When the proof plane 
(a small disc of copper foil at the end of a 
slender glass or shellac rod) is applied to 
the interior, and then brought near an 
electroscope, no electrical indications are 
produced. But if the proof plane is 
applied to the electroscope after having 
been in contact with the exterior, a con¬ 
siderable divergence ensues. 

ii. A hollow globe, fixed on an in¬ 
sulating support, is provided with two 
hemispherical envelopes which fit closely, 
and can be separated by glass handles. 
The interior is now electrified, and the two 
hemispheres brought in contact. On then 
rapidly removing them (fig. 467) the cover¬ 
ings will be found to be electrified, while 
the sphere is in its natural condition. 







-639] 


MEASUREMENT OF ELECTRICAL FORCES. 


595 



Fig. 468. 

iii. The distribution of electricity on the surface may also be shown 
by means of the following apparatus. It consists of a metallic cy¬ 
linder on insulated supports, on which is fixed a long strip of tin 














596 FRICTIONAL ELECTRICITY. [ 640 - 

foil, which can he rolled up by means of a small insulating handle 
(fig. 468). A quadrant electrometer is fitted in metallic communi¬ 
cation with the cylinder. When the sphere is rolled up, a charge is 
imparted to the cylinder, by which a certain divergence is produced. 
On unrolling the tin foil, this divergence gradually diminishes, and 
increases as it is again rolled up. The quantity of electricity remain¬ 
ing the same, the electrical force, on each unit of surface, is therefore 
less as the surface is greater. 

The following ingenious experiment by Faraday further illustrates 
this law: A metal ring is fitted on an insulating support, and a coni¬ 
cal gauze bag, such as is used for insects, is fitted to it (fig. 469). By 

means of a silk thread, the bag can be 
drawn inside out. After electrifying the 
bag it is seen by means of a proof plane, 
that the electricity is on the exterior, 
but if the positions are reversed by 
drawing the bag inside out, so that the 
interior has now become the exterior, 
the electricity will still be found on the 
exterior. 

The property of electricity, of accu¬ 
mulating on the outside of bodies is 
ascribed to the repulsion which the par¬ 
ticles exert on each other. Admitting 
the hypothesis of two fluids, and that op¬ 
posite electricities attract each other in 
the inverse ratio of their distances, while 
like electricities repel one another, accord¬ 
ing to the same law, Poisson, by the aid of mathematical analysis, has 
arrived at the same conclusion in reference to the distribution of elec¬ 
tricity on bodies, as that which follows from the previous experiments. 
Electricity tends constantly to pass to the surface of bodies, where it 
exists in very thin layers; it continually tends to escape, but is prevented 
by the resistance of the feebly conducting atmosphere. 

640. Influence of the shape of a body on the accumulation of 
electricity.— On a metallic sphere the distribution of the electrical fluid 
will be uniform in every part, simply from its symmetry. This has been 
demonstrated by means of the proof plane and the torsion balance. A 
metallic sphere placed on an insulating support was electrified, and touched 
at different parts of its surface with the proof plane, which each time was 
applied to the moveable needle of the torsion balance. As in all cases 
the torsion observed was sensibly the same, it was concluded that the 
proof plane had each time received the same quantity of electricity. In 










DISTRIBUTION OF ELECTRICITY. 


597 


- 641 ] 

the case of an elongated ellipsoid (fig. 470) it is found that the electrical 
layer has a different density at different points of the surface. In virtue 
of its repulsion the electricity accumulates at the most acute points, and 
here it has the greatest tension or tendency to escape. This is demon¬ 
strated by successively touching the ellipsoid at different parts with the 
proof plane, and then bringing this into the torsion balance. By this 
means Coulomb found that the greatest deflection was produced when the 
proof plane had been in contact with the point a, and the least by con¬ 
tact with the middle space e. Laplace has found by calculation that the 
tension at each point is proportional to the square of the thickness of the 


r 



Fig. 470. 


electric layer. The electric density or electric thickness is the term used 
to express the quantity of fluid found at any moment on a given surface. 
If s represents the surface and Q the quantity of electricity on that sur¬ 
face, then, assuming that the electricity^ is equally distributed, its elec¬ 
trical density is equal to Q. 

Coulomb found, by quantitative experiments, that in an ellipsoid the 
density of the electricity at the equator of the ellipsoid, is to that at the 
ends, in the same ratio as the length of the minor to the major axis. 
On an insulated cylinder, terminated by two hemispheres, the density of 
the electrical layer at the ends is greater than in the middle. In one case, 
the ratio of the two densities was found to be as 2-3:1. On a circular 
disc the density is greatest at the edges. 

641. Power of points. —On a sphere, the electric density is every¬ 
where uniform; the further a body is removed from the shape of a sphere, 
the more irregular is its accumulation. A pointed rod may be regarded 








598 


FRICTIONAL ELECTRICITY. 


[ 642 - 

as an elongated ellipsoid, and hence, at its extremity, the electric density 
will he greatest. But the tension is proportional to the density, and 
hence the greater the density the greater will be its power of overcoming 
the resistance of the air, and escaping. If the hand he brought near a 
point on an electrified conductor a slight wind is felt; and if the dis¬ 
engagement of electricity takes place in the dark a luminous brush is 
seen. In electrical apparatus, and experiments, frequent use is made of 
this property of points. 

642. Communication and distribution of electricity on bodies 
in contact.— If two conducting bodies, one electrified and the other in 
the natural state, be brought into contact, the electricity will be equally 
distributed over the two: the one will lose and the other gain a quantity 
of electricity proportional to its surface. If the bodies are not conductors, 
there will only be loss and gain at the points in contact. 

By means of the proof plane, and the torsion balance, Coulomb made 
numerous determinations of the distribution of electricity on bodies in 
contact. When two insulated equal metallic spheres were placed in 
contact and electrified, he found that the electric fluid was unequally 
distributed, and that in proportion to their diameters. The diameters 
being equal, the electrical density was zero at the point of contact, and 
only became sensible at 23° from this point; it increased rapidly from 20° 
to 30°, then more slowly from 60° to 90°, and was almost constant between 
60° and 180°. 

When the diameters were unequal, and in the ratio of 2 : 1, the 
density of the point of contact was still zero, but at first increased most 
rapidly on the large sphere : it then increased more rapidly on the small 
one, and at 180° from the point of contact its density was greatest on the 
small one. 

643. loss of electricity.— Experience shows that electrified bodies 
gradually lose their electricity, even when placed on insulating supports. 
This loss is due to two causes : firstly, to the imperfection of the insulat¬ 
ing supports, and, secondly, to the conductivity of the air. 

All substances conduct electricity in some degree; those which are 
termed insulators are simply very bad conductors. An electrified con¬ 
ductor resting on supports must, therefore, lose a certain quantity of its 
electricity. 

The loss by the atmosphere varies with the electrical tension, with the 
rapidity with which the air is renewed, and with the hygrometric state. 

Dry air is a very imperfect conductor, but when it contains aqueous 
vapour, it conducts pretty well, and the more moisture it contains, the 
better it conducts. Coulomb has attempted to show 1 that in a still at¬ 
mosphere, and with a constant hygrometric state, the loss for a very short 


DISTRIBUTION OF ELECTRICITY. 


599 


- 644 ] 

space of time is directly proportional to the tension: ’ a law analogous to 
Newton’s law of cooling (356). 

Coulomb experimented with moist air. In perfectly dry gases, Mat- 
teucci did not find the loss of electricity in accordance with Coulomb’s 
law. He found that within certain limits of tension, the loss was inde¬ 
pendent of the quantity of electricity, and proportional to the time; in 
other words, that in equal times there was an equal loss of electricity. 

He further found that for equal temperatures and pressures, the loss is 
the same in air, carbonic acid, and hydrogen, provided they are perfectly 
dry: at a high tension the loss of negative electricity is greater than 
that of positive; in dry gases, under a constant pressure, the loss in¬ 
creases with the temperature; and, lastly, that in dry gases the loss is 
independent of the nature of the electrified body; that is, it is the same 
whether it is a conductor or not. 

Coulomb found not only that supports never insulate completely, but 
that they are the cause of an abundant loss of electricity in bodies strongly 
electrified. The loss diminishes gradually, and is constant when the ten¬ 
sion is low. It may be neglected by giving to the supports an adequate 
length, which, according to Coulomb, must be proportional to the square 
of the electric tension of the charged body. Brown shellac is the best 
insulator; glass is a hygroscopic substance, and must be dried with great 
care. It is best covered with a thin layer of shellac varnish, as has already 
been stated. 

644. Xioss of electricity in vacuo. —Inasmuch as electricity is 
retained on the surface of bodies by the pressure of the insulating at¬ 
mosphere, when the pressure diminishes, the loss of electricity increases, 
and in vacuo, in which resistance is zero, all electricity escapes. This is 
a necessary consequence of the mathematical theory of electricity, which 
accounts for the equilibrium of electricity on the surface of bodies. But 
in opposition to this, Hawksbee, Gray, Snow Harris, and Becquerel have 
observed, that feeble electrical tensions may be retained in vacuo. Bec¬ 
querel showed that in a vacuum of a millimeter a body retained a feeble 
charge for fifteen days. And it is probable, that if an electrified body 
were in a perfect vacuum, it would retain an electrical charge, provided 
it were sufficiently removed from any body which could exert upon it an 
inductive action (645). 


600 


FRICTIONAL ELECTRICITY. 


[ 645 - 


CHAPTER III. 

ACTION OF ELECTRIFIED BODIES ON BODIES IN THE NATURAL STATE ; 

INDUCED ELECTRICITY. ELECTRICAL MACHINES. 

645. Electricity by influence or induction. —An insulated con¬ 
ductor, charged with either kind of electricity, acts on bodies in a natural 
state placed near it, in a manner analogous to that of the action of a mag¬ 
net on soft iron, that is, it decomposes the neutral fluid, attracting the 
opposite, and repelling the like kind of electricity. The action, thus 
exerted, is said to take place by influence or induction. 

The phenomena of induction may be demonstrated by means of a brass 
cylinder placed on an insulating support, and provided at its extremities 
with two small electric pendulums, which consist of pith balls suspended 
by linen threads (fig. 471). If this apparatus is placed near an insulated 



Fig. 471. 


conductor m, charged with either kind of electricity, for instance, the 
conductor of the electrical machine, which is charged with positive 
electricity, the natural fluid of the cylinder is decomposed, free electricity 
will be developed at each end, and both pendulums will diverge. If 
while they still diverge, a stick of sealing wax excited by friction with 
flannel, be approached to that end of the cylinder nearest the conductor, 
the corresponding pith ball will be repelled, indicating that it is charged 
with the same kind of electricity as the sealing wax, that is, with negative 
fluid; while if the excited sealing wax is brought near the other ball, it 














ELECTRICAL INDUCTION. 


601 


- 645 ] 

will be attracted, showing that it is charged with positive electricity. 
If further, a glass rod, excited by friction with silk, and therefore charged 
with positive electricity, be approached to the end nearest the conductor, 
the pendulum will be attracted,* while if brought near the other end, the 
corresponding pendulum will be repelled. If the influence of the charged 
conductor be suppressed, either by removing it, or placing it in commu¬ 
nication with the ground, the separated electricities will recombine, and 
the pendulums exhibit no divergence. The cause of this phenomenon is 
obviously a decomposition of the neutral fluid of the cylinder, by the free 
positive electricity of the conductor, the opposite or negative electricity 
being attracted to that end of the cylinder nearest the conductor, while 
the similar electricity is repelled to the other end. Between these two 
extremities, there is a space destitute of free electricity. This is seen by 
arranging on the cylinders a series of pairs of pith balls suspended by 
threads. The divergence is greatest at each extremity, and there is a point 
at which there is no divergence at all, which is called the neutral point. 
The two fluids, although equal in quantity, are not distributed over the 
cylinder in a symmetrical manner; the attraction which accumulates the 
negative electricity at the one end is, in consequence of the greater near¬ 
ness, greater than the repulsion which drives the positive electricity to 
the other end, and hence the neutral line is nearer one end than the other. 
Since, too, the gradual loss of positive electricity is less than that of ne¬ 
gative electricity, the cylinder, if the experiment be sufficiently pro¬ 
longed, will remain charged with positive electricity. The distribution 
of electricity is also dependent on the form and size of the cylinder, and 
on the proximity of the charged conductor. If the cylinder be placed in 
connection with the ground, by metallic contact with the posterior ex¬ 
tremity, and the charged conductor be still placed near the anterior ex¬ 
tremity, the conductor will exert its inductive action as before. But it 
is now no longer the conductor alone which is influenced. It is a con¬ 
ductor consisting of the conductor itself, the metallic wire, and the whole 
earth. The neutral line will recede indefinitely, and since the conductor 
has become infinite, the quantity of neutral fluid decomposed will be in¬ 
creased. Hence, when the posterior extremity is placed in contact with 
the ground, the pendulum at the anterior extremity diverges more widely. 
If the connecting rod be now removed, neither the quantity nor the dis¬ 
tribution will be altered; and if the conductor be removed, or be dis¬ 
charged, a charge of negative electricity will be left on the cylinder. It 
will, in fact, remain charged with electricity, the opposite of that of the 
charged conductor. 

If, instead of connecting the posterior extremity of the cylinder with 
the ground, any other part had been so connected, the general result 
would have been the same. All the parts of the cylinder would be 

D D 


FRICTIONAL ELECTRICITY. 


602 


[ 646 - 


charged with negative fluid, and, on interrupting the communication with 
the earth, would remain so charged. 

Thus a body can be charged with electricity by induction as well as by 
conduction. But in the latter case, the charging body loses part of its 
electricity, which remains unchanged in the former case. The electricity 
imparted by conduction is of the same kind as that of the electrified 
body, while that excited by induction is of the opposite kind. To 
impart electricity by conduction, the body must be quite insulated, while 
in the case of induction, it must be in connection with the earth at all 
events momentaneously. 

A body electrified by induction acts in turn on bodies placed near it, 
separating the two fluids in a manner shown by the signs on the sphere. 

What has here been said has referred to the inductive action exerted 
on good conductors. Bad conductors are not so easily acted upon by 
induction, owing to the great resistance they present to the circulation of 
electricity, but when once charged, the electric state is more permanent. 

This is analogous to what is met with in magnetism; a magnet in¬ 
stantaneously evokes magnetism in a piece of soft iron, but this is only 
temporary, and depends on the continued action of the magnet ,* a magnet 
magnetises steel with far greater difficulty, but this magnetism is 
permanent. 

646. Ziimit to the action of induction.— The inductive action 
which an electrified body exerts on an adjacent body in decomposing its 
neutral fluid is limited. On the surface of the insulated cylinder, which 
we have considered in the preceding paragraph, let there be at n any 
small quantity of neutral fluid (tig. 472). The positive electricity of 



Fig. 472. 


the source m first decomposes by induction the neutral fluid in n, at¬ 
tracting its negative fluid towards A, and repelling its positive towards 
B; but in the degree in which the extremity becomes charged with 
negative electricity, and the extremity B with positive electricity, there 
are developed at A and B two forces / and which act in the opposite 
direction to the original force. For the forces / and/' concur in driving 
towards B the negative fluid of n, and towards A its positive fluid. But 
as the inducing force F which is exerted at m is constant, while the 
forces / and /' are increasing, a time arrives at which the force F is 
balanced by the forces / and /'. All decomposition of the neutral fluid 
then ceases; the inducing action has attained its limit. 











ELECTRICAL INDUCTION. 


603 


- 647 ] 

If the cylinder be removed from the source of electricity, as the 
inducing action decreases, a portion of the free fluids at A and at B re¬ 
combine to form the neutral fluid. If, on the other hand, they are 
brought nearer, as the force F now exceeds the forces / and /', a new 
decomposition of the neutral fluid takes place, and fresh quantities of 
positive and negative fluids are respectively accumulated at A and B. 

647. Faraday’s theory of induction.*— The theory of electricity 
by induction as just elucidated, is the one hitherto admitted by all 
physicists. The recent researches of Faraday on electric polarity tend, 
however, to modify it, and may, perhaps, lead to overturn it entirely. 
Hitherto, the influence of the medium, which separates the electrified 
from the unelectrified body, has been neglected. But Faraday’s re¬ 
searches prove that it is in this medium that the inductive actions take 
place; and that the inductive action is not an action at a distance, or 
rather at no distance greater than that between any two molecules. 
Faraday supposes that, in this medium, successions of layers become 
alternately positively and negatively electrified. 

The following experiment was devised by Faraday to illustrate this 
polarisation of the medium, as he has called it. He placed small filaments 
of silk in a vessel of turpentine, and, having plunged two conductors 
in the liquid on opposite sides, he charged: one and placed the other in 
connection with the ground. The particles of silk immediately ar¬ 
ranged themselves end to end, and adhered closely together, forming 
a continuous chain between the two sides. An experiment by Matteucci 
also supports Faraday’s theory. He placed several thin plates of mica 
closely together, and provided the outside ones with metallic coatings, 
like a fulminating pane (667). Having electrified the system, the coatings 
were removed by insulating handles, and on examining the plates of 
mica successively, each was found charged with positive electricity on 
one side, and negative electricity on the other. 

On the new view, the action exerted by electrified bodies on bodies 
in the neutral state, is effected by the polarisation of the alternate layers 
of air or any other medium. On the old view, the air was supposed to 
be quite passive, or at most, in virtue of its nonconductivity, to oppose 
a resistance to the recombination of the two fluids. 

Objections have, nevertheless, been raised to Faraday’s theory, one of 

* ‘ This theory of Faraday,’ remarks M. De la Eive, * though needing further 
investigation, deserves the serious attention of physicists. It rests on a sound 
principle, namely, that electric actions take place through the intervention of 
material particles, and it tends to bring the electric force into closer connection with 
other natural forces. One important point follows from Faraday’s researches, the 
fact that the molecular polarisation of insulating bodies is probably also the mode 
by which electricity is propagated in conductors.’ 

du2 


604 


FRICTIONAL ELECTRICITY. 


[648- 



the most formidable of which is the action which electrified bodies 
exert on others at a distance even in vacuo; unless, indeed, it be admitted 
that even in the most perfect vacuum obtainable, sufficient material 
molecules remainto produce the polarisation. In some researches which 
Matteucci has recently made on the propagation of electricity in insu¬ 
lators, he has arrived at conclusions differing from those of Faraday. 

648. Specific inductive capacity. —Faraday names the property 
which bodies possess of transmitting the electric influence, the induc¬ 
tive power. All insulating bodies do not possess it in the same degree. 
To determine and compare the inductive power Faraday uses the ap¬ 
paratus represented in fig. 473, and of which fig. 474 represents a 


Fig. 473. Fig. 474. 

vertical section. It consists of a brass sphere made up of two halves, P 
and Q, which fit accurately into each other, like the Magdeburg hemi¬ 
spheres. In the interior of this spherical envelope, there is a smaller 
brass sphere, C, connected with a metallic rod, terminating in a ball, 
B. The rod is insulated from the envelope, PQ, by a thick layer of 
shellac, A. The space mn receives the substance whose inductive power 
is to be determined. The foot of the apparatus is provided with a screw 
and stopcock, so that it can be screwed on the air pump, and the air in 
mn either rarefied or exhausted. 

Two such apparatus perfectly identical are used, and at first they only 











ELECTRICAL INDUCTION. 


605 


- 648 ] 

contain air. The envelopes PQ are connected with the ground, and the 
knob B of one of them receives a charge of electricity. The sphere C 
thus becomes charged like the inner coating of a Leyden jar (668). 
The layer mn represents the insulator which separates the two coatings. 
By touching B with the proof plane, which is then applied to the 
torsion balance, the quantity of free electricity is measured. In one 
experiment Faraday observed a torsion of 250°, which represented the 
free electricity on B. The knob B was then placed in metallic con¬ 
nection with the knob B' of the other apparatus, and the torsion was 
now found to be 125°, showing that the electricity had become equally 
distributed on the two spheres, as might have been anticipated, since 
the pieces of apparatus were quite equal and each contained air in the 
space mn. 

This experiment having been made, the space mn in the second appar¬ 
atus was filled with the substance whose inductive power was to be 
determined ; for example, shellac. The other apparatus, in which mn is 
filled with air, having been charged, the tension of the free electricity 
on C was measured. Let it be taken at 290°, the number observed by 
Faraday, in a special case. When the knob B of the first apparatus was 
connected with the knob B' of the second, the tension was not found to 
be 145° as would be expected. The apparatus containing air exhibited 
a tension of 114°, and that with shellac of 118°. Hence the former had 
lost 176°, and had retained 114°, while the latter ought to have ex¬ 
hibited a tension of 176° instead of 113°. The second apparatus had 
taken more than half the charge, and hence a larger quantity of elec¬ 
tricity had been dissimulated by the shellac. Of the total quantity of 
electricity, the shellac had taken 176°, and the air 114 °; hence the 
specific inductive capacity of air is to that of shellac as 114 : 176, or- as 
1 : 1-55. That is, the inductive power of shellac is more than half as 
great again as air. 

Comparing together other substances by this general method, but 
varying the details, Faraday and Harris have obtained the following 
values for the specific inductive capacity of dielectrics , as they are called 
in opposition to dielectrics or conductors. 


Air ....*• .l’OO Wax.F86 

Spermaceti.1’45 Glass.1‘90 

Resin.1*76 Shellac.2-00 

Pitch.1*80 Sulphur.2*24 


By the following simple experiment the influence of the dielectric 
may be shown. At a fixed distance above a gold leaf electroscope, let 
an electrified sphere be placed by which a certain divergence of the 
leaves is produced. If now, the charges remaining the same, a disc of 
sulphur or of shellac be interposed, the divergence increases, showing 










FRICTIONAL ELECTRICITY. 


606 


[ 649 - 


that inductive action takes place through the sulphur to a greater extent 
than through a layer of air of the same thickness. 

In treating on induction produced by the voltaic battery some experi¬ 
ments of Matteucci will be adduced, which show, that the inductive 
action of current electricity, is independent of the nature of the insu¬ 
lator placed between the inducing and the induced body, a result which, 
of course, does not agree with the experiments of Faraday on frictional 
electricity. 

Faraday finds that all gases have the same inductive capacity, and that 
this is independent of the temperature and pressure. 

649. Communication of electricity at a distance.— In the ex¬ 
periment represented in figure 471 the opposite electricities of the 
conductor, and that of the separated cylinder, tend to unite, but are 
prevented by the resistance of the air. If the tension is increased, or if 
the distance of the bodies be diminished, the opposed electricities 
at length overcome this obstacle; they rush together and combine, 
producing a spark, accompanied by a sharp sound. The negative electri¬ 
city separated on the cylinder, being thus neutralised by the positive 
electricity of the charged body, a charge of positive electricity remains on 
the cylinder. The same phenomenon is observed when a finger is 
presented to a strongly electrified conductor. The latter decomposes by 
induction the natural fluid of the body, the opposite electricities combine 
with the production of a spark, while the electricity of the same kind as 
the electrified conductor, which is left on the body, passes off into the 
ground. 

The striking distance varies with the tension, the shape of the bodies, 
their conducting power, and with the resistance of the interposed medium. 

650. Motion of electrified bodies.— The various phenomena of 
attraction and repulsion which are among the most frequent mani¬ 
festations of electrical action, may all be explained by means of the 
laws of induction. If M (fig. 475) be a fixed insulated conductor 

charged with positive electricity, and N be a 
moveable insulated body, for instance an electrical 
pendulum, there are three cases to be considered. 

i. The moveable body is unelectrified , and is a 
conductor. In this case M acting inductively 
on N, attracts the negative and repels the posi¬ 
tive fluid, so that the maximum of tension is 
respectively at the points a and b. But since 
attractions and repulsions are inversely as the square of the distance, the 
attraction between a and c is greater than the repulsion between b c, and 
therefore N will be attracted to M by a force equal to the excess of the 
attractive over the repulsive force. 




ELECTRICAL INDUCTION. 


607 


- 651 ] 

ii. The moveable body is a conductor , and is electrified. If the electricity 
of the moveable body is different from that of the fixed body, there 
is always attraction, but if they are of the same kind there is at first 
repulsion and afterwards attraction. This anomaly may be thus explained : 
Besides its charge of electricity, the moveable body contains natural fluid. 
This is decomposed by the induction of the positive fluid on M, and 
consequently, the hemisphere b obtains an additional supply of positive 
electricity, while a becomes charged with negative electricity. There is 
thus attraction and repulsion as in the foregoing case. The force of 
repulsion is at first greater, because the quantity of positive fluid on N is 
greater than that of negative fluid ; but the distance ac diminishing, the 
attractive force increases more rapidly than the repulsive force, and 
finally exceeds it. 

iii. The moveable body is a bad conductor. If N is charged, repulsion or 
attraction takes place, according as the electricity is of the same 
or opposite kind to that of the fixed body. If it is in the natural state, 
since a powerful and permanent source of electricity can more or less de¬ 
compose the natural fluid even in bad conductors, the body M will 
decompose the natural fluid of N, and attraction will take place as in the 
first case. 

651. Gold leaf electroscope. —The name electroscope is given to 
instruments for detecting the presence, and determining the kind, of 
electricity in any body. The original pith ball pendulum is an electro¬ 
scope j but, though sometimes convenient, it is not sufficiently delicate. 
Many successive improvements 
have been made on it, and have 
resulted in the form now gene¬ 
rally used, which is due to 
Bennett. 

Bennett's or the gold leaf elec¬ 
troscope. This consists of a tu¬ 
bulated glass shade (fig. 476) 
standing on a metallic foot 
which thus communicates with 
the ground. A metal rod ter¬ 
minating at its upper extremity 
in a knob, and holding at its 
lower end two narrow strips of 
gold leaf, fits in the tubulure of 
the shade, the neck of which is 
coated with an insulating varnish. 

The air in the interior is dried by quicklime, or by chloride of calcium 



Fig. 476. 




FRICTIONAL ELECTRICITY. 


608 


[652- 


and on the insides of the shade there are two strips of gold leaf commu¬ 
nicating with the ground. 

When the knob is touched with a body charged with either kind of 
electricity, the leaves diverge; usually, however, the apparatus is charged 
by induction thus: 

If an electrified body, a stick of sealing wax for example, be brought 
near the knob, it will decompose the natural electricity of the system, 
attracting to the knob the fluid of the opposite kind and retaining it 
there, and repelling the electricity of the same kind to the gold leaves, 
which consequently diverge. In this way, the presence of an electrical 
charge is ascertained, but not its quality. 

To ascertain the kind of electricity the following method is pursued : 
If, while the instrument is under the influence of the body A, which we 
will suppose has a negative charge, the knob be touched by the finger, 
the negative electricity decomposed in induction passes off into the ground, 
and the previously divergent leaves will collapse: there only remains 
positive electricity retained in the knob by induction from A. If now the 
finger be first removed, and then the electrified body, the positive elec¬ 
tricity previously retained by A will spread over the system, and cause 
the leaves to diverge. If now, while the system is charged with positive 
electricity, a positively electrified body, as, for example, an excited glass 
rod, be approached, the leaves will diverge more widely; for the 
electricity of the same kind will be repelled to the extremities. If, on the 
contrary, an excited shellac rod be presented, the leaves will tend to col¬ 
lapse, the fluid, with which they are charged, being attracted by the 
opposite electricity. Hence we may ascertain the kind of electricity, 
either by imparting to the electroscope electricity from the body under 
examination, and then bringing near it a rod charged with positive or 
negative electricity; or the electroscope may be charged with a known 
kind of electricity, and the electrified body in question brought near the 
electroscope. 

It has been proposed to use the electroscope as an electrometer or 
measurer of electricity, by measuring the angle of divergence of the leaves. 
This is done by placing behind them a graduated scale. There are, how¬ 
ever, many objections to such a use, and it is rarely employed for this 
purpose. 

ELECTRICAL MACHINES. 

652. Electrophorus. — It will now be convenient to describe the 
various electrical machines, or apparatus, for generating and collecting 
large supplies of statical electricity. One of the most simple and inex¬ 
pensive of these is the electrophoi'us, which was invented by Volta. Its 
operation depends on the action of induction, of which it forms an excel- 


THE ELECTROPHORUS. 


609 


- 652 ] 

lent illustration. It consists of a cake of resin, B (fig. 477), of about 12 
inches diameter, and an inch thick, which is placed on a metallic surface, 
or very frequently fits in a wooden mould lined with tinfoil, which is 
called the form. Besides this, there is a wooden disc, A (fig. 478), of a 
diameter somewhat less than that of the cake, lined on its under surface 
with tinfoil, and provided with an insulating glass handle. The mode of 
working this apparatus is as follows: All the parts of the apparatus 
having been well warmed, the cake, which is placed in the form, or rests 
on a metallic surface, is briskly flapped with a catskin, by which it 



Fig. 477. Fig. 478. 


becomes charged with negative electricity. The cover is then placed on 
the cake. From the nonconductivity of the resin, the negative electricity 
of the cake does not pass off to the cover. On the contrary, it acts by 
induction on the neutral fluid of the cover and decomposes it, attracting 
the positive fluid to the under surface, and repelling the negative fluid to 
the upper. If the upper surface be now touched with the finger, the 
negative electricity passes off, and the cover remains charged with positive 
electricity, held, however, by the negative electricity of the cake; the 
two electricities do not unite in consequence of the nonconductivity of the 
cake. If now the cover be raised by its insulating handle, the charge 
diffuses itself over the surface, and, if a conductor be brought near it, a 
smart spark passes. 

The metallic form on which the cake rests plays an important part in 
the action of the electrophorus, as it increases the quantity of elec¬ 
tricity and makes it more permanent. For the negative electricity of the 

n d 3 













610 


FRICTIONAL ELECTRICITY. 


[ 653 - 

upper surface of the resin acting inductively on the neutral fluid of the 
lower, decomposes it, retaining on the under surface the positive elec¬ 
tricity, while the negative electricity passes off into the ground. The 
positive fluid thus developed on the under surface reacts on the negative 
fluid of the upper surface, binding it, and causing it to penetrate into the 
badly conducting mass, on the surface of which fresh quantities of elec¬ 
tricity can be produced, far beyond the limits possible without the action 
of the form. It is for this reason, that the electrophorus once charged, 
retains its state for a considerable time, and sparks can be taken from it 
even after a long interval. If the form be insulated, the charge obtained 
is far less than if it is on a conducting support. For the negative elec¬ 
tricity developed on the lower surface, by the inductive action of that 
produced by striking with cat-skin on the upper, acts repulsively on the 
latter, and thus prevents its penetration into the mass. The retention 
of electricity is greatly promoted by keeping the cake in the form, 
and placing the cover upon it, by which the access of air is hindered. 
Instead of a cake of resin, a disc of gutta percha, or vulcanised cloth, or 
vulcanite, may be substituted, and of course, if glass or any material 
which becomes positively electrified by friction be used the cover acquires 
a negative charge. 

653. Ramsden’s electrical machine.— The first electrical machine 
was invented by Otto von Guericke, the inventor also of the air pump. It 
consisted of a sphere of sulphur, which was turned on an axis by means 
of the hand, while the other, pressing against it, served as a rubber. 
Resin was afterwards substituted for the sulphur, which, in turn, 
Hawksbee replaced by a glass cylinder. In all these cases the hand 
served as rubber j and Winckler, in 1740, first introduced cushions of 
horsehair covered with silk as rubbers. At the same time, Bose 
collected electricity disengaged by friction, on "an insulated cylinder 
of tin plate. Lastly, Ramsden, in 1760, replaced the glass cylinder 
by a circular glass plate, which was rubbed by cushions. The form 
which the machine has now is but a modification of Ramsden’s original 
machine. 

Between two wooden supports (fig. 479) a circular glass plate, P, is 
suspended by an axis passing through the centre, and which is turned 
by means of a glass handle M. The plate revolves between two sets of 
cushions or rubbers, F, of leather or of silk, one set above the axis and one 
below, which, by means of screws, can be pressed as tightly against the 
glass as may be desired. The plate also passes between two brass rods 
shaped like a horse-shoe, and provided with a series of points in the 
sides opposite the glass: these rods are fixed to larger metallic cylinders, 
C, which are called the conductors. The latter are insulated by being sup¬ 
ported on glass feet, and are connected with each other by a smaller rod, r. 


ELECTRICAL MACHINE. 


611 



-653] 

The action of the machine is founded on the excitation of electricity 
by friction, and on the action of induction. By friction with the rubbers, 
the glass becomes positively, and the rubbers negatively electrified. If 
now the rubbers were insulated, they would receive a certain charge of 
negative electricity which it would be impossible to exceed, for the 
tendency of the opposed electricities to reunite would be equal to the 
power of the friction to decompose the neutral fluid. But the rubbers 
communicate with the ground by means of a chain, and, consequently, 


Fig. 479. 

as fast as the negative electricity is generated, it passes off. The positive 
electricity of the glass acts then by induction on the conductor, attract¬ 
ing the negative fluid. The conductors thus lose their negative elec¬ 
tricity, and remain charged with positive fluid. The plate accordingly 
gives up nothing to the conductors; in fact, it only abstracts from them 
their negative fluid. 



































612 


FRICTIONAL ELECTRICITY. 


[ 654 - 

If the hand be brought near the conductor when charged, a spark 
follows, which is renewed as the machine is turned. In this case, the 
positive electricity decomposes the neutral fluid of the body, attracting 
its negative fluid, and combining with it when the two have a sufficient 
tension. Thus, with each spark, the conductor reverts to the neutral 
state, but becomes again electrified as the plate is turned. 

654. Precautions in reference to tbe machine.— The glass, of 
which the plate is made, must be as little hygroscopic as possible. Of 
late ebonite has been frequently substituted for glass; it has the advan¬ 
tage of being neither hygroscopic nor fragile, and of readily becoming 
electrical by friction. The plate is usually from ~ to | of an inch in 
thickness, and from 20 to 30 inches in diameter, though these dimensions 
are not unfrequently exceeded. 

The rubbers require great care both in their construction and in their 
preservation. They are commonly made of leather stuffed with horse¬ 
hair. Before use they are coated either with powdered aurum musivum 
(sulphuret of tin), or graphite, or amalgam. The action of these sub¬ 
stances is not very clearly understood. Some consider that it merely 
consists in promoting friction. Others again believe that a chemical 
action is produced, and assign in support of this view the peculiar 
smell noticed near the rubbers when the machine is worked. Amalgams, 
perhaps, promote most powerfully the disengagement of electricity. 
Kienmayer's amalgam is the best of them. It is prepared as follows: 
one part of zinc and one part of tin are melted together, and removed 
from the fire and two parts of mercury stirred in. The mass is then 
transferred to a wooden box containing some chalk, and then well 
shaken. The amalgam, before it is quite cold, is powdered in an iron 
mortar, and then preserved in a stoppered glass vessel. For use, a little 
cacao butter or lard is spread over the cushion, some of the powdered 
amalgam sprinkled over it, and the surface smoothed by a ball of flattened 
leather. 

In order to avoid a loss of electricity, two quadrant-shaped pieces of 
oiled silk are fixed to the rubbers, so as to cover it on both sides, one at 
the upper part from a to F, and the other in the corresponding part of 
the lower rubbers. These flaps are not represented in the figure. Yellow 
oiled silk is the best, and there must be perfect contact between the plate 
and the cloth. 

Ramsden’s machine, a represented in figure 479, only gives positive 
electricity. But it may be arranged so as to give negative electricity' by 
placing it on a table with insulating supports. By means of a chain, 
the conductor is connected with the ground, and the machine worked as 
before. The positive electricity passes off by the chain into the ground, 
while the negative electricity remains in the supports and in the insulated 


ELECTRICAL MACHINE. 


G13 


- 657 ] 

table. On bringing the finger near the uprights, a sharper spark than 
the ordinary one is obtained. 

655. Maximum of tension. Quadrant electrometer. —It is im¬ 
possible to exceed a certain limit of electrical tension with the machine, 
whatever precautions are taken, or however rapidly the plate is turned. 
This limit is attained when the loss of electricity equals its production. 
The loss depends on three causes: i. The loss by the atmosphere, and 
the moisture it contains; this is proportional to the tension, ii. The 
loss by the supports, iii. The recombination of the electricities of the 
rubbers and the glass. 

The first two causes have been already mentioned. With reference to 
the latter, it must be noticed that the electrical tension increases with 
the rapidity of the rotation, until it reaches a point at which it over¬ 
comes the resistance presented by the nonconductivity of the glass. At 
this point, a portion of the two electricities separated on the rubbers and 
on the glass recombines, and the tension remains constant. It is, there¬ 
fore, ultimately independent of the rapidity of rotation. 

The electric tension is measured by the quadrant or Henley's electro¬ 
meter, which is attached to the conductor. This 
is a small electric pendulum, consisting of a 
wooden rod, d, to which is attached an ivory or 
cardboard scale, c (fig. 480). In the centre of this 
is a small whalebone index, moveable on an axis, 
and terminating in a pithball, a. Being attached 
to the conductor, the index rises as the machine 
is charged, ceasing to rise when the limit is 
attained. When the rotation is discontinued the 
index falls rapidly if the air is moist, but in dry 
air it only falls slowly, showing, therefore, that 
the loss of electricity in the latter case is less than 
in the former. 

656. Secondary conductors. — These are 
large cylinders of copper, or tin, or wood coated 
with tinfoil, which are insulated by placing them on glass supports, or 
suspending them by silk threads. They are then placed in connection 
with the conductors, C. The surface on which the electricity is accu¬ 
mulated being thus greater, the tension does not increase; but with an 
equal tension the quantity of electricity is proportional to the surface. In 
fact, when the machine is discharged, much more powerful luminous 
sparks are obtained. 

657. Nairne’s electrical machine. —The construction of the cylinder 
machines, as ordinarily used in England, is due to Nairne. They are 
well adapted for obtaining either kind of electricity. In Nairne’s machine 



Fig. 480. 




614 


FRICTIONAL ELECTRICITY. 


[658- 

(fig. 481) the cylinder is rubbed by only one cushion, C, which is made 
of leather stuffed with horsehair, and is screwed to an insulated conductor, 
A. On the opposite side of the cylinder, there is a similar insulated con¬ 
ductor, B, provided with a series of points on the sides next the glass. 
To the lower part of the cushion A, is attached a piece of oiled silk, 
which extends over the cylinder to just above the points. This is not re¬ 
presented in the figure. When the cylinder is turned, A becomes charged 
with negative and B with positive electricity collected, provided the 
other cylinder be connected with the ground. 



Fig. 481. 


658. Armstrong’s hydroelectrical machine. — In this machine 
electricity is produced by the disengagement of aqueous vapour through 
narrow orifices. The discovery of the machine was occasioned by an 
accident. A workman having accidentally held one hand in a jet of 
steam, which was issuing from an orifice in a steam boiler at high pres¬ 
sure, while his other hand grasped the safety valve, was astonished at 
experiencing a smart shock. Sir W. Armstrong (then Mr. Armstrong, 
of Newcastle), whose attention was drawn to this phenomenon, ascer¬ 
tained that the vapour was charged with positive electricity, and by 
repeating the experiment with an insulated locomotive, found that the 
boiler was negatively charged. Armstrong believed that the electricity 
was due to a sudden expansion of the vapour j Faraday, who afterwards 
examined the question, ascertained its true cause, which will be best 
understood after describing a machine which Armstrong devised for 
reproducing the phenomenon. 

It consists of a boiler of wrought-iron plate (fig. 482), with a central 





















ELECTRICAL MACHINE. 


615 



Fig. 482. 

goes partial condensation, and becomes charged with vesicles of water; 
a necessary condition, for Faraday found that no electricity is produced 
when the vapour is quite dry. 

The development of electricity in the machine was at first attributed 
to the condensation of the vapour, but Faraday found that it is solely 
due to the friction of the globules of water against the jet. For if the 
little cylinders which line the jets are changed, the kind of electricity is 


-658] 


fire, and insulated on four legs. It is about 5 feet long by 2 feet in 
diameter, and is provided at the side with a gauge to show the height 
of the water in the boiler. A small manometer, not represented in the 
drawing, indicates the pressure. C is the stopcock, which is opened 
when the vapour has sufficient tension. Above this is the box, B, in 
which are the tubes through which the vapour is disengaged. On these 
are fitted jets of a peculiar construction, which will be understood from 
the section of one of them, M, represented on a larger scale. They are 
lined with hard wood in a manner represented by the diagram. The 
box B contains cold water. Thus, the vapour, before escaping, under- 






































Fig. 483. 

electrical machines were known in this country in which the electricity 
was not developed by friction, but by the continuous inductive action of 
a body already electrified, as the electrophorus : within the last two or 
three years such machines have been reinvented and come into use. 
The form represented in fig. 483 was invented by M. Holtz, of Berlin. 

It consists of two circular plates of thin glass at a distance of 3 mm. 


616 FRICTIONAL ELECTRICITY. [ 659 - 

changed, and if ivory is substituted little or no electricity is produced. 
The same effect is produced if any fatty matter is introduced into the 
boiler. In this case, the linings are of no use. It is only in case the 
water is pure that electricity is disengaged, and the addition of acid, or 
saline solutions, even in minute quantity, prevents any disengagement of 
electricity. If turpentine is added to the boiler, the effect is reversed, 
the vapour becomes negatively and the boiler positively electrified. 

With a current of moist air, Faraday has obtained effects similar to 
those of this apparatus, but with dry air no effect is produced. 

659. Holtz’s electrical macbine a —Before the end of last century 






































holtz’s electrical machine. 


617 


-659] 

from each other; the larger one A A, which is 2 feet in diameter, is fixed 
by means of 4 wooden rollers, resting on glass axes and glass feet. The 
diameter of the second plate, B B, is 2 inches less ; it turns on a horizontal 
glass axis, which passes through a hole in the centre of the large fixed 
plate. In the plate A, on the same diameter, are two large apertures, or 
windows, FF'. Along the lower edge of the window F, on the posterior 
face of the plate, a hand of paper p is glued, and on the anterior face 
a sort of tongue of thin cardboard n, j oined to p by a thin strip of paper, 
and projecting into the window. At the upper edge of the window 
F', there are corresponding parts p' and n'. The papers p and p' 
constitute the armatures. The two plates, the armatures, and their 
tongues, are carefully covered with shellac varnish, but more especially 
the edges of the tongues. 

In front of the plate B at the height of the armatures are two brass 
combs, o o', supported by two conductors of the same metal c c'. In the 
front end of these conductors are two pretty large brass knobs, through 
which pass two brass rods terminated by smaller knobs r r' and provided 
with wooden handles K K'. These rods, besides moving with gentle 
friction in the knobs, can also be turned so as to be more or less 
approached and inclined towards each other. The plate is turned by 
means of a winch M, and a series of pulleys, which transmit its motion to 
the axis; the velocity which «it thus receives is 12 to 15 turns in a 
second, and the rotation should take place in the direction indicated by 
the arrow, that is, towards the points of the cardboard tongues n n'. 

To work the machine the armatures p p' must be first primed; that is, 
one of them is positively and the other negatively electrified. This is 
effected by means of a sheet of ebonite, which is excited by striking it 
with flannel, or, better, with catskin ; the two knobs r r' having been con¬ 
nected, the electrified plate is brought near one of them p, for instance, 
and the plate is turned. The ebonite is charged with negative elec¬ 
tricity, which acting inductively on the armature p decomposes its 
neutral fluid, and the negative electricity repelled is discharged by the 
tongue on to the moveable plate, the armature remaining charged with 
positive electricity. After half a turn the negative electricity of the plate 
coming in front of the window F' acts in the same way on the 
armature p', charging it with positive electricity by taking from it a 
corresponding quantity of negative electricity by the tongue n'. After 
a few turns the two armatures being thus electrified, one positively 
and the other negatively, the inducing plate of ebonite is removed, 
and the knobs r r' separated as represented in the figure. On continuing 
to turn the plate uninterrupted, a torrent of sparks strikes across from 
one knob to the other. 

These details being known the following is the explanation of the 


618 


FRICTIONAL ELECTRICITY. 


[ 659 - 

action as given by the inventor. Looking first at that portion of the 
moveable plate which corresponds to the positive armature p, the 
neutral electricity of this portion being decomposed by the induction 
of the armature, the repelled positive electricity is discharged on the 
conductor C (or in other words the positive electricity of this armature, 
acting inductively on this conductor, withdraws negative electricity, which 
is deposited on the moveable plate and leaves the conductor charged 
with positive electricity). As the rotation of the plate continues, its 
negative electricity is neutralised from F to F' by the induction which 
it exerts on the fixed plate; but become free in front of the window C', 
it is discharged on the tongue n' and on the conductor E (the ex¬ 
pression ‘discharged’ being used in the same sense as before). The 
portion of the plate hitherto considered is thus virtually restored to 
the neutral state; but as soon as it comes in front of the negative 
armature p ', this acting by induction, the two electricities are again 
separated, and the negative is repelled to the conductor C', while the 
positive, which remains on the rotating plate, is neutralised from F' to F. 
Become free at F the same effect is produced as at F', that is, the plate 
discharging its positive electricity on the tongue n, and on the conductor 
C, is restored to the neutral state, but the induction of the armature, p', 
decomposing the neutral fluid formed, repels to the conductor a fresh 
quantity of positive electricity, and so on as long as the plate is turned. 
Hence it will be observed that each time a portion of the surface of the 
plate comes in front of the windows F, F', the conductors C C' receive 
two charges of the same kind, the first being due to the fluid which has 
become free on the rotating plate, and the second to the induction of 
the armature. It must at the same time be remarked that the 
armatures are kept charged by the successive discharges of the plate 
turning on the tongues n n', and hence it is that in dry air the machine, 
like the electrophorus, can work for an indefinite period. 

With plates of equal dimensions Holtz’s machine is far more powerful 
than the ordinary electrical machine (653). The power is still further 
increased by suspending to the conductors C C' two condensers H, H' 
(663), which consist of two glass tubes coated with tinfoil inside and 
out, to within a fifth of their height. Each of them is closed by a cork, 
through which passes a rod, communicating at one end with the inner 
coating, and suspended to one of the conductors by a crook at the other 
end. The two external coatings are connected by a conductor G. They 
are in fact only two small Leyden jars, (668) one of them H becoming 
charged with positive electricity on the inside, and negative on the out¬ 
side, the other H', with negative electricity on the inside, and positive on 
the outside. Becoming charged by the intervention of the machine, and 


619 


- 660 ] EXPERIMENTS WITH THE ELECTRICAL MACHINE, 

being' discharged at the same rate by the knobs rr they strengthen the 
spark, which may attain a length of 6 or 7 inches. 

The current of the machine is utilised by placing in part of the frame 
two brass uprights QQ' with binding screws in which are copper wires ; 
then by means of the handles KK', the rods which support the knobs rr', 
are inclined, so that they are in contact with the uprights. The current 
being then directed by the wires, a battery of six jars can be charged in 
a few minutes, water can be decomposed, a galvanometer deflected, and 
Geissler’s tubes worked as with the voltaic pile. 

Holtz’s machine is very much affected by the moisture of the air; but 
M. Kuhmkorff, the constructor of these machines, has found that, spread¬ 
ing on the table a few drops of petroleum, the vapours which condense 
on the machine protect it against the moisture of the atmosphere. 

These machines are small in compass, and not very expensive, and 
require less force for working them than frictional machines. When the 
armatures, are electrified, more resistance is experienced in turning the 
plate than if they are not electrified ; in the former case part of the 
mechanical force exerted by the arm of the operator is transformed into 
electricity. 


EXPERIMENTS WITH THE ELECTRICAL MACHINE. 

660. Spark. Insulating: stool. —One of the most curious pheno¬ 
mena observed with the electrical machine, is the spark drawn from the 
conductor when a finger is presented to it. The positive electricity of 
the conductor acting inductively on the neutral fluid of the body, de¬ 
composes it, repelling the positive and attracting the negative fluid. 
When the tension of the opposed electricities is sufficiently great to 
overcome the resistance of the air, they recombine with a smart crack 
and a spark. The spark is instantaneous, and is accompanied by a sharp 
prickly sensation, more especially with a powerful machine. Its shape 
varies. When it strikes at a short distance, it is rectilinear, as seen in 
fig. 484. Beyond two or three inches in length, the spark becomes irre¬ 
gular, and has the form of a sinuous curve with branches (fig. 485). If the 
discharge is very powerful, the spark takes a zigzag shape (fig. 486). 
These two latter appearances are seen in the lightning discharge. 

A spark may be taken from the human body by the aid of the insulating 
stool, which is simply a low stool with stout glass legs. The person stand¬ 
ing on this stool touches the prime conductor, and as the human body is 
a conductor, the electrical fluid is distributed over its surface as over an 
ordinary insulated metallic conductor. The hair diverges in consequence 
of repulsion, a peculiar sensation is felt on the face, and if another person, 
standing on the ground, presents his hand to any part of the body, a smart 
crack with a pricking sensation is produced. 


620 


FRICTIONAL ELECTRICITY. 


[ 661 - 


A person standing on an insulated stool maybe positively electrified by 
being struck with a catskin. If the person holding the catskin stands on an 


Fig. 484. 


Fig. 485. 


Fig. 486. 



insulated stool, the striker becomes positively, and the person struck ne¬ 
gatively electrified. 

661. Electrical chimes. —The electrical chimes is a piece of apparatus 



and after contact repel them. Being 


consisting of three bells suspended 
to a horizontal metal rod (fig. 
487). Two of them, A and B, 
are in metallic connection with 
the conductor; the middle bell 
hangs by a silk thread, and is 
thus insulated from the conductor, 
but is connected with the ground 
by means of a chain. Between 
the bells are small copper balls 
suspended by silk threads. When 
the machine is worked, the bells 
A and B being positively elec¬ 
trified, attract the copper balls, 
now positively electrified, they are 















































































621 


-662] EXPERIMENTS WITH THE ELECTRICAL MACHINE. 

in turn attracted by the middle bell, C, which is charged with negative 
electricity by induction from A and B. After contact they are again 
repelled, and this process is repeated as long as the machine is in action. 

Fig. 488 represents an apparatus originally devised by Volta for the pur¬ 
pose of illustrating what he supposed to be the motion of hail between two 
clouds oppositely electrified. It consists of a tubulated glass shade, with 
a metal base, on which are some pithballs. The tubulure has a metal cap, 
through which passes a brass rod, provided with a metallic disc or sphere 
at the lower end, and at the upper with a knob, which touches the prime 
conductor. 

When the machine is worked, the sphere, becoming positively electri¬ 
fied, attracts the light pithballs, which are then immediately repelled, and, 
having lost their charge of positive electricity, are again attracted, again 
repelled, and so on, as long as the machine continues to be worked. An 
amusing modification of this experiment is frequently made by placing 
between the two plates small pith figures, somewhat loaded at the base. 
When the machine is worked, the figures execute a regular dance. 



662. Electrical whirl or vane. —The electrical whirl or vane consists 
of 5 or 6 wires, terminating in points, all bent in the same direction, and 
fixed in a central cap, which rotates on a pivot (fig. 489). When the 
apparatus is placed on the conductor, and the machine worked, the 
whirl begins to revolve in a direction opposite that of the points. This 
motion is not analogous to that of the hydraulic tourniquet (193). . It 
is not caused by a flow of material fluid, but is owing to a repulsion 
between the electricity of the points and that which they impart to the 






















622 


FRICTIONAL ELECTRICITY. 


[ 663 - 


air by conduction. The electrical fluid, being accumulated on the points 
in a high state of tension, passes into the air, and imparting thus a 
charge of electricity, repels this electricity while it is itself repelled. 
That this is the case, is evident from the fact that on approaching the 
hand to the whirl while in motion, a slight draught is felt, due to 
the movement of the electrified air; while in vacuo the apparatus does not 
act at all. This draught or wind is known as the electrical aura. 

When the electricity thus escapes by a point, the electrified air is 
repelled so strongly as not only to be perceptible to the hand, but also 
to engender a current strong enough to blow out a candle. Fig. 490 



Fig. 491 


Fig. 490 


shows this experiment. The same effect is produced by placing a taper 
on the conductor, and bringing near it a pointed wire held in the hand 
(fig. 491). The current arises, in this case, from the contrary fluid, which 
escapes by the point under the influence of the machine. 

The electrical orrery and the electrical inclined plane are analogous to 
these pieces of apparatus. 


CHAPTER IV, 


CONDENSATION OF ELECTRICITY, 


663. Condensers. Theory of condensers. —A condenser is an appa¬ 
ratus for condensing a large quantity of electricity on a comparatively 
small surface. The form may vary considerably, but in all cases consists 
essentially of two insulated conductors, separated by a nonconductor, and 
the working depends on the action of induction. 

Epinus’s condenser consists of two circular brass plates, A and B (fig. 
492), with a sheet of glass, C, between them. The plates, each provided 
with a pitliball pendulum, are mounted on insulating glass legs, and can 











CONDENSATION OF ELECTRICITY. 


623 


- 663 ] 

be moved along a support, and fixed in any position. When electricity 
is to be accumulated, the plates are placed in contact with the glass, and 


c 



Fig. 492. 

then one of them, B for instance, is connected with the electrical machine, 
and the other placed in connection with the ground, as shown in fig. 493. 
In explaining the action of the condenser, it will be convenient in each 


c 



Fig. 493. 


case to call that side of the metal plate nearest the glass, the anterior , 
and the other the posterior side. And first let A be at such., a distance 





































624 


FRICTIONAL ELECTRICITT. 


[663- 




Fig. 494. 


from B as to be out of the sphere of its action. The plate B which is 
then connected with the conductor of the electrical machine, takes its 
maximum charge, which is distributed equally on its two faces, and the 
pendulum diverges widely. If the connection with the machine be 
interrupted, nothing would be changed j but if the plate A be slowly 
approached, its neutral fluid being decomposed by the influence of B, 
the negative is accumulated on its anterior face n (fig. 494), and the 
positive passes into the ground. But as the negative electricity of 

the plate A reacts in its turn on the 
positive of the plate B, the latter 
fluid ceases to be equally distributed 
on both faces, and is accumulated 
on its interior face m. The pos¬ 
terior face, p , having thus lost a por¬ 
tion of its electricity, its tension has 
diminished, and is no longer equal 
to that of the machine, and the pen¬ 
dulum, b, diverges less widely. 
Hence B can receive a fresh quantity 
from the machine, which acting as just described decomposes by induc¬ 
tion a second quantity of neutral fluid on the plate A. There is then a 
new accumulation of negative fluid on the face n , and consequently of 
positive fluid on m. But each time that the machine gives off* electricity 
to the plate, only a part of this passes to the face m, the other remaining 
on the face p ; the tension here, therefore, continues to increase until it 
equals that of the machine. From this moment equilibrium is established, 
and a limit to the charge attained, which cannot be exceeded. The 
quantity of electricity accumulated now on the two faces m and n is 
very considerable, and yet the pendulum diverges just as much as it did 
when A was absent and no more; in fact, the tension at p is just what it 
was then, namely, that of the machine. 

The accumulation of electricity in condensers was formerly explained 
by saying that the electricity of the condensing plate A neutralised the 
contrary electricity of the collecting plate, and it was because the elec¬ 
tricity on this latter was then dissimulated or latent that it could receive a 
fresh supply. But from what has been said, it is unnecessary to recur to 
any special hypothesis as to the state of electricity to explain the theory 
of condensers. 

When the condenser is charged, that is, when the opposite electricities 
are accumulated on the anterior faces, connection with the ground is 
broken by raising the wires. The plate A is charged with negative 
electricity, but simply on its anterior face (fig. 494), the other side being 
neutral. The plate B, on the contrary, is electrified on both sides, but 







CONDENSATION OF ELECTRICITY. 


625 


- 664 ] 

unequally; the accumulation is only on its anterior face, while on the 
posterior, p, the tension is simply equal to that of the machine at the 
moment the connections are interrupted. In fact, the pendulum b 
diverges and a remain's vertical. But if the two plates are removed the 
two pendulums diverge (fig. 492), which is owing to the circumstance 
that as the plates no longer act on each other, the positive fluid is 
equally distributed on the two faces of the plate B, and the negative on 
those of the plate A. 

664. Slow discharge and instantaneous discharge. —While the 
plates A and B are in contact with the glass (fig. 493), and the connec¬ 
tions interrupted, the condenser may be discharged, that is, restored to 
the neutral state, in two ways; either by a slow or by an instantaneous 
discharge. To discharge it slowly the plate B, that is, the one containing 
an excess of electricity, is touched with the finger; a spark passes, all 
the electricity on p passes into the ground, the pendulum, b, falls, but a 
diverges. For B having lost part of its electricity only retains on the 
face in, that held by the inductive influence of the negative on A. But 
the quantity thus retained at B is less than that on A; this has free 
electricity which makes the pendulum a diverge, and if it now be 
touched a spark passes, the pendulum a sinks while b rises, and so on 
by continuing to touch alternately the two plates. The discharge only 
takes place slowly; in very dry air it may require several hours. If the 
plate A were touched first, no electricity would be removed, for all it has 
is retained by that of the plate B. To remove the total quantity of 
electricity by the method of alternate contacts, an infinite number of 
such contacts would theoretically be required, as will be seen from the 
following calculation. 

Let the total quantity of positive electricity on B be taken = 1; by 
induction it retains on A a quantity less than its own of negative elec¬ 
tricity ; let this quantity be called in; m being a fraction in all cases 
less than unity, but which varies with the distance of the plates and the 
nature of the dielectric. Now the m of negative electricity on A 
reacting in turn on the positive on B, retains there mXm=m i of posi¬ 
tive electricity, and therefore the free electricity on B, that which 
makes the pendulum b diverge, is 1 - m 2 , and if B be touched this 
quantity is removed. The m of negative on A now retains, on B, m 2 of 
positive; this binds in turn m times its own quantity, that is, m % of negative 
on A, and the free negative electricity which now makes the pendulum 
a diverge is represented by m—m 3 ~m(l — m 2 ). If A be now touched 
this quantity is removed, the pendulum a sinks and b rises, for B has 
now an excess of free electricity, which it is readily seen is represented 
by m 2 ( 1—m 2 ). By pursuing this reasoning it will be seen that the 


FRICTIONAL ELECTRICITY. 


626 


[665- 


following expresses the quantities removed and left after each successive 
contact:— 

Positive. Negative. 



1 

m 


1 — rri 1 ; 

rri 2 

m*; 

in (1 — m 2 ) 

(1 — w 2 )m 2 ; 

m* 

rri ; 

m 3 (l — rri 1 ) 

(1 - m 2 )m 4 ; 

m 6 

rri ; 

m 5 ( 1 — rri 2 ) 

(1 — m 9 )m n 2 ; 

m n 

m n+1 ; 

7w n _ 1 (l - rri 2 ) 



An instantaneous discharge may he effected by means of the discharg¬ 
ing rod (fig. 495). This consists of two bent 
brass wires, terminating on knobs, and joined by 
a hinge. When provided with glass handles, as 
in fig. 495, it forms a glass discharging rod. In 
using this apparatus one of the knobs is pressed 
against one plate of the condenser, and the other 
knob brought near the other. At a certain dis¬ 
tance a spark strikes from the plate to the knob, 
caused by the sudden recomposition of the two 
opposite electricities. 

When the condenser is discharged by the 
discharger no sensation is experienced, even 
though the latter be held in the hand; of the 
two conductors, the electric fluid always chooses the better, and hence 
the discharge is effected through the metal, and not through the body. 
But if while one hand is in contact with one plate, the other touches 
the second, the discharge takes place through the breast and arms, and a 
considerable shock is felt; and the larger the surface of the condenser, 
and the greater the electric tension, the more violent is the shock. 

665. Calculation of the condensing: force. —The condensing force 
is the relation between the whole charge, which the collecting plate can 
take while under the influence of the second plate, to that which it 
would take if alone; in other words, it is the relation of the total 
quantity of electricity on the collecting plate to that which remains 
free; for it is assumed that the quantity of free electricity on the 
collecting plate, is the same as that which it would take if it were 
alone. 

To calculate the condensing force, let us, as before, express the total 
quantity of positive electricity which the collecting plate B can take 
while under the influence of the condensing plate, by 1, then m is the 
whole quantity of negative electricity on the second plate. But, as we 


have just seen, the quantity of free electricity on B is 1 - 

——„ is the fraction which expresses the condensing force. 

1 - nr 


Hence 



FULMINATING PANE. 


627 


-667] 

The value of in is determined experimentally by means of the proof 
plane and the torsion balance. Thus, if m were 0-99 the quantity of 
electricity which could be accumulated on the collecting plate B, under 
the influence of A, would be 50 times as much as the quantity it could 
receive if alone; while if m were 0*75 the quantity would be 2*28 times 
as great. 

666. Limit of the charge of condensers. —The quantity of elec¬ 
tricity which can be accumulated on each plate is, ceteris paribus , 
proportional to the tension of the electricity on the conductor, and to 
the surface of the plates: it decreases as the insulating plate is thicker, 
and it differs with the specific inductive capacity of the substance. 
Two causes limit the quantity of electricity which can be accumulated. 
First, that the electric tension of the collecting plates gradually in¬ 
creases, and ultimately equals that of the machine, which cannot, 
therefore, impart any free electricity. The second cause is the imperfect 
resistance which the insulating plate offers to the recombination of the 
two opposite electricities; for when the force which impels the two 
fluids to recombine, exceeds the resistance offered by the insulating plate, 
it is perforated, and the contrary fluids unite. 

667. Fulminating pane. —This is a simple form of the condenser, 
and is more suitable for giving strong shocks and sparks. It consists 



Fig. 496. 

of a glass plate fixed in a wooden frame (fig. 496) ; on each side of the 
glass pieces of tin foil are fastened opposite each other, leaving a space 
free between the edge and the frame. It is well to cover this part of 
the glass with an insulating layer of shellac varnish. One of the sheets 

E E 2 











628 


FRICTIONAL ELECTRICITY. 


[ 668 - 

of tin foil is connected with a ring on the frame by a strip of tin foil, 
so that it can be put in communication with the ground by means of a 
chain. To charge the pane the insulated side is connected with the machine. 
As the other side communicates with the ground, the two coatings play 
exactly the part of a condenser. On both plates there are accumulated 
large quantities of contrary electricities. 

The pane may be discharged by simply pressing the knob of the dis¬ 
charger against the lower surface, while the other knob is brought near 
the upper coating. A spark ensues, due to the recomposition of the two 
electricities, but the operator experiences no sensation, for the discharge 
takes place through the wire. But if the connection between the two 
coatings be made by touching them with the hands, a violent shock is 
felt in the hands and breast, for the combination then takes place through 
the body. 

668. Iieyden jar.— The Leyden jar, so named from the town Leyden, 
where it was invented, is nothing more than a modified condenser or 



Franklin’s pane. Fig. 497 represents a Leyden jar in the process of being 
charged. It consists of a glass bottle of any convenient size, the interior 
of which is either coated with tin foil or filled with thin leaves of 
copper, or with gold leaf. Up to a certain distance from the neck the 
outside is coated with tin foil. The neck is provided with a cork, through 
which passes a brass rod, which terminates at one end in a knob, and 
communicates with the metal in the interior. The metallic coatings 
are called respectively the internal and external armatures or coatings. 
Like the condenser, the jar is charged by connecting one of the arma¬ 
tures with the ground, and the other with the source of electricity. 
When it is held in the hand by the external coating, and the knob pre¬ 
sented to the conductor of the machine, positive electricity is accumu¬ 
lated on the inner, and negative electricity on the outer coating. 
The reverse is the case if the jar is held by the knob, and the external 
coating presented to the machine. The theory of the jar is identical 
with that of the condenser, and all that has been said of this applies to 



LEYDEN JAR. 


629 


-669] 

the jar, substituting the two armatures for the two plates, A and B, of 

fig. 493. 

Like the condenser, the Leyden jar maybe discharged either slowly or 
instantaneously. For the latter it is held in the hand by the outside 
coating (fig. 498), and the two coatings are then connected by means of 
the simple discharger. Care must be taken to touch first the external 
coating with the discharger, otherwise a smart shock will be felt. To 
discharge it slowly the jar is placed on an insulated plate, and first the 
internal and then the external coating touched, either with the hand or 
with a metallic conductor. A slight spark is seen at each discharge. 

Fig. 499 represents a very pretty experiment for illustrating the slow 



Fig. 498. 


Fig. 499. 


discharge. The rod terminates in a small bell, d, and the outside coating 
is connected with an upright metallic support, on which is a similar bell, 
e. Between the two bells a light copper ball is suspended by a silk 
thread. The jar is then charged in the usual manner and placed on the 
support m. The internal armature contains a quantity of free electricity ; 
the pendulum is attracted and immediately repelled, striking against the 
second bell, to which it imparts its free electricity. Being now neutral¬ 
ised it is again attracted by the first bell, and so on for some time, espe¬ 
cially if the air be dry, and the jar pretty large. 

(369. Leyden jar with moveable coatings. —This apparatus (fig. 
500) is used to demonstrate that in the Leyden jar, the opposite electri¬ 
cities are not distributed on the coatings merely, but reside principally on 
the opposite sides of the glass. It consists of a somewhat conical glass 
vessel, B, with moveable coatings of zinc or tin, C and D. These separate 
pieces placed one in the other, as shown in figure A, form a complete 










630 


FRICTIONAL ELECTRICITY. 


[ 670 - 

Leyden jar. After having charged the jar, it is placed on a cake of 
resin; the internal coating is first -•removed by the hand, and then the 
glass vessel. The coatings are found to contain very little electricity, and 
if they are placed on the table they are reduced to the neutral state. 
Nevertheless, when the jar is put together again, as represented in the 
figure at A, a shock may be taken from it almost as strong as if the coat¬ 
ings had not been removed. It is therefore concluded that the electri- 



Fig. 500. 


cities in virtue of their mutual attraction, leave the coatings to adhere to 
the sides of the glass. 

The experiment may be conveniently made by forming a Leyden jar, 
of which the inside and outside coatings are of mercury, charging it; 
then, having mixed the two coatings, the apparatus is put together 
again, upon which a discharge may once more be taken. 

670. Xiichtenberg-’s figures.— This experiment well illustrates the 
opposite electrical conditions of the two coatings of a Leyden jar. Hold¬ 
ing ajar charged with positive electricity by the hand, a series of lines 
are drawn with the knob on a cake of resin or vulcanite; then having 
placed the jar on an insulator, it is held by the knob, and another series 
traced by means of the outer coating. If now an intimate mixture of 
red lead and flour of sulphur be projected on the cake, the sulphur will 
attach itself to the positive lines, and the red lead to the negative lines. 
The sulphur will arrange itself in tufts with numerous diverging 
branches, while the red lead will take the form of small circular spots, in¬ 
dicating a difference in the distribution of the two electricities on the 
surface of the resin. 

671. Penetration of the charge. Residual charge _Not only do 

the electricities adhere to the two surfaces of the insulating medium 
which separates them, but they penetrate to a certain extent into the 
interior, as is shown by the following experiments: A condenser is formed 
of a plate of shellac, separated by moveable metallic plates. It is then 
charged, retained in that state for some time, and afterwards discharged. 





ELECTRIC BATTERIES. 


631 


- 672 ] 

On removing the metallic coatings and examining both surfaces of the 
insulator, they show no signs of electricity. After some time, however, 
each face exhibits the presence of some electricity of the same kind as 
that of the plate with which it was in contact, while the apparatus was 
charged. This can be explained by assuming that the electricity had 
slowly penetrated from the exterior to the interior during the first phase 
of the experiment, and had returned to the surface during the second. 

A phenomenon frequently observed in Leyden jars is of the same 
nature. When a jar has been discharged and allowed to stand a short 
time, it exhibits a second charge, which is called the electric residue. The 
jar may be again discharged, and a second residue will be left, feebler 
than the first, and so on, for three or four times. Indeed with a delicate 
electroscope a long succession of such residues may be demonstrated. 
Time is required for the penetration of the electricities into the mass; 
and hence the residue is greater the longer the jar has remained charged. 
The magnitude of the residue further depends on the intensity of the 
charge, and also on the degree of contact of the metallic plates with the 
insulator. It varies with the nature of the substance, but there is no 
residue with either liquids or gaseous insulators. Faraday found that 
with paraffine the residue was greatest, then with shellac, while with 
glass and sulphur it was least of all. Kohlrausch has found that the 
residue is nearly proportional to the thickness of the insulator. 

672. Electric batteries. —The charge which a Leyden jar can take 
depends on the extent of the coated surface, and for small thicknesses is 
inversely proportional to the thickness of the insulator. Hence, the 
larger and thinner the jar the more powerful the charge. But very large 
jars are expensive, and liable to break; and when too thin, the accu¬ 
mulated electricities are apt to discharge themselves through the glass, 
especially if it is not quite homogeneous. Leyden jars have usually from 
£ to 3 square feet of coated surface. For more powerful charges electric 
batteries are used. 

An electric battery consists of a series of Leyden jars, whose internal 
and external coatings are respectively connected with each other (fig. 
501). They are usually placed in a wooden box lined on the bottom 
with tin foil. This lining is connected with two metallic handles in the 
sides of the box. The internal coatings are connected with each other 
by metallic rods, and the battery is charged by placing the internal coat¬ 
ings in connection with the prime conductor, while the external coatings 
are connected with the ground by means of a chain fixed to the handles. 
A quadrant electrometer fixed to the jar serves to indicate the charge of 
the battery. Although there is a large quantity of electricity accu¬ 
mulated in the apparatus the divergence is not great, for it is simply due 
to the free electricity on the internal coating. The number of jars is 


632 


FRICTIONAL ELECTRICITY. 


[673- 

usually four, six, or nine. The larger and more numerous they are, the 
longer is the time required to charge the battery, but the effects are so 
much the more powerful. 

When a battery is to be discharged, the coatings are connected by means 
of the discharging rod, the outside coating being touched first. Great 



Fig. 501. 


care' is required, for with large batteries serious accidents may occur, 
resulting even in death. 

673. The universal discharger. —This is an' almost indispensable 
apparatus in experiments with the electric battery. On a wooden stand 
(fig. 502) are two glass legs, each provided with universal joints, in 
which moveable brass rods are fitted. Between these legs is a small 
ivory table, on which is placed the object under experiment. The two 
metal knobs being directed towards the object, one of them is connected 
with the external coating of the battery, and the moment communication 
is made between the other and the internal coating by means of the glass 
discharging rod, a violent shock passes through the object on the table. 

674. Charging by cascade— A series of Leyden jars are placed each 
separately on insulating supports. The knob of the first is in connection 
with the prime conductor of the machine, and its outer coating with the 
knob of the second, the outer coating of the second, with the knob of the 
third, and so on ; the outer coating of the last communicating with the 
ground. The inner coating of the first receives a charge of positive elec¬ 
tricity from the machine, and the corresponding positive -electricity set 
free by induction on its outer coating instead of passing to the ground, 



















































ELECTRIC BATTERIES. 


633 


674 ] 

gives a positive charge to the inner coating of the second, which, acting 
in like manner, develops a charge in the third jar, and so on, to the last, 
where the positive electricity developed by induction on the outer coat¬ 
ing passes to the ground. The jars may be discharged either singly, by 
connecting the inner and outer coatings of each jar, or simultaneously by 
connecting the inner coating of the first with the outer of the last. In 
this way the quantity of electricity necessary to charge one jar is avail¬ 
able for charging a series of jars. 



For from the preceding explanation, it is clear that with a series of 
similar Leyden jars charged by cascade, if we call the charge of positive 
electricity which the inside of the first jar receives 1, it will develope by 
induction on the outside a quantity m (m< 1) of negative electricity, and 
the same quantity m of positive electricity Which will pass into the inside 
of the second jar ; this in turn will develope m x m=m 2 of negative elec¬ 
tricity on the outside of that jar, and the same quantity m 2 of positive 
electricity will pass into the inside of the third jar and so forth. Thus it 

£ e 3 



































634 


FRICTIONAL ELECTRICITY. 


[ 675 - 

will be seen that the quantities of positive electricity developed in a series 
of n similar j ars by the unit charge of positive electricity will be / 

1 _ rn n 

1 +m+m 2 -f-m 3 d-.. m n — 1 = -- 

L—m 

and of negative electricity on the corresponding outsides of 

.m n = ——). 

L—m 

Thus, if there be six jars and m = 0-9, the quantity of positive electricity 
developed by the unit charge is 4*69. 

675. Measurement of tbe charge of a battery. Laue's electro¬ 
meter. —When the outer and inner coatings of a charged Leyden jar' 
are gradually brought near each other, at a certain distance a spontaneous 
discharge ensues. This distance is called the striking distance. It is pro¬ 
portional to the electric density of that point of the inner coating at 
which the discharge takes place ; and as the density of any point of the 
inner coating, other things remaining the same, is proportional to the 
entire charge, the striking distance is proportional to the quantity of 
electricity in ajar. The measurement of the charge of a battery, how¬ 
ever, by means of the striking distance, can only take place when the 
charge disappears. 

By means of Lane’s electrometer, which depends on an application of 
this principle, the charge of a jar or battery may be measured. This 



Fig. 503. 


apparatus, c (fig. 503), consists of an ordinary Leyden jar, near which 
there is a vertical metallic support. At the upper end is a brass rod 
with a knob at one end, which can be placed in metallic connection with 
the outside of the jar; the rod being moveable, the knob can be kept at a 
measured distance from the knob of the inner coating. Fig. 504 repre¬ 
sents the operation of measuring the charge of a jar by means of this ap¬ 
paratus. The jar b, whose charge is to be measured, is placed on an insu¬ 
lated stool with its outer coating in metallic connection with the inner 













LAWS OF ELECTRIC DISCHARGE. 


635 


- 676 ] 

coating of Lane’s jar, c, the outer coating of which is in connection with 
the ground, or still better with a system of gas or water pipes; a is the 
conductor of the machine. When the machine is worked positive elec¬ 
tricity passes into the jar b ; a proportionate quantity of positive electri¬ 
city is repelled from its outer coating, passes into the inner coating of the 
electrometer, and there produces a charge. When this has reached a 
certain limit it discharges itself between the two knobs, and so often as 
such a discharge takes place the same quantity of positive electricity will 
have passed from the machine into the battery j and hence its charge is 
proportional to the number of discharges of the electrometer. 

Harris s unit jar (fig. 504) is an application of the same principle, and is 
very convenient for measuring quantities of electricity. It consists of a 
small Leyden phial 4 inches in length, and £ of an inch in diameter, coated 
to about an inch from the end, so as 
to expose about 6 inches of coated 
surface. It is fixed horizontally on 
a long insulator, and the charging 
rod connected at P with the con- J 
ductor of the machine, while the 
outer coating is connected with the 
jar or battery by the rod tp. When 
the accumulation of electricity in 
the interior has reached a certain 
height depending on the distance of the two balls m and n, a discharge 
ensues, and marks a certain quantity of electricity received as a charge by 
the battery in terms of the small jar. 

676. Xiaws of electric charge. —Harris, by means of experiments 
with the unit jar suitably modified, and Riess, by analogous arrangements, 
have found, by independent researches, that for small distances the strik¬ 
ing distance is directly proportional to the quantity of electricity, and in¬ 
versely proportionate to the extent of coated surface ; in other words, it 
is proportional to the electric density. Thus, taking the surface of one jar 
as unity, if a battery of six Leyden jars charged by 100 turns of the 
machine has a striking distance of 9 millimeters, a battery of four similar 
jars charged by 120 turns will have the striking distance of 16-2 milli¬ 
meters. For 

100 q 120 

tt :9 = 4- ; * 
x = 16*2. 

Riess has also found that when a battery or a jar is discharged in the 
striking distance, a charge still remains, for when the coatings are brought 
nearer a similar discharge may be taken, and so on. The amount of this 
residual charge when the discharge takes place at the greatest striking 



Fig. 504. 





636 


FRICTIONAL ELECTRICITY. 


[ 677 -' 

distance is always in the same proportion to the entire charge. In Riess’s 
experiments 0 846 or — of the total charge disappear, and only ~ remain. 

677. Volta’s condensing electroscope. —The condensing electro¬ 
scope invented by Volta is a modification of the ordinary gold leaf elec¬ 
troscope (651). The rod to which the gold leaves are affixed, terminates 
in a disc instead of in a knob, and there is another disc of the same size 
provided with, an insulating glass handle. The discs are covered with a 
layer of insulating shellac varnish (fig. 505). 

To render very small quantities of electricity perceptible by this appa¬ 
ratus, one of the plates, which thus becomes the collecting plate , is touched 
with the body under examination. The other plate, the condensing plate, 



l ? ig. 505. Fig. 506. 


is connected with the ground, by touching it with the finger. The 
electricity of the body, being diffused over the collecting plate, acts 
inductively through the varnish on the neutral fluid of the other plate, 
attracting the opposite electricity, but repelling that of like kind. The 
two electricities thus become accumulated on the two plates just as in 
Epinus’ condenser, but there is no divergence of the leaves, for the oppo¬ 
site electricities counteract each other. The finger is now removed, and 
then the source of electricity, and still there is no divergence; but if the 
upper plate be raised (fig. 506) the neutralisation ceases, and the elec- 




















- 678 ] 


THOMSON S ELECTROMETER. 


637 


•tricity being free to move diffuses itself over the rod and the leaves, 
which then diverge widely. The delicacy of the apparatus is increased 
by adapting to the foot of the apparatus two metallic rods, terminating 
in knobs, for these knobs being excited by induction from the gold leaves 
react upon them. 

A still further degree of delicacy is attained by replacing the rods by 
two Bohnenberger’s dry piles, one of which presents its positive and the 
other its negative pole. Instead of two gold leaves there is only one ; 
the least trace of electricity causes it to oscillate either to one side or to 
the other, and at the same time shows the kind of electricity. 

678. Thomson’s electrometer. —Sir William Thomson has devised 
a new and delicate form of electrometer, by which quantitative measure¬ 
ments of the amount of electrical charge may be made. The principle 
of this instrument may be understood from the following description 
of a model of it constructed for lecture purposes by Messrs. Elliott, by 
whom the drawing has been kindly furnished. 

A light flat aluminium needle B, balanced by a counterpoise, is sus¬ 
pended by a platinum wire from a support connected with the inner 
coating of a Leyden jar A. CC are two 
half rings of metal, resting on glass sup - 
ports, but connected by means of wires 
with the two knobs DD. W T hen the 
needle B is at rest it is directly over the 
division between the two rings. Sup¬ 
posing the needle B not charged with 
electricity, then if one knob, I), the left 
hand one, for instance, be connected with 
any body charged with electricity while 
the other is connected with the earth, 
the needle will turn slightly towards 
C, and this whether the electricity of 
the D in question is positive or nega¬ 
tive. But if the Leyden jar be charged, 
say with negative electricity, the needle 
will receive an equal charge, or, as is now 
generally expressed, will be at the same 
potential. It will now be more strongly 
attracted than before, if the charge of D be positive, and would be more 
powerfully repelled, if the charge of D were negative. If D loses its 
electricity, and is therefore in the same condition as the earth, B returns 
to its original position between the two rings. One object of connecting 
the needle with a Leyden jar is to provide a considerable supply of 
electricitv for the needle, so that the small leakage which occurs may 



Fig. 507. 

































638 


FRICTIONAL ELECTRICITY. 


[ 679 - 

not affect one test, or even a series of tests. The deflections will be 
greater and the instrument more powerful the higher the jar is charged, 
but the indications will only be constant so long as the jar is charged to 
the same degree. The apparatus is placed under a bell jar, and the 
vessel E contains sulphuric acid, by which the air in the interior is 
kept dry. In the instrument a little mirror is hung above the needle, 
as in the reflecting galvanometers (713), and the deflections noted by a 
spot of light reflected from a lamp. 

THE ELECTRIC DISCHARGE. 

679. Effects of the electric discharge. —The recombination of the 
two electricities which constitutes the electrical discharge may be either 
continuous or sudden ; continuous, or of the nature of a current, as when 
the two conductors of a cylinder machine are joined by a chain or a wire ; 
and sudden, as when the opposite electricities accumulate on the surface 
of two adjacent conductors, till their mutual attraction is strong enough 
to overcome the intervening resistances, whatever they may be. But the 
difference between a sudden and a continuous discharge is one of degree, 
and not of kind, for there is no such thing as an absolute non-conductor, 
and the very best conductors, the metals, offer an appreciable resistance 
to the passage of electricity. Still, the difference at the two extremes of 
thes cale is sufficiently great to give rise to a wide range of phenomena. 

The phenomena of the discharge are usually divided into the physio¬ 
logical, luminous, mechanical, magnetical, and chemical effects. 

680. Physiological effects.— The physiological effects are those pro¬ 
duced on living beings, or on those recently deprived of life. In the first 
case they consist of a violent excitement which the electric fluid exerts 
on the sensibility and contractibility of the organic tissues through which 
it passes ; and in the latter, of violent muscular convulsions which resem¬ 
ble a return to life. 

The shock from the electrical machine has been already noticed (668). 
The shock taken from a charged Leyden jar by grasping the external 
coating with one hand, and touching the inner with the other, is much 
more violent, and has a peculiar character. With a small jar the shock 
is felt in the elbow ; with a jar of about a quart capacity it is felt across 
the chest, and with jars of still larger dimensions in the stomach. 

A shock may be given to a large number of persons simultaneously bv 
means of the Leyden jar. For this purpose they must form a chain by 
joining hands. If then the first touches the outside coating of a charged 
jar, while the last at the same time touches the knob, all receive a simul¬ 
taneous shock, the intensity of which depends on the charge, apd on the 
number of persons receiving it. Those in the centre of the chain are 
found to receive a less violent shock than those near the extremities. The 


THE ELECTRIC DISCHARGE. 


639 


-682] 

Abbe Nollet discharged a Leyden jar through an entire regiment of 1,500 
men, who all received a violent shock in the arms and shoulders. 

With large Leyden jars and batteries the shock is sometimes very 
dangerous. Priestley killed rats with batteries of 7 square feet coated 
surface, and cats with a battery of about square yards coating. 

681. Luminous effects. —The recomposition of two electricities of 
high tension is always accompanied by a disengagement of light, as is 
seen when sparks are taken from a machine, or when a Leyden jar is 
discharged. The better the conductors on which the electricities are 
accumulated the more brilliant is the spark; its colour varies not only 
with the nature of the bodies, but also with the nature of the surrounding 
medium, and with the pressure. The spark between two charcoal points 
is yellow, between two balls of silvered copper it is green, between knobs 
of wood or ivory it is crimson. In atmospheric air at the ordinary pres¬ 
sure the electric spark is white and brilliant; in rarefied air it is reddish; 
and in vacuo it is violet. In oxygen, as in air, the spark is white; in 
hydrogen it is reddish ; and green in the vapour of mercury; in carbonic 
acid it is also green, while in nitrogen it is blue or purple, and accom¬ 
panied by a peculiar sound. Generally speaking, the higher the tension 
the greater is the lustre of the spark. It is asserted by Fusinieri that in 
the electric spark there is always a transfer of material particles in a 
state of extreme tenuity, in which case the modifications in colour must 
be due to the transport of ponderable matter. 

When the spark is viewed through a prism, the spectrum obtained is 
full of dark lines (490), the number and arrangement of which depend 
on the nature of the poles. 

682. Spark and brush discharge.— The shapes which luminous 
electric phenomena assume may be classed under two heads—the spark 
and the brush. The brush forms when the electricity leaves the con¬ 
ductor in a continuous flow; the spark, when the discharge is discon¬ 
tinuous. The formation of one or the other of these depends on the 
nature of the conductor, and on the nature of the conductor in its vicinity; 
and small alterations in the position of the surrounding conductors 
transform the one into the other. 

The spark which at short distances appears straight, at longer distances 
has a zigzag-shape with diverging branches. Its length depends on 
the tension at the part of the conductor from which it is taken; and to 
obtain the longest sparks the electricity must be of as high tension as 
possible, but not so high as to discharge spontaneously. With long 
sparks the luminosity is different in different parts of the spark. 

The brush derives its name from the radiating divergent arrangement 
of the light, and presents the appearance of a luminous cone, whose apex 
touches the conductor. Its size and colour differ with the nature and 


640 


FRICTIONAL ELECTRICITY. 


[ 683 - 

form of the conductor; it is accompanied by a peculiar hissing noise, very 
different from the sharp crack of the spark. Its luminosity is far less 
than that of the spark, for while the latter can easily be seen by daylight, 
the former is only visible in a darkened room. The brush discharge may 
be obtained by placing on the conductor a wire filed round at the end, or, 
with a powerful machine, by placing a small bullet on the conductor. 
The brush from a negative conductor is less than from a positive con¬ 
ductor ; the cause of this difference has not 
been very satisfactorily made out, but origin¬ 
ates probably in the fact which Faraday has 
observed, that negative electricity discharges 
into the air at a somewhat lower tension than 
positive electricity ; so that a negatively 
charged knob sooner attains that tension at 
which spontaneous discharge takes place, than 
does a positively charged one, and therefore 
discharges the electricity at smaller intervals 
and in less quantities. 

When electricity in virtue of its high ten¬ 
sion issues from a conductor, no other conductor 
being near, the discharge takes place without 
noise, and at the places at which it appears 
there is a pale blue luminosity, called the 
electrical (flow, or on points, a star-like centre 
of light. It is seen in the dark by placing a 
point on the conductor of the machine. 

683. Electric eg-g-. —The influence of the 
pressure of the air, or rather of its noncon¬ 
ductivity, on the electric light, may be studied 
by means of the electric egg. This consists 
of an ellipsoidal glass-vessel (fig. 508), with metallic caps at each end. 
The lower cap is provided with a stopcock, so that it can be screwed into 
an air pump, and also into a heavy metallic foot. The upper metallic 
rod moves up and down in a leather stuffing box; the lower one is fixed 
to the cap. A vacuum having been made, the stopcock is turned, and 
the vessel screwed into its foot; the upper part is then connected with a 
powerful electrical machine, and the lower one with the ground. On 
working the machine, the globe becomes filled with a feeble violet light 
continuous from one end to the other, and resulting from the recomposi¬ 
tion of the positive fluid of the upper cap with the negative of the lower. 
If the air be gradually allowed to enter by opening the stopcock, the 
tension increases with the resistance, and the light which appears white 
and brilliant is only seen as an ordinary spark 



- 684 ] 


THE ELECTRIC DISCHARGE. 


641 


Some beautiful effects of the electric light are obtained by means of 
Geissler’s tubes, which will be noticed under Dynamical Electricity. 

684. Luminous tube, square, and bottle.— The luminous tube 
(tig. 509) is a glass tube about a yard long, round which are arranged 



Fig. 509. 


in a spiral form a series of lozenge-shaped pieces of tin-foil, between 
which are very short intervals. There is a brass cap which hooks at 
each end, in which the spiral terminates. If one end be presented to a 
machine in action, while the other is held in the hand, sparks appear 
simultaneously at each interval, and produce a brilliant luminous 
appearance, especially in the dark. 

The luminous pane (fig. 510) is constructed on the same principle, and 
consists of a square of ordinary glass, on which is fastened a narrow 



Fig. 510. 


strip of tin-foil folded parallel to itself for a great number of times v 
Spaces are cut out of this strip so as to represent any figure, a portico 

















642 


FRICTIONAL ELECTRICITY. 


[685- 


for example. The pane being fixed between two insulating supports, 
the upper extremity of the strip is connected with the electrical 
machine, and the lower part with the ground. When the machine is 
in operation, a spark appears at each interval, and reproduces in luminous 
flashes the object represented on the glass. 

The luminous jar (fig. 511) is a Leyden jar, whose outer coating 
consists of a layer of varnish strewed over with metallic powder. A 
strip of tin fitted on the bottom is connected with the ground by means 
of a chain ; a second band at the upper part of the coating has a 
projecting part, and the rod of the bottle is curved so that the knob is 



about f of an inch distant from the projection. This bottle is suspended 
from the machine, and as rapidly as this is worked, large and brilliant 
sparks pass between the knob and the outer'Coating, illuminating the 
outside of the apparatus. 

685. Calorific effects.— Besides being luminous, the electric spark 
is a source of intense heat. When it passes through inflammable 
liquids, as ether or alcohol, it inflames them. An arrangement for 
effecting this is represented in figure 512. It is a small glass cup 
through the bottom of which passes a metal rod, terminating in a knob 












THE ELECTRIC DISCHARGE. 


643 


- 685 ] 

and fixed to a metal foot. A quantity of liquid sufficient to cover the 
knob ia placed in the vessel. The outer coating of the jar having been 
connected with the foot by means of a chain, the spark which passes 
when the two knobs are brought near each other, inflames the liquid. 
With ether the experiment succeeds very well, but alcohol requires to be 
first warmed. 

Coal gas may also be ignited by means of the electric spark. A person 
standing on an insulated stool places one hand on the conductor of a 
machine which is then worked, while he presents the other to the jet of gas 
issuing from a metallic burner. The spark which passes ignites the gas. 
When a battery is discharged through an iron or steel wire it becomes 
heated, and even made incandescent or melted, if the discharge is very 
powerful. The laws of this heating effect have been investigated inde¬ 
pendently by Harris and by Riess by means of the electric thermometer. 
This is essentially an air thermometer, across the bulb of which is a fine 
platinum wire. When a discharge is passed through the wire it becomes 
heated, expands the air in the bulb, and this expansion is indicated in 
the motion of the liquid along the graduated stem of the thermometer. 
In this way it has been found that the increase in temperature in the wire 
is proportional to the electric density multiplied by the quantity of 
electricity; and since the electric density is equal to the quantity of 
electricity, usually measured by the number of discharges of the unit 
jar (675), divided by the surface, the heating effect is proportional to the 

02 

square of the number of discharges divided by the surface; that is, A =-±- 

Riess has also found that with the same charge , hut with wires of 
different dimensions, the rise of temperature is inversely as the fourth 
power of the diameter. Thus, compared with a given wire as unity, the 
rise of temperature in a wire of double or treble the diameter would be ^ 
or gV as small; but as the masses of these wires are four and nine times 
as great, the heat produced would be respectively £ and f as great as in a 
wire of unit thickness. 

When an electric discharge is sent through gunpowder placed on the 
table of a Henley’s discharger, it is not ignited, but is projected in all 
directions. But if a wet string be interposed in the circuit a spark 
passes which ignites the powder. This arises from the retardation 
which electricity experiences in traversing a semi-conductor, such as a 
wet string; for the heating effect is proportional to the duration of the 
discharge. 

When a charge is passed through sugar, heavy spar, fluorspar, and 
other substances, they afterwards become phosphorescent in the dark. 
Eggs, fruit, etc., may be made luminous in the dark in this way. 

When a battery is discharged through a gold leaf, pressed between two 


644 


FRICTIONAL ELECTRICITY, 


[686 


glass plates or between two silk ribbons, the gold is volatilised in a violet 
powder which is finely divided gold. In this way the electric portraits 
are obtained. 

686. Magnetic effects.— By the discharge of a large Leyden jar or 
battery, a steel wire may be magnetised if it is laid at right angles to a 
conducting wire through which the discharge is effected, either in 
contact with the wire or at some distance. And even with less powerful 
discharges a steel bar or needle may be magnetised by placing it in a 
tube on which is coiled a .fine insulated copper wire. On passing the 
discharge through this wire the steel becomes magnetised. 

To effect a deflection of the magnetic needle by the electric current 
produced by frictional electricity is more difficult. It may be accom¬ 
plished by making use of a galvanometer (712) consisting of 400 or 500 
turns of fine silk-covered wire, which is further insulated by being 
coated with shellac varnish, and by separating the layers by means of 
oiled silk. When the prime conductor of a machine in action is 
connected with one end of the galvanometer wire, and the other with the 
ground, a deflection of the needle is produced. 

687. Mechanical effects.— The mechanical effects are the violent 



Fig. 513 


lacerations, fractures, and sudden expansions which ensue when a power¬ 
ful discharge is passed through a badly conducting substance. Glass is 
perforated, wood and stones are fractured, and gases and liquids are vio- 










THE ELECTRIC DISCHARGE. 


645 


-687J 

lently disturbed. The mechanical effects of the electric spark may be de¬ 
monstrated by a variety of experiments. 

Figure 513 represents an arrangement for perforating a piece of 
glass or card. It consists of two glass columns, with a horizontal 
cross piece, in which is a pointed conductor, B. The piece of glass, 
A, is placed on an insulating glass support, in which is placed a second 
conductor, terminating also in a point, which is connected with the 
outside of the battery, while the knob of the inner coating is brought 
near the knob of B. When the discharge passes between the two con¬ 
ductors the glass is perforated. The experiment only succeeds with a 
single jar when the glass is very thin ; otherwise a battery must be 
used. 

The perturbation and sudden expansion which the discharge produces 
may be illustrated by means of Kinnersley’s thermometer. This 
consists of two glass tubes (fig. 514), which fit into metallic caps, and 
communicate with each other. At the top of the large tube is a rod 
terminating in a knob, and moving in a stuffing-box, and at the bottom 
there is a similar rod with a knob. The apparatus contains water 



Fig. 514. 


up to the level of the lower knob. When the electric shock passes 
between the two knobs, the water is driven out of the larger tube and 
rises to a slight extent in the small one. The level is immediately 







FRICTIONAL ELECTRICITY. 


646 


[ 688 - 


re-established, and therefore the phenomenon is not due to an increase of 
temperature. 

For the production of mechanical effects the universal discharger, 
fig. 502, is of great service. A piece of wood, for instance, placed on 
the table between the two conductors, is split when the discharge 
passes. 

688. Chemical effects. —The chemical effects are the decompositions 
and recombinations effected by the passage of the electric discharge. 
Where two gases which act on each other are mixed in the proportions 
in which they combine, a single spark is o'ften sufficient to determine 
their combination; but where either of them is in great excess, a 
succession of sparks is necessary. Priestley found that when a series of 
electric sparks was passed through moist air, its volume diminished, and 
blue litmus introduced into the vessel was reddened. This, Cavendish 
found, was due to the formation of nitric acid. 

Several compound gases are decomposed by the continued action of 
the electric spark. With olefiant gas, sulphuretted hydrogen, and 
ammonia, the decomposition is complete ; while carbonic acid is partially 
decomposed into oxygen and carbonic oxide. The electric discharge 
also decomposes water, oxides, and salts ; but though the same in kind, 
the chemical effects of statical electricity are by no means so powerful 
and varied as those of dynamical electricity. The chemical action of the 
spark is easily demonstrated by means of a solution of iodide of potassium. 
A small lozenge-shaped piece of filtering paper, impregnated with iodide 
of potassium, is placed on a glass plate, and one corner connected with 
the ground. When a few sparks from a conductor charged with positive 
electricity are taken at the other corner, brown spots are produced, due 
to the separation of iodine. 

Among the chemical effects must be enumerated the formation of 
ozone, which is recognised by its peculiar odour and by certain chemical 
properties. The odour is perceived when electricity issues through a 
series of points from a conductor into the air. Its true nature is not 
accurately known: some regard it, and with great probability, as 
an allotropic modification of oxygen, and others as a teroxide of 
hydrogen. 

The electric pistol is a small apparatus which serves to demonstrate 
the chemical effects of the spark. It consists of a brass vessel (fig. 515), 
in which is introduced a detonating mixture of two volumes of hydrogen 
and one of oxygen, and which is then closed with a cork. In a tubulure 
in the side there is a glass tube, in which fits a metallic rod, terminated 
by the knobs A and B. The knob is held as represented in fig. 516, 
and brought near the machine. The knob A becomes negatively, and B 
positively electrified by induction from the machine, and a spark passes 


FIRING MINES BY ELECTRICITY. 


647 


-689] 

between the conductor and A. Another spark passes at the same time 
between the knob B and the side ; this determines the combination of 
the gases, which is accompanied by a great disengagement of heat, and 



Fig. 515. Fig. 516. 


the vapour of water formed acquires such an expansive force, that the 
cork is projected with a report like that of a pistol. 

689. Application of the electrical discharge to firing mines.— 
By the labours of Prof. Abel, in this country, and of Baron von Ebner 
in Austria, the electrical discharge has been applied to firing mines 
for military purposes, and the methods have acquired a high degree 
of perfection. The principle on which the method is based may be 
understood from the following statement. 

One end of an insulated wire in which is a small break is placed in 
contact with the outside of a charged Leyden jar, the other end being 
placed near the inner coating. If now this end be brought in contact 
with the inner coating the jar is discharged and a spark strikes across 
the break; and if there be here some explosive compound it is ignited, 
and this ignition may of course be communicated to any gunpowder in 
which it is placed. If on one side of the break, instead of having an 
insulated wire direct back to the outer coating of the Leyden jar, an 
uncovered wire be led into the ground, the outside of the jar being also 
connected with the ground, the result is unchanged, the earth acting as 
a return wire. Moreover, if there be several breaks, the explosion will 
still ensue at each of them provided the charge be sufficiently powerful. 

In the actual application it is of course necessary to have an arrange¬ 
ment for generating frictional electricity, which shall be simple, port¬ 
able, powerful, and working in any weather. In these respects the 
electrical machine devised by Von Ebner is admirable. Fig. 517 repre¬ 
sents a view of this instrument as constructed by Messrs Elliot, part of 
the case being removed to show the internal construction. 

It consists of two circular plates of ebonite a mounted on an axis 
so that they are turned by a handle 5, between rubbers, which are so 










648 


FRICTIONAL ELECTRICITY. 


[ 689 - 


arranged as to be easily removed for the purposes of amalgamation, etc. 
Fastened to a knob on tbe base of the apparatus and projecting between 
the plates is a pointed brass rod, which acts as a collector of the 
electricity. The condenser or Leyden jar arrangement is inside the 
case, part of which has been removed to show the arrangement. It 
consists of India-rubber cloth, coated on each side with tinfoil, and 
formed into a roll for the purpose of greater compactness. By means of 


a 



Fig. 517. 


a metal button the knob is in contact with one tinfoil coating which thus 
receives the electricity of the machine, and corresponds to the inner 
coating of the Leyden jar. Another button connected with the other 
tinfoil coating, rests on a brass band at the base of the apparatus which 
is in metallic contact with the cushions, the knob d, and the perforated 
knob in which slides a rod at the front of the apparatus. These are all 
in connection with the earth. The knob e is in metallic connection with 
a disc g provided with a light arm. By means of a flexible chain this is so 
connected with a trigger on the side of the apparatus, not represented in 














































- 689 ] 


FIRING MINES BY ELECTRICITY. 


649 


the figure, that when the trigger is depressed, the arm, and therewith the 
knoh e, is brought into contact with the inner coating of the condenser. 

On depressing the trigger after a certain number of turns a spark 
passes between the knob e and the sliding rod, and the striking distance 
is a measure of the working condition of the instrument. 

The fuse used is known as Abel’s electrical fuse, and has the following 
construction. The ends of two fine copper wires, fig. 518, are imbedded 
in a thin solid gutta percha rod, parallel to each other, but at a distance 
of about 1*5 mim. At the lower end of the gutta percha a small cap of 
paper or tinfoil cc is fastened, in which is placed a small quantity of the 





Fig. 519, 


Fig. 518. 


priming composition, which consists of an intimate mixture of subsulphide 
of copper, subphosphide of copper, and chlorate of potassium. The paper 
is fastened down so that the exposed ends of the wires are preserved in 
close contact with the powder. 

This is the actual fuse j for service the capped end of the fuse is placed 
in a perforation in the rounded head of a wooden cylinder, so as to project 
slightly into the cavity g of the cylinder. This cavity is filled with meal 
powder which is well rammed down, so that the fuse is firmly imbedded. 
It is afterwards closed by a plug of gutta percha, and the whole is finally 
coated with black varnish. 



















650 


FRICTIONAL ELECTRICITY. 


[ 690 - 

The free ends of the wires a a are pressed into small grooves in the 
head of the cylinder (fig. 519), and each end is bent into one of the 
small channels with which the cylinder is provided, and which are at 
right angles to the central perforation. They are wedged in here by 
driving in small copper tubes, the ends of which are then filed flush 
with th§ surface of the cylinder. The bared ends of two insulated 
conducting wires are then pressed into one of the small copper tubes 
or eyes, and fixed there by bending the wire round on to the wood, as 
shown at e. 

The conducting wire used in firing may be thin but it must be well 
insulated. One end, which is bared, having been pressed into the hole d 
of the fuse, the other is placed in proximity to the exploder. Into the 
other hole d of the fuse a wire is placed which serves as earth wire ; care 
being taken that there is no connection between the two wires. The fuse 
having been introduced into the charge the earth wire is placed in good 
connection with the ground. The knob f of the exploder is also con¬ 
nected with the earth by leading uncovered wire into water or moist 
earth, and the condition of the machine tested. The end of the in¬ 
sulated wire is then connected with the knob e and the rod drawn down ; 
at the proper signal the handle is turned the requisite number of times, 
and when the signal is given the trigger is depressed, and the explosion 
ensues. 

When a number of charges are to be fired they are best placed in a 
single circuit, care being taken that the insulation is good. 

690. Duration of the electric spark. Velocity of electricity.— 
Wheatstone has measured the duration of the electric spark, and the 
velocity of electricity, by means of the rotating mirror, which he invented 
for this purpose. At some distance from this instrument, which can be 
made to rotate with a measured velocity, a Leyden jar is so arranged, 
that the spark of its discharge is reflected from the mirror. Now, from 
the laws of reflection (Note, p. 401) the image of the luminous point 
describes an arc of double the number of degrees which the mirror de¬ 
scribes, in the time in which the mirror passes from the position in which 
the image is visible, to that in which it ceases to be so. If the duration 
of the image were absolutely instantaneous the arc would be reduced to 
a mere point. Knowing the number of turns which the mirror makes in 
a second, and measuring, by means of a divided circle, the number of de¬ 
grees occupied by the image, the duration of the spark could be deter¬ 
mined. In one experiment Wheatstone found that this arc was 24°. 
Now, in the time in which the mirror traverses 360° the image traverses 
720°; but in the experiment the mirror made 800 turns in a second, and 
therefore the image traversed 576,000° in this time; and as the arc was 
24°, the image must have lasted the time expressed by ^^ - o 5 - or of 



-690J VELOCITY OF ELECTRICITY. 651 

a second. Thus the discharge is not instantaneous, but has a certain dura¬ 
tion, which, however, is excessively short. 

To determine the. velocity of electricity, Wheatstone constructed an 
apparatus the principle of which will be understood from figure 520; 
six insulated metal knobs were arranged in a horizontal line on a piece 
of wood called the spark hoard ; of these the knob 1 was connected with 
the outer, while 6 could be connected with the inner coating of a 
charged Leyden jar; the knob 1 was a tenth of an inch distant 

from the knob 2; while between 2 and 3 a quarter of a mile of insulated 

wire was interposed ; 3 was likewise a tenth of an inch from 4, and there 
was a quarter of a mile of wire between 
4 and 5; lastly, 5 was a tenth of an inch 
from 6, from which a wire led directly to the 
outer coating of the Leyden jar. Hence, 
when the jar was discharged by connecting 
the wire from 6 with the inner coating of the 
jar, sparks would pass between 1 and 2, 

between 3 and 4, and between 5 and 6. 

Thus the discharge, supposing it to proceed 
from the inner armature, has to pass in its 
course through a quarter of a mile of wire 
between the first and second spark, and 
through the same distance between the se¬ 
cond and third. 

The spark board was arranged at a distance of 10 feet from the rotating 
mirror, and at the same height, both being horizontal; and the observer 
looked down on the mirror. Thus the sparks were visible when the 
mirror made an angle of 45° with the horizon. 

Now, if the mirror were at rest or had only a small velocity, the images 
of the three sparks would be seen as three dots • , but when the mirror 
had a certain velocity these dots appeared as lines, which were longer as 
the rotation was more rapid. The greatest length observed was 24°, 
which, with 800 revolutions in a second, corresponds to a duration of 
of a second. With a slow rotation the lines present the appear¬ 
ance - ; they are quite parallel, and the ends in the same line. 
But with greater velocity, and when the rotation took place from left to 

right, they presented the appearance - and when it turned from 

right to left the appearance - —, because the image of the centre 

spark was formed after the lateral ones. Wheatstone found that this 
displacement amounted to half a degree before or behind the others. 

This arc corresponds to a duration of 2 x 720 X 800 ° r 1152000 a 

second ; the space traversed in this time being a quarter of a mile, gives 

F F 2 


Fig. 520. 













FRICTIONAL ELECTRICITY. 


652 


[ 690 - 


for the velocity of electricity, 288,000 miles in a second, which is greater 
than that of light. 

In the above experiment the images of the two outer sparks appear 
simultaneously in the mirror, from which it follows that the electric 
current issues simultaneously from the two coatings of the Leyden 
jar. 

For atmospheric electricity, reference must be made to the chapter on 
Meteorology. 





- 691 ] 


THE VOLTAIC PILE. 


653 


BOOK X. 

DYNAMICAL ELECTRICITY. 


CHAPTER I. 

VOLTAIC PILE. ITS MODIFICATIONS. 

691. G-alvani’s experiment and theory.— The fundamental experi¬ 
ment which led to the discovery of dynamical electricity is due to Galvani, 
professor of anatomy in Bologna. Occupied with investigations on the 
influence of electricity on the nervous excitability of animals, andespeci- 



Fig. 521. 

ally of the frog, he observed that when the lumbar nerves of a dead frog 
were connected with the crural muscles by a metallic circuit, the latter 
became briskly contracted. 

To repeat this celebrated experiment, the legs of a recently killed frog 





654 


DYNAMICAL ELECTRICITY. 


[692- 

are prepared, and the lumbar nerves on each side of the vertebral column 
are exposed in the form of white threads. A metallic conductor, com¬ 
posed of zinc and copper, is then taken (fig. 521), and one end introduced 
between the nerves and the vertebral column, while the other touches 
one of the muscles of the thighs or legs ; at each contact a smart con¬ 
traction of the muscles ensues. 

Galvani had some time before observed that the electricity of machines 
produced in dead frogs analogous contractions, and he attributed the 
phenomena first described to an electricity inherent in the animal. He 
assumed that this electricity, which he called vitalfluid, passed from the 
nerves to the muscles by the metallic arc, and was thus the cause of 
contraction. This theory met with great support, especially among 
physiologists, but it was not without opponents. The most considerable 
of these was Alexander Volta, professor of physics in Pavia. 

692. Volta’s fundamental experiment. —Galvani’s attention had 
been exclusively devoted to the nerves and muscles of the frog ; Volta’s 
was directed upon the connecting metal. Resting on the observation, 
which Galvani had also made, that the contraction is more energetic 
when the connecting arc is composed of two metals, than when there is 
only one, Volta attributed to the metals the active part in the phenomenon 
of contraction. He assumed that the disengagement of electricity was 
due to their contact, and that the animal parts only officiated as con¬ 
ductors, and at the same time as a very sensitive electroscope. 

By means of the then recently invented electroscope, Volta devised 
several modes of showing the disengagement of electricity on the contact 
of metals, of which the following is the easiest to perform : 

The moistened finger being placed on the upper plate of a condensing 
electroscope (fig, 505, p. 636), the lower plate is touched with a plate 
of copper, c, soldered to a plate of zinc, z, which is held in the other 
hand. On breaking the connection and lifting the upper plate (fig. 506), 
the gold leaves diverge, and, as may be proved, with negative electricity. 
Hence, when soldered together, the copper is charged with negative 
electricity, and the zinc with positive electricity. The electricity could 
not be due either to friction or pressure; for if the condenser plate, 
which is of copper, is touched with the zinc plate z, the copper plate to 
which it is soldered being held in the hand, no trace of electricity is 
observed. 

A memorable controversy arose between Galvani and Volta. The 
latter was led to give greater extension to his contact theory, and pro¬ 
pounded the principle that when two heterogeneous substances are placed 
in contact , one of them always assumes the positive and the other the negative 
electrical condition. In this form Volta’s theory obtained the assent of 
the principal philosophers of his time. Galvani, however, made a number 


volta’s experiment. 


655 


- 693 ] 

of highly interesting experiments with animal tissues. In some of these 
he obtained indications of contraction, even though the substances in 
contact were quite homogeneous. He thus discovered the existence of 
animal electricity, which, within the last few years, has been established 
by Matteucci, under the name of frog-current. 

693. Disengagement of electricity in chemical actions. —The 
contact theory which Volta had propounded, and in which he explained 
the action of the pile, soon encountered objectors. Fabroni, a country¬ 
man of Volta, having observed that in the pile the discs of zinc became 
oxidised in contact with the acidulated water, thought that this oxida¬ 
tion was the principal cause of the disengagement of electricity. In 
England Wollaston soon advanced the same opinion, and Davy supported 
it by many ingenious experiments. 

It is true that in the fundamental experiment of the contact theory 
(692) Volta obtained signs of electricity. But M. de la Rive has shown 
that if the zinc be held in a wooden clamp, all signs of electricity dis¬ 
appear, and that the same is the case if the zinc be placed in gases, such 
as hydrogen or nitrogen, which exert upon it no chemical action. De la 
Rive has accordingly concluded that in Volta’s original .experiment the 
disengagement of electricity is due to the chemical actions which result 
from the perspiration and from the oxygen of the atmosphere. 

The development of electricity in chemical actions may be demonstrated 
in the following manner by means of the condensing electroscope (677). 
A disc of moistened paper is placed on the upper plate of the condenser, 
and on this a zinc capsule, in which some dilute sulphuric acid is poured. 
A platinum wire, communicating with the ground, but insulated from 
the sides of the vessel, is immersed in the liquid, and at the same time 
the lower plate of the condenser is also connected with the ground by 
touching it with the moistened finger. On breaking contact and removing 
the upper plate, the gold leaves are found to be positively electrified, 
proving that the upper plate has received a charge of negative electri¬ 
city due to the chemical action of the sulphuric acid on the zinc. 

By a variety of analogous experiments it may be shown that all 
chemical actions are accompanied by a disturbance of the electrical 
equilibrium. This is the case whether the substances concerned in the 
action are in the solid, liquid, or gaseous state, though of all chemical 
actions those between metals and liquids are the most productive of 
electricity. All the various resultant effects may be explained on the 
general principle, that when a liquid acts chemically on a metal the 
liquid assumes the positive electrical, and the metal the negative electri¬ 
cal condition. In the above experiment the sulphuric acid, by its action 
on zinc, became positively electrified, and its electricity passed off through 
the platinum wire into the ground, while the negative electricity excited 


DYNAMICAL ELECTRICITY. 


656 


[ 694 - 


in the zinc acted on the condenser just as an excited rod of sealing wax 
would have done. 

In many cases the electrical indications accompanying chemical actions 
are of a very feeble nature, and require the use of a very delicate electro¬ 
scope to render them sensible. Thus, one of the most energetic chemical 
actions, that of sulphuric acid upon zinc, gives no more free elec¬ 
tricity than water alone does with zinc. In the former case, both the 
metal and the liquid are good conductors, and hence the two electricities 
tend to recombine directly at the place of their separation, instead of one 
passing into the earth and another into the condenser. Only a small 
portion escapes neutralisation, and it is this which the instruments 
indicate. It is important not to confound the electricity generated with 
the electricity perceived. 

694. Current electricity.— When a plate of zinc and a plate of 
copper are partially immersed in dilute sulphuric acid a disturbance of 
the electrical equilibrium ensues, for, by means of delicate electroscopic 
arrangements, it may be shown that the zinc plate possesses a feeble 
charge of negative and the copper plate a feeble charge of positive 
electricity. At the same time there is a slight disengagement of 
hydrogen from the surface of the zinc. If now the plates be placed 
in direct contact, or, more conveniently, be connected by means of 
a metallic wire, the chemical action increases, but the hydrogen 

is now disengaged from the surface of the 
copper (fig. 522); and if the connecting wire 
be examined it will be found to possess 
many remarkable thermal, magnetic, and 
other properties, to be hereafter described. 
So long as the metals remain in the liquid, 
the opposite electrical conditions of the two 
plates discharge themselves by means of the 
wire, but are instantaneously restored, and as 
rapidly discharged; and as these successive 
charges and discharges take place at such 
Tig. 522. infinitely small intervals of time that they 

may be considered continuous, the wire is 
said to be traversed by an electric or voltaic current. The direction of 
this current in the connecting wire is assumed to be from the copper to 
the zinc, or in other words, this is the direction in which the positive 
electricity is supposed to flow, the direction of the negative current in 
the wire being from the zinc to the copper. But the existence of this 
current is purely hypothetical, and must not be taken as more than a con¬ 
venient mode of explaining the phenomena developed in the wire. 

695. Voltaic couple. Electromotive series. —The arrangement 








VOLTAIC COUPLE. 


657 


-695] 

j ust described, consisting of two metals in metallic contact, and a conduct¬ 
ing liquid in which they are placed, constitutes a simple voltaic element or 
couple. So long as the metals are not in contact, the couple is said to he 
open, and when connected it is closed. 

For the production of a voltaic current it is not necessary that one of 
the metals be unaffected by the liquid, but merely that the chemical 
action upon the one be greater than upon the other. For then, in 
accordance with what has been before stated (694), the two metals may 
be considered to give rise to two separate currents, of which the one 
proceeding from the metal most attacked is the stronger, and the current 
perceived is therefore the difference between two unequal currents. If 
the currents were absolutely equal, a condition, however, practically 
impossible to realise, we must assume that no electrical effects would be 
produced. The metal which is most attacked is called the positive or 
generating plate, and that which is least attacked the negative or collecting 
plate. The positive metal determines the direction of the current, which 
proceeds in the liquid from the positive to the negative plate, and out of 
the liquid through the connecting wire from the negative to the positive 
plate. 

In speaking of the direction of the current the positive current is 
always understood; to avoid confusion, the existence of the current 
in the opposite direction, the negative current, is tacitly ignored. 

The mere immersion of two different metals in a liquid is not alone 
sufficient to produce a current, there must be chemical action. When a 
platinum and a gold plate are connected with a delicate galvanometer 
and immersed in pure nitric acid no current is produced; but on adding a 
drop of hydrochloric acid a strong current is excited, which proceeds in 
the liquid from the gold to the platinum, because the gold is attacked by 
the nitro-hydrochloric acid, while the platinum is less so, if at all. 

As a voltaic current is produced whenever two metals are placed in 
metallic contact in a liquid which acts more powerfully upon one than 
upon the other, there is great choice in the mode of producing such 
currents. In reference to their electrical deportment, the metals have 
been arranged in what is called an electromotive series, in which the most 
electropositive are at one end, and the most electronegative at the other. 
Hence when any two of these are placed in contact in dilute acid, the 
current in the connecting wire proceeds from the one lower in the list 
to the one higher. The principal metals are as follows:— 


Zinc 

Nickel 

Gold 

Cadmium 

Bismuth 

Platinum 

Tin 

Antimony 

Graphite. 

Lead 

Copper 


Iron 

Silver 



FF 3 



658 


DYNAMICAL ELECTRICITY. 


[ 695 - 


It will be seen that the electrical deportment of any metal depends 
on the metal with which it is associated. Iron, for example, in dilate 
sulphuric acid, is electronegative towards zinc, but is electropositive 
towards copper; copper in turn is electronegative towards iron and zinc 
but is electropositive towards silver, platinum or graphite. 

The force produced by the contact of two metals in a liquid is called 
the electromotive force ; it is greater in proportion to the distance of the 
two metals from one another in the series. Thus the electromotive force 
between zinc and platinum is greater than that between zinc and iron, or 
between zinc and copper. The law established by Poggendorff is, that 
the electromotive force between any two metals is equal to the sum of the 
electromotive forces between all the intervening metals. Thus the electro¬ 
motive force between zinc and platinum is equal to the sum of the elec¬ 
tromotive forces between zinc and iron, iron and copper, and copper and 
platinum. 

The electromotive force is influenced by the condition of the metal; 
rolled zinc, for instance, is negative towards cast zinc. It also depends 
on the degree of concentration of the liquid; in dilute nitric acid zinc 
is positive towards tin, and mercury positive towards lead; while in con¬ 
centrated nitric acid the reverse is the case, mercury and zinc being re¬ 
spectively electronegative towards lead and tin. 

The nature of the liquid also influences the direction of the current. 
If two plates, one of copper and one of iron, are immersed in dilute sul¬ 
phuric acid, a current is set up proceeding through the liquid from the 
iron to the copper; but if the plates, after being washed, are placed in 
solution of sulphide of potassium, a current is produced in the opposite 
direction, the copper is now the positive metal. Other examples may be 
drawn from the following table, which shows the electric deportment of 
the principal metals with three different liquids. It is arranged like 
the preceding one; each metal being electropositive towards any one 
lower in the list, and electronegative towards any one higher. 


Caustic potass. 

Hydrochloric acid. 

Sulphide of 
potassium. 

Zinc 

Zinc 

Zinc 

Tin 

Cadmium 

Copper 

Cadmium 

Tin 

Cadmium 

Antimony 

Lead 

Tin 

Lead 

Iron 

Silver 

Bismuth 

Copper 

Antimony 

Iron 

Bismuth 

Lead 

Copper 

Nickel 

Bismuth 

Nickel 

Silver 

Nickel 

Silver. 

Antimony. 

Iron. 


VOLTAIC BATTERY. 


659 


-697] 

A voltaic current may also be produced by means of two liquids and 
one metal. This may be shown by the following experiment: In a 
beaker containing strong nitric acid is placed a small porous cylinder 
closed at one end, and containing strong solution of caustic potass. If 
now two platinum wires connected with the two ends of a galvanometer 
(712) are immersed respectively in the alkali and in the acid, a voltaic cur¬ 
rent is produced proceeding in the wire from the nitric acid to the potass, 
which thus correspond respectively to the negative and positive plates in 
an ordinary couple. 

A metal which is acted upon by a liquid can be protected from 
solution by placing in contact with it a more electropositive metal and 
thus forming a simple voltaic circuit. This principle is the basis of 
Davy’s proposal to protect the copper sheathing of ships, which are 
rapidly acted upon by sea water. If zinc or iron be connected with 
the copper, these metals are dissolved and the copper protected. Davy 
found that a piece of zinc the size of a nail was sufficient to protect a 
surface of forty or fifty square inches, but unfortunately the proposal has 
not been of practical value, for the copper must be attacked to a certain 
extent to prevent the adherence of marine plants and shellfish. 

696. Poles and electrodes.— If the wire connecting the two ter¬ 
minal plates of a voltaic couple be cut, it is clear from what has been 
said about the origin and direction of the current, that positive elec¬ 
tricity will tend to accumulate at the end of the wire attached to the 
copper or negative plate, and negative electricity on the wire attached 
to the zinc or positive plate. These terminals have been called the 
poles of the battery. For experimental purposes, more especially in the 
decomposition of salts, plates of platinum are attached to the ends of 
the wires. Instead of the term poles the word electrode (tf\eKrpov and 
656s, a way) is now commonly used ; for these are the ways through which 
the respective electricities emerge. It is important not to confound the 
positive plate with the positive pole or electrode. The positive electrode 
is that connected with the negative plate, while the negative electrode is 
connected with the positive plate. 

697. Voltaic pile. Voltaic battery. —When a series of voltaic ele¬ 
ments or pairs are arranged in such a manner that the zinc of one element 
is connected with the copper of another; the zinc of this with the copper 
of another, and so on, such an arrangement is called a voltaic battery ; and 
by its means the effects produced by a single element are capable of being 
very greatly increased. 

The earliest of these arrangements was devised by Volta himself. It 
consists (fig. 523) of a series of discs piled one over the other in the fol¬ 
lowing order; at the bottom on a frame of wood, is a disc of copper, then 


GGO 


DYNAMICAL ELECTRICITY. 


[ 697 - 


a disc of cloth moistened by acidulated water or by brine, then a disc of 
zinc; on this a disc of copper, and another disc of moistened cloth, to 
which again follow as many sets of zinc-cloth- 
copper, always in the same order, as may be con¬ 
venient, the highest disc being of zinc. The 
discs are kept in vertical positions by glass rods, 
and it is convenient to have the discs of copper 
and zinc soldered together as represented in the 
diagram. 

The terminal discs however are single, the 
one at the top being of zinc and that at the bot¬ 
tom of copper. 

It will be readily seen that we have here a 
series of simple voltaic couples, the moistened 
disc acting as the liquid, and that the terminal 
zinc is the negative and the terminal copper the 
positive pole. From the mode of its arrange¬ 
ment, and from its discoverer, the apparatus is 
known as the voltaic pile , a term applied to all 
apparatus of this kind for accumulating the ef¬ 
fects of dynamical electricity. 

The distribution of electricity in the pile varies 
according as it is in connection with the ground 
by one of its extremities, or as it is insulated by 
being placed on a nonconducting cake of resin or 
glass. 

In the former case, the end in contact with 
the ground is neutral, and the rest of the ap¬ 
paratus only contains one kind of electricity; 
this is negative if a copper disc is in contact 
with the ground, and positive if it is a zinc disc. 

In the insulated pile the electricity is not uniformly distributed. By 
means of the proof-plane and the electroscope it may be demonstrated 
that the middle part is in a neutral state, and that one half is charged 
-with positive and the other with negative electricity, the tension increas¬ 
ing from the middle to the ends. The half terminated by a zinc is 
charged with negative electricity, and that by a copper with positive 
electricity. The effects of the pile will be discussed in other places. 

The original form of the voltaic pile has a great many inconveniences, 
and possesses now only an historical interest. It has received a great 
many improvements, the principal object of which has been to facilitate 
manipulation, and to produce greater electromotive force. 

One of the earliest of these modifications was the crown of cups, or 



Fig. 523. 














VOLTAIC BATTERY. 


661 



-697] 

couronne des tasses, invented by Volta himself; an improved form of this 
is known as Wollaston's battery (fig. 524) ; it is arranged so that when 
the current is not wanted, the action of the battery can be stopped. 

The plates Z are of thick rolled zinc, and usually about eight inches 
in length by six in breadth. The copper plates C are of thin sheet, and 
bent so as to surround the zincs without touching them : contact being 
prevented by small pieces of cork. To each copper plate a narrow strip 
of copper, o, is soldered, which is bent twice at right angles and is 
soldered to the zinc plate; the first zinc Z is surrounded by the first 


Fig. 524. 

copper C; these two constitute a couple, and each couple is immersed in 
a glass vessel, containing acidulated water. The copper C is soldered to 
the second zinc by the strip o', and this zinc is in turn surrounded by a 
second copper C', and so on. 

Figure 524 represents a pile of sixteen couples united in two parallel 
series of eight each. All these couples are fixed to a cross frame of 
wood, by which they can be raised or lowered at pleasure. When the 
battery is not wanted, the couples are lifted out of the liquid. The 
water in these vessels is usually acidulated with ~ sulphuric and ~ of 
nitric acid. 

Hare's deflagrator. This is a simple voltaic arrangement, consisting 
of two large sheets of copper and zinc rolled together in a spiral, but 
preserved from direct contact by bands of leather or horsehair. The 
whole is immersed in a vessel containing acidulated water, and the two 
plates are connected outside the liquid by a conducting wire. 































662 


DYNAMICAL ELECTRICITY. 


[ 698 - 

698. Enfeeblement of the current in batteries. Secondary 
currents. Polarity.— The various batteries already described, Volta’s, 
Wollaston’s, and Hare’s, which consist essentially of two metals and one 
liquid, labour under the objection that the currents produced rapidly 
diminish in intensity. 

This is principally due to two causes ; the first is the decrease in the 
chemical action owing to the neutralisation of the sulphuric acid by its 
combination with the zinc : the second arises from secondary currents. 
These are currents which are produced in the battery in a contrary 
direction to the principal current, and which destroy it either totally or 
partially. In the fundamental experiment (fig. 522), when the current 
is closed, sulphate of zinc is found, which dissolves in the liquid, and at 
the same time a layer of hydrogen gas is gradually deposited on the 
surface of the copper plate. Now it has been found that the hydrogen 
deposited in this manner on metallic surfaces acts far more energetically 
than ordinary hydrogen. In virtue of this increased activity it gradually 
reduces some of the sulphate of zinc formed, and a layer of metallic 
zinc is formed upon the copper; hence, instead of having two different 
metals unequally attacked, the two metals become gradually less dif¬ 
ferent, and, consequently, in the wire there are two currents tending to 
become equal; the total effect, and the current really observed, become 
weaker and weaker. 

The polarisation of the plate (as this phenomenon is termed) may be 
destroyed by breaking the circuit j the deposit then dissolves, and on 
again closing the circuit the intensity increases. The same result is 
obtained when the current of another battery is transmitted in a direction 
opposite to that of the first. 

De la Hive found that when the platinum electrodes which had been 
used in decomposing a liquid were removed from this liquid and placed 
in distilled water, they produced a current when connected, in a direction 
opposite to that which they had at first transmitted. He calls this the 
polarisation of the electrodes. Becquerel and Faraday have shown that 
this polarity of the metals results from the deposits produced by 
secondary currents. 

Platinum electrodes, however, which have been used to decompose 
pure water, may also become polarised. This phenomenon, as Matteucci 
has shown, arises from a deposit of hydrogen on the one, and of oxygen 
on the other electrode. 


CONSTANT CURRENTS. 

699. Constant currents.— With one exception, batteries composed of 
elements with a single liquid have gone almost entirely out of use, ir con- 


daniell’s battery. 


663 


- 700 ] 

sequence of the rapid enfeeblement of the current produced. They have 
been replaced by batteries with two liquids, which are called constant bat¬ 
teries, because their action is without material alteration for a considerable 
eriod of time. The essential point to be attended to in securing a constant 
current is to prevent the polarisation of the inactive metal; in other words, 
to hinder any permanent deposition of hydrogen on its surface. This is 
effected by placing the inactive metal in a liquid upon which the depo¬ 
sited hydrogen can act chemically. 

700. Saniell’s battery. —This was the first form of the constant 
battery, and was invented by Daniell in the year 1836. As regards the 
constancy of its action, it is still the best of all constant batteries. Fig. 
525 represents a single element. A glass or porcelain vessel, V, contains 
a saturated solution of sulphate of copper, in which is immersed a copper 
cylinder, C, open at both ends, and perforated by holes. At the upper 
part of this cylinder there is an annular shelf, G, also perforated by 
small holes, and below the level of the solution; this is intended to 
support crystals of sulphate of copper to 
i replace that decomposed as the electrical 
ij action proceeds. Inside the cylinder is a 
thin porous vessel, P, of unglazed earth- 
i enware. This contains either solution of 
| common salt or dilute sulphuric acid, in 
1 which is placed the cylinder of amalga- 
j mated zinc, Z. Two thin strips of copper, 
p and n, fixed by binding screws to the cop- 
I per and to the zinc, serve for connecting the 
i elements in series. 

When a Daniell’s element is closed, the 
' hydrogen resulting from the action of the 
dilute acid on the zinc is liberated on the 
I surface of the copper plate, but meets there 
, the sulphate of copper, which is reduced, 
l forming sulphuric acid, and metallic copper,, which is deposited on the 
surface of the copper plate. In this way sulphate of copper in solution is 
taken up, and if it were all consumed, hydrogen would be deposited on 
i the copper, and the current would lose its constancy. This is prevented 
by the crystals of sulphate of copper which keep the solution saturated. 
The sulphuric acid produced by the decomposition of the sulphate per¬ 
meates the porous cylinder, and tends to replace the acid used up by its 
action on the zinc ; and as the quantity of sulphuric acid formed in the 
I solution of sulphate of copper is regular, and proportional to the acid used 
i in dissolving the zinc, the action of this acid on the zinc is regular also, 
“ and thus a constant current is produced. 



Fig. 525. 

































664 


DYNAMICAL ELECTRICITY. 


[ 701 - 

In order to join together several of these elements to form a battery, 
the zinc of one is connected either by a copper wire or strip with the 
copper of the next, and so on, from one element to another, as shown in 
fig. 529, for another kind of battery. 

Instead of a porous vessel a bag of sailcloth may be used for the dia¬ 
phragm separating the two liquids. The effect is at first more powerful, 
but the two solutions mix more rapidly, which weakens the current. The 
object of the diaphragm is to allow the current to pass, but to prevent as 
much as possible the mixture of the two liquids. 

The current produced by a Daniell’s battery is constant for some hours; 
its action is stronger when it is placed in hot water. 

701. Grove’s battery.— In this battery the sulphate of copper solution 
is replaced by nitric acid, and the copper by platinum, by which greater 
electromotive force is obtained. Fig. 526 represents one of the forms of a 
couple of this battery. It consists of a glass vessel, A, partially filled with 
dilute sulphuric acid (1:8); of a cylinder of zinc, Z, open at both ends ; 

of a vessel, V, made of porous 
pipeclay, and containing ordi¬ 
nary nitric acid; of a plate of 
platinum, P (fig. 527), bent in 
the form of an S, and fixed to 
a cover, <?, which rests on the 
porous vessel. The platinum 
is connected with a binding 
screw, b, and there is a similar 
binding screw on the zinc. In 
this battery the hydrogen, 
which would be disengaged 
on the platinum, meeting the 
nitric acid, decomposes it, 
forming hyponitrous acid, 
which dissolves or is disen- 
Grove’s battery is the most convenient and one 
It is, however, the most 




Fig. 527 


gaged as nitrous fumes. 

of the most powerful of the two-fluid batteries, 
expensive, owing to the high price of platinum; besides which the pla¬ 
tinum is liable, after some time, to become brittle and break very easily. 
But as the platinum is not consumed, it retains its value; and M. Adam 
has shown that when the plates which have been used in a battery are 
heated to redness, they regain their elasticity. 

702. Bunsen's battery.— Bunsen's battery , also known as the zinc- 
carbon battery, was invented in 1843; it is nothing more than Grove’s 
battery, in which the sheet of platinum is replaced by a cylinder of 
carbon. This is made either of the graphitoidal carbon deposited in gas 








































bunsen’s battery. 


G65 


- 702 ] 

retorts, or by calcining in an iron mould an intimate mixture of coke and 
bituminous coal, finely powdered and strongly compressed. Botb these 
modifications of carbon are good conductors. Each element consists of 



Fig. 528. 


the following parts: 1. a vessel, F (fig. 528), either of stoneware or of 
glass, containing dilute sulphuric acid ; 2. a hollow cylinder, Z, of amal¬ 
gamated zinc ; 3. a porous vessel, Y, in which is ordinary nitric acid ; 4. 



Fig. 529. 


a cylinder of carbon, C, prepared in the above manner. In the vessel F 
the zinc is first placed, and in it the carbon as seen in P. To the carbon 
is fixed a binding screw, m, to which a copper wire is attached; forming 
the positive pole. The zinc is provided with a similar binding screw, w, 
and wire, which is thus the negative pole. 










































































































666 


DYNAMICAL ELECTRICITY. 


[ 703 - 

The elements are arranged to form a battery by connecting each 
carbon to the zinc of the following one by means of the clamps mn and a 
strip of copper c represented in the top of the figure. The copper is 
pressed at one end between the carbon and the clamp, and at the other 
it is soldered to the clamp n which is fitted on the zinc of the following 
element, and so forth. The clamp of the first carbon and that of the 
last zinc are alone provided with binding screws to which are attached 
the wires. 

The action of Bunsen’s battery is the most energetic of all the con¬ 
stant batteries, and is almost universally used on the continent. But 
though its first cost is less than that of Grove’s battery, it is more ex¬ 
pensive to work, and is not so convenient to manipulate. 

Callan's battery is a modified form of Grove’s. Instead of zinc and 
platinum, zinc and platinised lead are used, and instead of pure nitric 
acid Callan uses a mixture of sulphuric acid, nitric acid, and saturated 
solution of nitre. The battery is said to be equal in its action to Grove’s, 
and is much cheaper. 

Callan has also constructed a battery in which zinc in dilute sulphuric 
acid forms the positive plate, and cast iron in strong nitric acid the 
negative. Under these circumstances the iron becomes passive; it is 
strongly electronegative, and does not dissolve. If, however, the nitric 
acid becomes too weak, the iron is dissolved with simultaneous disen¬ 
gagement of nitrous fumes. 

After being in use some time, all the batteries in which the polari¬ 
sation is prevented by nitric acid disengage nitrous fumes in large 
quantities, and this is a serious objection to their use, especially in closed 
rooms. To prevent this, nitric acid is frequently replaced by chromic 
acid, or better, by a mixture of 4 parts bichromate of potassium, 4 parts 
sulphuric acid, and 18 water. The liberated hydrogen reduces the 
chromic acid to the state of oxide of chromium, which remains dissolved 
in sulphuric acid. With the same view, sesquichloride of iron is some¬ 
times substituted for nitric acid; it becomes reduced to protochloride. 
But the action of the elements thus modified is considerably less than 
when nitric acid is used, owing to the increased resistance. 

703. Smee’s battery.— In this battery the polarisation of the 
negative plate is prevented by mechanical means. Each element con¬ 
sists of a sheet of platinum placed between two vertical plates of zinc, 
as in Grove’s battery; but as there is only a single liquid, dilute sul¬ 
phuric acid, the elements have much the form of those in Wollaston’s 
battery. The adherence of hydrogen to the negative plate is prevented 
by covering the platinum with a deposit of finely divided platinum. In 
this manner the surface is roughened, which facilitates the disengagement 
of hydrogen to a remarkable extent, and, consequently, diminishes the 


NEW BATTERIES. 


667 


- 704 ] 


resistance of the couple. Instead of platinum, silver covered with a 
deposit of finely divided platinum is frequently substituted, as being 
cheaper. 

Walker's battery .—This resembles Smee’s battery, but the electro¬ 
negative plate is either gas graphite or platinised graphite j it is excited 
by dilute sulphuric acid. This battery is used in all the stations of the 
South Eastern Railway, and promises to come into more extensive use, 
for it has considerable electromotive force ; it is convenient and econo¬ 
mical in manipulation, and large-sized elements can be constructed at a 
cheap rate. 

704. New batteries.— The sulphate of mercury battery (fig. 530) 
devised by M. MaritS Davy is essentially a zinc-carbon element, but 
of smaller dimensions than those elements usually are. In the outer 
vessel V ordinary water or brine is placed, and in the porous vessel sulphate 
of mercury. This salt is agitated with about three times its volume of 
water, in which it is difficultly soluble, and the liquid poured off from the 
pasty mass. The carbon being placed in the porous vessel the spaces are 
filled with the residue and then the decanted liquid poured upon it. 

Chemical action takes place only when the pile is closed. The zinc 
then decomposes the water, liberating hydrogen, which traversing the 
porous vessel reduces the sulphate of mercury, forming metallic mercury, 
which collects at the bottom of the vessel, whilfe the sulphuric acid 
formed at the same time traverses the diaphragm to act on the zinc 
and thus increase the action. The mercury which is deposited may be 
used to prepare a quantity of sulphate equal to that which has been 
consumed. A small quantity of the solution of sulphate of mercury may 



Eig. 530. Fig. 531. Fig. 532. 

also pass through the diaphragm ; but this is rather advantageous, as its 
effect is to amalgamate the zinc. 

The electromotive force of this element is about a quarter greater than 
that of 4 Daniell’s element, but it has greater resistance, it is rapidly 





























































DYNAMICAL ELECTRICITY. 


668 


[705- 


exhausted when continuously worked, though it appears well suited for 
discontinuous work, as with the telegraph, and with alarums. 

Gravity batteries. The use of porous vessels is liable to many objec¬ 
tions, more especially in the case of Daniell’s battery, in which they 
gradually become encrusted with copper, which destroys them. A kind 
of battery has been devised in which the porous vessel is entirely 
dispensed with, and the separation of the liquids is effected by their 
difference of density. Such batteries are called gravity batteries $ the one 
in use at the telegraphic establishment of the Royal Engineers at 
Chatham is based on this principle. 

Figure 531 represents a form devised by M. Callaud of Nantes. 
Y is a glass or earthenware vessel in which is a copper plate soldered 
to a wire insulated by gutta percha. On the plate is a layer of crystals 
of sulphate of copper C; the whole is then filled with water, and the 
zinc cylinder Z is immersed in it. The lower part of the liquid becomes 
saturated with sulphate of copper; the action of the battery is that of a 
Daniell, and the sulphate of zinc which gradually forms floats on the solu¬ 
tion of sulphate of copper owing to its lower density. 

This battery is easily manipulated, the consumption of sulphate of 
copper is economical, and when not agitated it works constantly for some 
months, provided care be taken to replace the water lost by evaporation. 

Menotti's battery. This may be described as a Darnell’s element, in 
which the porous vessel is replaced by a layer of sawdust or of sand. 
At the bottom of an earthenware vessel (fig. 532) is placed a layer of 
coarsely-powdered sulphate of copper a, and on this a copper plate pro¬ 
vided with an insulated copper wire i. On this there is a layer of sand or 
of sawdust be, and then the whole is filled with water in which rests a 
zinc cylinder Z. The action is just that of a Daniell; the sand prevents 
the mixture of the liquids but it also offers great resistance which 
increases with its thickness. 

This battery is coming into use for telegraphic work, and from its 
simplicity and economy, and the facility with which it is constructed, 
merits increased attention. 

705. Electromotive force of different elements.— The following 
values have been obtained for the electromotive force of the most usual 
combinations; they are the means of many careful determinations. 


Bunsen’s element 





. 839 

Grove’s „ 





. 829 

Daniell’s „ 





. 470 

Smee’s „ 





. 210 

Wollaston’s ,, 





. 208 


706. Tension of the battery. —The tension of the battery is usually 






AMALGAMATED ZINC. 


669 


- 707 ] 

defined as being the tendency of the electricity accumulated at the ex¬ 
tremities to free itself, and to overcome the obstacles offered to its 
passage. It is proportional to the electromotive force ; thus the tension 
of a zinc-carbon battery is greater than that of a zinc-copper battery. 
The tension of a battery must not be confounded with the quantity of 
’ electricity which it can disengage. The tension of a battery is propor¬ 
tional to the number of couples, while the quantity, other things being 
equal, is proportional to their surface. The larger this surface the greater 
is the quantity of electricity which flows in the circuit. This quantity 
also increases with the conductivity of the liquid interposed between the 
couples; the tension on the contrary is independent of the nature of this 
liquid. 

Except in the case of a very considerable number of couples, the tension 
at the extremities of the battery is always far weaker than in electrical 
machines. For neither of the extremities gives a spark or attracts light 
bodies, and it is only by means of a condensing gold-leaf electroscope, and 
by extremely careful insulation, that the tension can be observed. For 
this purpose one of the plates of the electroscope is connected with one 
end of the pile and the other with the other end or with the groimd. The 
apparatus is then charged, and on breaking the communications the gold 
leaves diverge. A Leyden jar may even be charged when the interior 
coating is connected with one end of the pile, and the external coating 
with the other ; but this charge is far feebler than that furnished by the 
electrical machine. 

707. Amalgamated zinc. —De la Rive observed that perfectly pure 
distilled zinc was not attacked by dilute sulphuric acid, but became so 
when immersed in that liquid in contact with a plate of copper or of 
platinum. Ordinary commercial zinc, on the contrary, is rapidly dissolved 
by dilute acid. This, doubtless, arises from the impurity of the zinc, 
which always contains traces either of iron or lead. Being electro¬ 
negative towards zinc they tend to produce local electrical currents , which 
accelerate the chemical action without increasing the quantity of elec¬ 
tricity in the connecting wire. 

Zinc, when amalgamated, acquires the properties of perfectly pure zinc, 
and is unaltered by dilute acid, so long as it is not in contact with a cop¬ 
per or platinum plate immersed in the same liquid. To amalgamate a 
zinc plate, it is first immersed in dilute sulphuric or hydrochloric acid so 
as to obtain a clean surface, and then a drop of mercury is placed on the 
plate and spread over it with a brush. The amalgamation takes place 
immediately, and the plate has the brilliant aspect of mercury. 

Zinc plates may also be amalgamated by dipping them in a solution of 
mercury prepared by dissolving at a gentle heat one poimd of mercury in 


DYNAMICAL ELECTRICITY. 


670 


[ 708 - 


fiye pounds of aqua regia (one part of nitric to three of hydrochloric acid) 
and then adding five parts more of hydrochloric acid. 

The amalgamation of the zinc removes from its surface all the impuri¬ 
ties, especially the iron. The mercury effects a solution of pure zinc, 
which covers the surface of the plate, as with a liquid layer. 

The amalgamation of zinc was first applied to electrical batteries by 
Kemp. Amalgamated zinc is not attacked so long as the circuit is not 
closed, that is, when there is no current. With amalgamated zinc the 
current is more regular, and at the same time more intense, for the same 
quantity of metal dissolves. 

708. Dry piles.— In dry piles the liquid is replaced by a solid hygro- 
metric substance, such as paper or leather. They are of various kinds; 
in Zamboni’s, which is most extensively used, the electromotors are tin or 
silver, and binoxide of manganese. To construct one of these a piece of 
paper silvered or tinned on one side is taken; the other side of the paper 
is coated with finely powdered binoxide of manganese by slightly moisten¬ 
ing it, and rubbing the powder on with a cork. Having placed together 
seven or eight of these sheets, they are cut by means of a punch into discs 
an inch in diameter. These discs are then arranged in the same order, 
so that the tin or silver of each disc is in contact with the manganese of 
the next. Having piled up 1,200 to 1,800 couples, they are placed in a 
glass tube, which is provided with a brass cap at each end. In each cap 
there is a rod and knob, by which the leaves can be pressed together, so as 
to produce better contact. The knob in contact with the manganese 
corresponds to the positive pole, while that at the other end, which is in 
contact with the silver or tin, is the negative pole. 

The dry piles are remarkable for the permanence of their action, which 
may continue for several years. Their action depends greatly on the 
temperature and on the hygrometric state of the air. It is stronger in 
summer than in winter, and the action of a strong heat revives it when it 
appears extinct. A Zamboni’s pile of 2,000 couples gives neither shock 
nor spark, but can charge a Leyden jar and other condensers. A certain 
time is however necessary, for electricity only moves slowly in the 
interior. 

709. Bobnenbergrer’s electroscope. —Bohnenberger has constructed 
a dry-pile electroscope of extreme delicacy. It is a condensing elec¬ 
troscope (fig. 505), from the rod of which is suspended a single gold leaf. 
This is at an equal distance from the opposite poles of two dry piles 
placed vertically, inside the bell jar, on the plate of the apparatus. As 
soon as the gold leaf possesses any free electricity it is attracted by one of 
the poles and repelled by the other, and its electricity is obviously con¬ 
trary to that of the pole towards which it moves. 


- 711 ] 


DETECTION OF VOLTAIC CURRENTS. 


671 


CHAPTER II. 

DETECTION AND MEASUREMENT OF VOLTAIC CURRENTS. 

710. Detection and measurement of voltaic currents. —The 

remarkable phenomena of the voltaic battery may be classed under the 
heads physiological, chemical, mechanical, and physical effects; and 
these latter may be again subdivided into the thermal, luminous, and 
magnetic effects. For ascertaining the existence and measuring the 
intensity of voltaic currents, the magnetic effects are more suitable than 
any of the others, and, accordingly, the fundamental magnetic pheno¬ 
mena will be described here, and the description of the rest postponed 
to a special chapter on electro-magnetism. 

711. Oersted’s experiment. —Oersted published in 1819 a dis¬ 
covery which connected magnetism and electricity in a most intimate 
manner, and became in the hands of Ampere and of Faraday, the source 
of a new branch of physics. The fact discovered by Oersted is the 
directive action which a fixed current exerts at a distance on a magnetic 
needle. 

To make this experimenf/a popper wire is suspended horizontally in 
the direction of the magnetic 
meridian over a moveable mag¬ 
netic needle, as represented in 
fig. 533. So long as the wire is 
not traversed by a current the 
needle remains parallel to it, but 
as soon as the ends of the wire 
are respectively connected with 
the poles of a battery or of a 
single element, the needle is de¬ 
flected, and tends to take a position 
which is the more nearly at right 
angles to the magnetic meridian in proportion as the current is more intense. 

In reference to the direction in which the poles are deflected, there 
are several cases, which may, however, be referred to a single principle. 
Remembering our assumption (694) that in the connecting wire the 
current proceeds from the negative to the positive plate, the preceding 
experiment presents the following four cases:— 

i. If the current passes above the needle, and goes from south to 
north, the north pole of the magnet is deflected towards the west; this 
arrangement is represented in the above figure. 











672 DYNAMICAL ELECTRICITY. [ 712 - 

ii. If the current passes below the needle, also from south to north, 
the north pole is deflected towards the east. 

iii. When the current passes above the needle, but from north to south, 
the north pole is deflected towards the east. 

iv. Lastly, the deflection is towards the west when the current goes 
from north to south below the needle. 

Ampere has given the following memoria technica by which all the 
various directions of the needle under the influence of a current may 
be remembered. If we imagine an observer placed in the connecting 
wire in such a manner that the current entering by his feet issues by his 
head, and that his face is always turned towards the needle, we shall 
see that in the above four positions the north pole is always deflected 
towards the left of the observer. By thus personifying the current, the 
different cases may be comprised in this general principle : In the direc¬ 
tive action of currents on magnets , the north pole is always deflected towards 
the left of the current. 

712. Galvanometer or multiplier.— The name galvanometer , multi¬ 
plier , or rheometer is given to a very delicate apparatus by which the 




existence, direction, and intensity of currents may be determined. It 
was invented by Schweigger in Germany a short time after Oersted’s 
discovery. 

In order to understand its principle, let us suppose a magnetic needle 
suspended by a filament of silk (fig. 534), and surrounded in the plane 
of the magnetic meridian by a copper wire forming a complete circuit 
round the needle in the direction of its length. When this wire is 
traversed by a current, it follows, from -\yhat has been said in the 
previous paragraph, that in every part of the circuit an observer lying 
in the wire in the direction of the arrows, and looking at the needle ah, 
would have his left always turned towards the same point of the 
horizon, and consequently, that the action of the current in every part 
would tend to turn the north pole in the same direction : that is to say 
that the actions of the four branches of the circuit concur to give the 




























galvanometer. 


673 


- 712 ] 


north pole the same direction. By coiling the copper wire in the 

direction of * he neecUe ’ 88 r «P^sented in the figure, the action of the 

current has been multiplied. If instead of a single one, there are 
several circuits provided they are insulated, the action becomes still 
more multiplied, and the deflection of the needle increases. Never¬ 
theless, the action of the current cannot be multiplied indefinitely by 
increasing the number of windings, for, as we shall presently se/ 

the intensity of a current diminishes as the length of the circuit is’ 
increased. ■ 



As the directive action of the earth continually tends to keep the 
needle in the magnetic meridian, and thus opposes the action of the 
current, the effect of the latter 
is increased by using an astatic 
system of two needles as shown 
in tig. 535. The action of the 
earth on the needle is then very 
feeble,] and, further, the actions 
of the current on the two needles 
become accumulated. In fact, 
the action of the circuit, from 
the direction of the current in¬ 
dicated by the arrows, tends to 
deflect the north pole of the 
lower needle towards the west. 

The upper needle, a'b', is sub¬ 
jected to the action of two con¬ 
trary currents mn and qp, but as 
the first is nearer, its action 
preponderates. Now this current 
passing below the needle, evi¬ 
dently tends to turn the pole a ' 
towards the east, and, conse¬ 
quently, the pole b' towards the 
west: that is to say, in the same 
direction as the pole a of the 
other needle. 

From these principles it will 
be easy to understand the theory 
of the multiplier. The apparatus 


Fig. 536. 


represented in fig. 536 consists of a copper frame, D, round which is 
coiled a copper wire, covered with silk so as to insulate the coils. Above 
the frame is a horizontal circle, the zero of which corresponds to the 
diameter parallel to the direction of the wire j there are two graduations 




















674 


DYNAMICAL ELECTRICITY. 


[ 712 - 

on the scale, the one on the right and the other on the left of zero, but 
they only extend to 90°. By means of a very fine filament of silk, an 
astatic system is suspended; it consists of two needles, ab and A, one 
above the scale, and the other in the circuit itself. These needles, which 
are joined together by a copper wire, like those in fig. 454, and fig. 535, 
and cannot move separately, must not have exactly the same magnetic 
intensity ; for if they are exactly equal, every current, strong or weak, 
would always put them at right angles with itself. 

The bent wires K and H, underneath the apparatus, serve for placing 
the galvanometer in connection with the current to be investigated. By 
means of the levelling screws C, the apparatus can be placed in a horizontal 
position, so that the filament of silk is exactly in the centre of the scale. 
By means of a screw, E, the frame E and the scale can be moved so that 
the wires of the circuit are placed in the direction of the magnetic 
meridian without displacing the apparatus. 

The length and diameter of the wire vary with the purpose for 
which the galvanometer is intended. For one which is to be used in 
observing the currents due to chemical actions, a wire about | milli¬ 
meter in diameter, and making about 800 turns, is well adapted. Tho i e 
for thermoelectric currents, which have low intensity, require a thicker and 
shorter wire, for example, thirty turns of a wire § millimeter in diameter. 
For very delicate experiments, as in physiological investigations, galvano¬ 
meters with as many as 30,000 turns have been used. 

By means of a delicate galvanometer consisting of 2,000 or 3,000 turns 
of fine wire, the coils of which are carefully insulated by means of silk and 
shellac, currents of high intensity, as those of the electrical machine, may 
be shown. One end of the galvanometer is connected with the conductor 
and the other with the ground, and on working the machine the 
needle is deflected; affording thus an illustration of the identity of 
statical with dynamical electricity. 

The deflection of the needle increases with the intensity of the 
current; the relation between the two is, however, so complex that it 
cannot well be deduced from theoretical considerations, but requires to be 
determined experimentally for each instrument. And in the majority of 
cases the instrument is used rather as a galvanoscope or rheoscope , that is, 
to ascertain the presence and direction of currents, than as a galvanometer 
or rheometer in the strict sense, that is, as a measurer of their intensity. 
The latter term galvanometer is however commonly used. 

The differential galvanometer consists of a needle as in an ordinary gal¬ 
vanometer, but round the frame of which are coiled two wires of the same 
kind and dimensions, carefully insulated from each other, and provided 
with suitable binding screws, so that separate currents can be passed 
through each of them. If the currents are of the same intensity but in 



MARINE GALVANOMETER. 


675 


-713] 

different directions, no deflection is produced; where the needle is de¬ 
flected one of the currents differs from the other. Hence the apparatus 
is used to ascertain a difference in intensity of two currents and to this 
circumstance owes its name. 

713. Sir W. Thomson’s marine galvanometer. —In laying sub¬ 
marine cables the want was felt of a galvanometer sufficiently sensitive 
to test insulation, which at the same time was not affected by the pitch¬ 
ing and rolling of the ship. For this purpose, Sir W. Thomson invented 
his marine galvanometer. Fig. 537 is from a drawing of this instrument 
kindly furnished by Messrs. Elliotts, by whom it is made. B represents 
a coil of many thousand turns of the finest copper wire, carefully insu- 



Fig. 537. 

lated throughout, terminating in the binding screws EE. In the centre 
of this coil is a slide, which carries the magnet, the arrangementof which 
is represented on a larger scale in D. The magnet itself is made of a piece 
of fine watch spring about § of an inch in length, and does not weigh 
more than a grain; it is attached to a small and very slightly concave 
mirror of very thin silvered glass. A single fibre of silk is stretched 
across the slide, and the mirror and magnet are attached to it in such a 
manner, that the fibre exactly passes through the centre of gravity in 
every position. As the mirror and magnet weigh only a few grains, they 
retain their position respecting the instrument, however the ship may 
pitch and roll. The slide fits in a groove in the coil, and the whole is 
enclosed within a wrought-iron case with an aperture in front, and a 
wrought-iron lid on the top. The object of this is to counteract the in¬ 
fluence of the terrestrial magnetism when the ship changes its course. 

G G 2 














676 


DYNAMICAL ELECTRICITY. 


[ 714 - 

Underneath the coil is a large curved steel magnet N, which compensates 
the earth’s directive action upon the magnet I), and in the side of the 
case, and on a level with D, a pair of magnets are placed with opposite 
poles together. By a screw suitably adjusted the poles of the magnets 
may be brought together ; in which case they quite neutralise each other, 
and thus exert no action on the suspended magnet, or they may be slid 
apart from each other in such a manner that the action of either pole on 
D preponderates to any desired extent. This small magnet is then 
capable of very delicate adjustment. The large magnet N, and the pair 
of magnets C, are analogous to the coarse and fine adjustment of a 
microscope. 

At a distance of about three feet, there is a scale with the zero in the 
centre and the graduation extending on each side. Underneath this zero 
point, is a narrow slit through which passes the light of a paraffine lamp, 
and which traversing the window is reflected from the curved mirror 
against the graduated scale. By means of the adjusting magnets the 
image of the slit is made to fall on the centre of the graduation. 

This being the case, if any arrangement for producing a current how¬ 
ever weak be connected with the terminals, the spot of light is deflected 
either to one side or the other, according to the direction of the current; 
the stronger the current the greater the deflection of the spot; and if the 
current remains of constant strength for any length of time, the spot is 
tationary in a corresponding position. 

It will be seen from the article on the Electric Telegraph, how alternate 
deflections of the spot of light may be utilised in forming a code of signals. 

714. Tangent compass, or tangent boussole.— When a magnetic 
needle is suspended in the centre of a voltaic current in the plane of the 
magnetic meridian, it can be proved that the intensity of a current is 
directly proportional to the tangent of the angle of deflection, provided 
the dimensions of the needle are sufficiently small as compared with the 
diameter of the circuit. An instrument based on this principle is called 
the tangent boassole, or tangent compass. It consists of a copper ring, 12 
inches in diameter, and about an inch in breadth, mounted vertically on 
a stand ; the lower half of the ring is generally fitted in a semicircular 
frame of wood to keep it steady. In the centre of the ring is suspended 
a delicate magnetic needle ; in order to fulfil the conditions of the law 
its length must not exceed A or A 0 f the diameter of the circle. Under¬ 
neath the needle there is a graduated circle. The ends of the ring 
are prolonged in copper wires, fitted with mercury cups, ab, by which 
it can be connected with a battery or element. The circle is placed in 
the plane of the magnetic meridian, and the deflection of the needle 
is directly read off on the circle, and its corresponding value obtained 
from a table of tangents. 




ohm’s law. 


677 


- 715 ] 

On account of its small resistance, the tangent compass is well adapted 
for currents of low tension, but in which a considerable quantity of 



electricity is set in motion. For currents which can overcome great 
resistance, but have only a small quantity of electricity, the multiplier 
is best fitted. 

715. Ohm’s law. —For a knowledge of the conditions which regulate 
the action of the voltaic current, science is indebted to the late Professor 
Ohm. 

His results were at first deduced from theoretical considerations, but by 
his own researches as well as by those of Fechner, Pouillet, Daniell, De 
la Rive, Wheatstone, and others, they have received the fullest confir¬ 
mation, and their great theoretical and practical importance has been 
fully established. 

i. The force or cause by which electricity is set in motion in the voltaic 
circuit is called the electromotive force. The quantity of electricity which 
in any unit of time flows through a section of the circuit is called the 
intensity of the current. Ohm found that this intensity is the same in all 
parts of one and the same circuit however heterogeneous they were; and 
also tk#t it is proportional to the electromotive force. 

It has further been found that when the same current is passed 
respectively through a short and through a long wire of the same 
material, its action on the magnetic needle is less in the latter case than 
in the former. Ohm accordingly supposed that in the latter case there 



678 


DYNAMICAL ELECTRICITY. 


[ 715 - 


was a greater resistance to the passage of the current than in the former; 
and he proved that 1 the resistance is inversely proportional to the intensity 
of the current .’ 

On these principles Ohm founded the celebrated law which bears his 
name, that— 

The intensity of the current is equal to the electromotive force'dimded by 
the resistance. 

Which is expressed by the simple formula 



where I is the intensity of the current, E the electromotive force, and K 
the resistance. 

ii. The resistance of a conductor depends on three properties ; its con¬ 
ductivity, which is a constant, determined for each conductor; its section ; 
and its length. The resistance is obviously inversely proportional to the 
conductivity, that is, the less the conducting power the greater the resis¬ 
tance. This has been experimentally shown, and it has also been proved 
that the resistance is inversely as the section and directly as the length of a 
conductor. If then k is the conductivity, « the section, and \ the length 
of a conductor, we have 


\ E k«E 

11 = -“ and I —— — - > 

KU A \ 


KU 

that is, the intensity of a current is invet'sely proportional to the length of the 
conductor and directly proportional to its section and conductivity. 

iii. In a voltaic battery composed of different elements, the intensity 
of the current is equal to the sum of the electromotive forces of all the 
elements divided by the sum of the resistances. Usually, however, a 
battery is composed of elements of the same kind, each having the same 
electromotive force and the same resistance. 

In an ordinary element there are essentially two resistances to be 
considered: 1. That offered by the liquid conductor between the two 
plates, which is frequently called the internal or essential resistance ; and 
2, That offered by the interpolar conductor which connects the two 
plates outside the liquid; this conductor may consist either wholly of 
metal, or partly of metal and partly of liquids to be decomposed j it is 
the external or non-essential resistance. Calling the former K and the 
latter r, Ohm’s formula becomes # 



iv. If any number, n, of similar elements are joined together, there is 
n times the electromotive force, but at the same time n times the 


679 


“ 715 ] ohm’s law. 

internal resistance, and the formula becomes — wE .. If the resistance 

wR-f- r 

in the interpolar, r, is very small, which is the case, for instance, when 
it is a short thick copper wire, it may be neglected in comparison with 
the internal resistance, and then we have 

I = wE = E 
wR R 

that is, a battery consisting of several elements produces in this case no 
greater effect than a single element. If, however, the external resist¬ 
ance r is very great, which is the case where the current has to pass 
through a long thin wire, or through a liquid, the intensity is within 
certain limits very nearly proportional to the number of elements. 

v. If the plates of an element be made m times as large, there is no 
increase in the electromotive force, for this depends on the nature of the 
metals and of the liquid, but the resistance is m times as small, for the 
section is m times larger, the expression becomes then— 

j_ E _ mE 

R+r R-j-mr* 

m 

Hence, an increase in the size of the plate, or, what is the same thing, 
a decrease in the internal resistance, does not increase the intensity to an 
indefinite extent; for ultimately the resistance of the element R 
vanishes in comparison with the resistance r, and the intensity always 

E 

approximates to the value I =—. 

r 

In a thermoelectric pile, which consists of very short metallic con¬ 
ductors, the internal resistance R is very small. It may hence be 
neglected, and Ohm’s formula becomes 



that is, the intensity is inversely as the length of the connecting wire. 

vi. Ohm’s law enables us to arrange a battery sq as to obtain the 
greatest effect in any given case. For instance, with a battery of six 
Bunsen’s elements there are the following four ways of arranging them : 
1. In a single series (fig. 539), in which the zinc Z of one element is 
united with the copper C of the second; the zinc of this with the 
copper of the third, and so on ; 2. Arranged in a system of three double 
elements, each element being formed by joining two of the former 
(fig. 540); 3. In a system of two elements, each of which consists of 
three of the original elements joined, so as to form one of triple the 
surface (fig. 541); 4. Lastly, of one large element, all the zincs and all 
the coppers being joined, so as to form a larger pair of six times the 
surface (fig. 542). 




680 DYNAMICAL ELECTRICITY. [ 715 - 

With a series of twelve elements there may be six different combina¬ 
tions, and so on for a larger number. 



Fig. 540. Fig. 541. 



Now let us suppose that in the particular case of a battery of six ele¬ 
ments the internal resistance R of each element is 3 and the external re¬ 
sistance r = 12. Then in the first case where there are six elements we 
have the value 

1 _ 6E _ 6E _ 6E 
6R + r 6 x 3 -f- 12 30‘ 

If they were united so as to form three elements, each of double the 
surface, as in the second case (fig. 540), the electromotive force then 
would be, the electromotive force E in each element; there would also 
be a resistance R in each element, but this would only be half as great, 
for the section of the plate is now double ; hence the intensity in this 
case would be 



















- 715 ] 


ohm’s law. 


681 


r = 


3E 



_ 3E 

| + 12 


6E . • 
33 ’ 


hence this change would lessen the intensity. 

If with the same elements the resistance in the connecting wire 
were only r = 2, we should have the values in the two cases respec¬ 
tively— 


and I' = 


j _ 6 x E _ 6E 

6x3 + 2 20’ 

3E _ 6E _6E 
3R 9 + 4 T3’ 


The result in this case is, therefore, more favourable. If the resist¬ 
ance r were 9 the intensity would be the same in both cases. Hence, 
by altering the size of the plates or the arrangement favourable or 
unfavourable results are obtained according to the relation between It 
and r. 

In any given combination the maximum effect is obtained when the 
total resistance in the elements is equal to the resistance of the inter- 
polar. Suppose that in a given case n elements are arranged so as to form 
a battery of s couples, each consisting of t cells, n — st. Denoting the re¬ 


sistance of a single element by r , the total resistance is —. Now accord- 

t 


ing to the above law the maximum effect is obtained when ^ = l, where 

Tt 7*S^ 

l is the resistance of the interpolar. But t — hence — = l, or 

s n 



If in a given case we have 8 elements, each offering a resistance 15 and 
an interpolar with the resistance 40, we get s = 4'3. But this is an im¬ 
possible arrangement, for it is not a whole number, and the nearest whole 
number must be taken. This is 4, and it will be found on making a cal¬ 
culation analogous to that above, that when arranged so as to form 4 
elements, each of double surface, the greatest effect is obtained. 


o o 3 









682 


DYNAMICAL ELECTRICITY. 


[ 716 - 


CHAPTER III. 

, EFFECTS OF THE CURRENT. 

716. Physiological actions. —Under this name are included the 
effects produced by the battery on dead or living animals. They consist 
in very energetic shocks and muscular contractions when the batteries are 
powerful. 

When the electrodes of a strong battery are held in the two hands a 
violent shock is felt, resembling that of a Leyden jar, especially if the 
hands are moistened with acidulated or saline water, which increases the 
conductivity. The shock is more violent in proportion to the number of 
elements used; with a Bunsen’s battery of 50 to 60 couples the shock 
is very strong, with 150 or 200 couples it is unbearable, and even dan¬ 
gerous when continued. It is less perceptible in the forepart of the 
arms than the shock of the Leyden jar, and when transmitted through 
a chain of several persons, it is generally only felt by those nearest the 
poles. 

The shock, as in the case of the Leyden jar, is due to the recomposition 
of the two electricities; with this difference, that with the Leyden jar 
the discharge being instantaneous, the resultant shock is so also; while 
in the latter case as the battery is immediately recharged after each dis¬ 
charge, the shocks succeed each other with rapidity. The action of the 
voltaic current on animals differs with its direction. Lehot and Marianini 
have shown that when the current is transmitted in one direction through 
the ramifications of the nerves, a muscular contraction is experienced 
when it commences, and a painful sensation when it ceases : whereas if it 
passes in the opposite direction through the nerves, pain is felt as long as 
it continues, and a contraction at the moment of its interruption. This 
difference of effects, however, is only produced in the case of feeble 
currents. With intense currents the contractions and the painful effects 
take place both on closing and opening the current, whatever be its 
direction. 

With a single couple no perceptible action is produced in the 
fingers, but when it is applied to the tongue a peculiar effect is 
observed. The experiment may be made in a very simple manner. 
A piece of zinc as large as a sixpence is applied with its edge on the 
lower part of the tongue, and a sixpence is placed on the upper side: 
on bringing the two in contact a peculiar saline taste is perceived, 
which does not belong either to the silver or to the zinc, for it is 
only perceived when the plates touch, and disappears when they are 
separated. 


THERMAL EFFECTS. 


683 


-717] 

By means of a powerful current, rabbits which have been suffocated 
half an hour have been restored to life; the head of a man who had 
been executed experienced such dreadful contractions that the spec¬ 
tators were horrified. The trunk, submitted also to the action of the 
current, partially raised itself, the hands were agitated, and struck adja¬ 
cent objects, and the pectoral muscles imitated the respiratory movement. 
All vital actions were imperfectly reproduced, but ceased immediately 
with the current. 

717. Thermal effects.— When a voltaic current is passed through a 
metallic wire the same effects are produced as by the discharge of an 
electric battery; the wire becomes heated and even incandescent if it 
is very short and thin. With a powerful battery all metals are melted, 
even iridium and platinum, the most infusible of metals. Carbon is the 
only body which hitherto has not been fused by it. M. Despretz, how¬ 
ever, with a battery composed of 600 Bunsen’s elements joined in six 
series (715), has raised rods of very pure carbon to such a temperature 
that they were softened and could be welded together, indicating an 
incipient fusion. 

A battery of -30 to 40 Bunsen’s elements is sufficient to melt and vola¬ 
tilise fine wires of lead, tin, zinc, copper, gold, silver, iron, and even pla¬ 
tinum, with differently coloured sparks. Iron and platinum burn with a 
brilliant white light; lead with a purple light; the light of tin and of 
gold is bluish white ; the light of zinc is a mixture of white and gold; 
finally, copper and silver give a green light. 

The thermal effects of the voltaic current are used in firing mines for 
military purposes and for blasting operations. The following arrange¬ 
ment is adopted in the English service. Fig. 543 represents a small 
wooden box provided with a lid. Two moderately stout copper wires, 
insulated by being covered with gutta percha, are deprived of this coating 
at the ends, which are then passed through and through the box in the 
manner represented in the figure. The distance between them is § of an 
inch, and a very fine platinum wire (one weighing T92 grains to the yard 
is the regulation size) is soldered across. The object of arranging the wires 
m this manner is that they shall not be in contact, and the strain which 
they exert may be spent on the box and not on the platinum wire joining 
them, which, being very thin, would be broken by a very slight pull. 
The box is then filled with fine-grained powder, and the lid tied down. 
The wires of the fuse are then carefully joined to the long conducting 
wires, which lead to the battery; these should be of copper, and as thick as 
is convenient, so as to offer very little resistance: No. 16 gauge copper wire 
is a suitable size. The fuse is then introduced into the charge to be fired: 
if it is for a submarine explosion the powder is contained in a canister, 
the neck of whiph, after the introduction of the fuse, is carefully fas- 


684 


DYNAMICAL ELECTRICITY 


[717 


tened by means of cement. When contact is made with the battery, 
which is effected through the intervention of mercury cups, the current 
traversing the platinum wire renders it incandescent, which fires the fuse ; 
and thus the ignition is communicated to the charge in which it is placed. 

Although the thermal effects are most obvious in the case of thin wires 
they are not limited to them ; with thicker wires they may be perceived 



v 


Fig. 543 


by means of delicate thermometric arrangements, by which also the laws 
of the heating effect may be investigated. 

Such an arrangement is called a galvano-thei'mometer. It consists 
essentially of a glass vessel containing alcohol, in which is a delicate 
thermometer; the wire to be investigated is fitted to two platinum wires 
fused in the well-ground stopper of the vessel. The current is passed 
through the platinum wires, and its intensity measured by means of a 
tangent compass interposed in the circuit. By observing the increase of 
temperature in the thermometer in a given time, and knowing the weight 
of the alcohol, the mass of the wire, the specific heat, and the calorimetric 
values (389) of the vessel, and of the thermometer, compared with al¬ 
cohol, the thermal effect which is produced by the currrent in a given 
time can be calculated. 

By apparatus of this kind the laws of the thermal effects have been 
investigated by Lenz, Joule, and Becquerel. They are as follows: 

I. The heat disengaged in a given time is directly proportional to the 
square of the intensity of the current , and to the resistance of the wire. 

II. Whatever he the length of the wire , provided its diameter remains the 
same , and that the same quantity of electricity passes , the increase of tem¬ 
perature is the same in all parts of the wire. 





THERMAL EFFECTS. 


685 


-717] 

III. For the same quantity of electricity , the increase of temperature in 
different parts of the wire is inversely as the fourth powei' of the diameter. 

If the current passes through a chain of platinum and silver wire of 
equal sizes, the platinum becomes more heated than the silver from its 
greater resistance ; and with a suitable current the platinum may become 
incandescent while the silver remains dark. This experiment was devised 
by Children. If a long thin platinum wire be raised to dull redness 
by passing a voltaic current through it, and if part of it be cooled down 
by ice, the resistance of the cooled part is diminished, the intensity of 
the current increases, and the rest of the wire becomes brighter than 
before. 

If, on the contrary, a part of the feebly incandescent wire be heated 
by a spirit lamp, the resistance of the heated part increases, the intensity 
of the current diminishes, and the wire ceases to be incandescent in the 
non-heated part. 

The cooling by the surrounding medium exercises an important in¬ 
fluence on the phenomenon of ignition. A round wire is more heated 
by the same current than the same wire which has been beaten out 
flat; for the latter with the same section offers a greater surface to the 
cooling medium to the others, for the same reason, when a wire is 
stretched in a glass tube on which two brass caps are fitted air-tight, and 
the wire is raised to dull incandescence by the passage of a current, the 
incandescence is more vivid when the air has been pumped out of the 
tube, because it now simply loses heat by radiation, and not by commu¬ 
nication to the surrounding medium. 

Similarly, a current which will melt a wire in air will only raise it 
to dull redness in ether, and in oil or in water will not heat it to red¬ 
ness at all, for the liquids conduct heat away more readily than air does. 

From the above laws it follows that the heating effect is the same in 
a wire whatever be its length, provided the current is constant ; but it 
must be remembered that by increasing the length of the wire we 
increase the resistance, and consequently diminish the intensity of the 
current; further, in a long wire there is a greater surface, and hence 
more heat is lost by radiation and by conduction. 

The thermal effect depends more on the size than on the number of 
the plates of a battery, for the resistance in the connecting wires is small. 
An iron wire may be melted by a single Wollaston’s element, the zinc, 
of which is 8 inches by 6. Hare’s battery (697) has received its name 
deflagrator on account of its greater heating effect produced by the great 
surface of its plates. 

When any circuit is closed a definite amount of heat is produced 
throughout the entire circuit; and the amount of heat produced in 
any particular part of the circuit is greater, the greater the proportion 


686 


DYNAMICAL ELECTRICITY. 


[ 718 - 

which the resistance of this part hears to the entire circuit. Hence 
in firing mines the wire to he heated should be of as small section 
and of small conductivity as are practical. These conditions are well 
satisfied by platinum, which has over iron the advantage of being less 
brittle and of not being liable to rust. Platinum too has* a low specific 
heat, and is thus raised to a higher temperature by the same amount of 
heat than a wire of greater specific heat. 

On the other hand, the conducting wires should present as small a re¬ 
sistance as possible, a condition satisfied by a stout copper wire; and again, 
as the heating effect of any circuit is proportional to the square of the 



Fig. 544. 


intensity, and as this is directly as the electromotive force, and inversely 
as the resistance, a battery with a high electromotive force, and small re¬ 
sistance, such as Grove’s or Bunsen’s, should be selected. 

By means of a heated platinum wire, parts of the body may be safely 
cauterised which could not be got at by a red-hot iron ; the removal of 
tumours may be effected by drawing a loop of platinum round their base, 
which is then gradually pulled together. It has been observed that when 
the temperature of the wire is about 600° C., the combustion of the tis¬ 
sues is so complete that there is no haemorrhage; while at 1,600° the 
action of the wire is like that of a sharp knife. 

718. Luminous effects. —In closing a voltaic battery a spark is 
obtained at the point of contact, which is frequently of great brilliance. 
















LUMINOUS EFFECTS. 


687 


-718] 

A similar spark is also perceived on breaking contact. These luminous 
effects are obtained when the battery is sufficiently powerful, by bringing 
the two electrodes very nearly in contact; a succession of bright sparks 
springs sometimes across the interval, which follow each other with such 
rapidity as to produce a continuous light. With eight or ten of Grove’s 
elements brilliant luminous sparks are obtained by connecting one 
terminal of the battery with a file, and moving its point along the teeth 
of another file connected with the other terminal. 

The most beautiful effect of the electric light is obtained when with 
the terminals of the battery two pencils of charcoal are connected in 
the manner represented in fig. 544. The charcoal b is fixed, while the 
charcoal a can be raised or lowered by means of a rack and pinion 
motion, c. The two charcoals being placed in contact the current 
passes, and their ends soon become incandescent. If they are then 
removed to a distance of about the tenth of an inch, according to the 
intensity of the current, a luminous arc extends between the two 
points, which has an exceedingly brilliant lustre, and is called the 
voltaic arc. 

The length of this arc varies with the force of the current. In air it 
may exceed 2 inches with a battery of 600 elements, arranged in six series 
of 100 each, provided the positive pole is uppermost, as represented in 
the figure; if it is undermost, the arc is about one-third shorter. In 
vacuo the distance of the charcoal may be greater than in air; in fact, 
as the electricity meets with no resistance, it springs between the two 
charcoals, even before they are in contact. The voltaic arc can also be 
produced in liquids, but it is then much shorter, and its brilliancy is 
greatly diminished. 

The voltaic arc has the property that it is attracted when a mag¬ 
net is presented to it; a consequence of the action of magnets on 
currents. 

Some physicists have considered the voltaic arc as formed of a very 
rapid succession of bright sparks. Its colour and shape depend on the 
nature of the conductors between which it is formed, and hence it is 
probable that it is due to the incandescent particles of the conductor, 
which are volatilised and transported in the direction of the current, 
that is, from the positive to the negative pole. The more easily the 
electrodes are disintegrated by the current, the greater is the distance 
at which the electrodes can be placed. Charcoal, which is a very 
friable substance, is one of the bodies which gives the largest lumi¬ 
nous arc. 

Davy first made the experiment of the electric light, in 1801, by means 
of a battery of 2000 plates, each 4 inches square. He used charcoal points 
made of light wood charcoal which had been heated to redness, and im- 


688 


DYNAMICAL ELECTRICITY. 


[ 719 - 

mersed in a mercury bath ; the mercury penetrating into the pores of the 
charcoal, increased its conductivity. When any substance was introduced 
into the voltaic arc produced by this battery, it became incandescent; 
platinum melted like wax in the flame of a candle ; sapphire, magnesia, 
lime, and most refractory substances were fused. Fragments of diamond, 
of charcoal, and of graphite, rapidly disappeared without undergoing any 
previous fusion. 

As charcoal rapidly burns in air, it was necessary to operate in vacuo, 
and hence the experiment was for a long time made by fitting the 



two points in an electric egg, like that represented in fig. 508. At 
present the electrodes are made of gas graphite, a modification of 
charcoal deposited in gas retorts; this is hard and compact, and only 
burns slowly in air: hence it is unnecessary to operate in vacuo. 
When the experiment is made in vacuo, there is no combustion, but 
the charcoal wears away at the positive pole, while it is somewhat 
increased on the negative pole, indicating that there is a transport of 
solid matter from the positive to the negative pole. 

719. Foucault’s experiment. —This consists in projecting on a 
screen the image of the charcoal points produced in the camera obscura 
at the moment at which the electric light is formed (fig. 545). By 
means of this experiment, which is made by the photoelectric micro¬ 
scope, already described (fig. 392, page 487), the two charcoals can be 
readily distinguished, and the positive charcoal is seen to become some¬ 
what hollow and diminish, while the other increases. The globules 
represented on the two charcoals .arise from the fusion of a small 
quantity of silica contained in the charcoal. When the current begins 














THE ELECTRIC LIGHT. 


689 


- 720 ] 

to pass, the negative charcoal first becomes luminous, hut the light of 
the positive charcoal is the brightest; as it also wears away the most 
rapidly, it ought to he rather the larger. 

720. Regulator of the electric light. —When the electric light 
is to be used for illumination, it must be as continuous as other modes 
of lighting. For this purpose, not only must the current be constant, 
but the distance of the charcoals must not alter, which necessitates the 
use of some arrangement for bringing them nearer together in proportion 
as they wear away. One of the best modes of effecting this is by an 
apparatus invented by M. Duboscq. 

In this regulator the two charcoals are moveable, but with unequal 
velocities, which are virtually proportional to their waste. The motion 
is transmitted by a drum placed on the axis, xy (fig. 546). This turns 
in the direction of the arrows two wheels, a and b, the diameters of 
which are as 1 : 2, and which respectively transmit their motion to 
two rack-works, C' and C. C lowers the positive charcoal, p, by 
means of a rod sliding in the tube, H, while the other C' raises the 
negative charcoal, n, twice as rapidly. By means of the milled head, 
y , the drum can be wound up, and at the same time the positive char¬ 
coal moved by the hand; the milled head, x, moves the negative 
charcoal also by the hand, and independently of the first. For this 
purpose the axis, xy, consists of two parts pressing against each other 
with some force, so that holding the milled head, x, between the fingers, 
the other, y, may be moved, and by holding the latter the former can be 
moved. But the friction is sufficient when the drum works to move 
the two wheels a and b and the two rack-works. 

The two charcoals being placed in contact, the current of a powerful 
battery of 40 to 50 elements reaches the apparatus by means of the 
wires, E and E'. The current rising in H, descends by the positive 
charcoal, then by the negative charcoal, and reaches the apparatus, but 
without passing into the rackwork, C, or into the part on the right of 
the plate, N; these pieces being insulated by ivory discs placed at their 
lower part. The current ultimately reaches the bobbin B, which forms 
the foot of the regulator, and passes into the wire, E'. Inside the 
bobbin is a bar of soft iron, which is magnetised as long as the current 
passes in the bobbin, and demagnetised when it does not pass, and this 
temporary magnet is the regulator. For this purpose it acts attractively 
on an armature of soft iron, A, open in the centre so as to allow the 
rackwork O' to pass, and fixed at the end of a lever, which works on 
two points, mm, and transmits a slight oscillation to a rod, d, which, by 
means of a catch, i, seizes the wheel z , as is seen on a larger scale in 
figure 547. By an endless screw, and a series of toothed wheels, the 
stop is transmitted to the drum, and the rackwork being fixed, the same 


690 


DYNAMICAL ELECTRICITY. 



[ 720 - 

is the case with the carbons. This is what takes place so long as the 
magnetisation in the bobbin is strong enough to keep down the arma¬ 
ture, A: but in proportion as the carbons wear away, the current 
becomes feebler, though the voltaic arc continues, so that ultimately 


the attraction of the magnet no longer counterbalances a spring, r, 
which continually tends to raise the armature. It then ascends, the 
piece d disengages the stop i, the drum works, and the carbons come, 
nearer; they do not, however, touch, because the intensity of the 
current gains the upper hand, the armature A is attracted, and the 


Fig. 546. 

























THE ELECTRIC LIGHT. 


691 


- 721 ] 

carbons remain fixed. As their distance only varies within very narrow 
limits, a regular and continuous light is obtained with this apparatus 
until the carbons are quite used. 

By means of this regulator, M. Duboscq illuminates the photogenic 
apparatus represented fig. 392, by which all the optical experiments may 
be performed for which solar light was formerly necessary. 

721. Properties and intensity of the electric light. —The electric 
light has similar chemical properties to solar light; it effects the 
combination of chlorine and hydrogen, acts chemically on chloride of 
silver, and applied to photography gives fine impressions, remarkable 
for the warmth of the tones; it is, however, inapplicable for taking 
portraits, as it fatigues the sight too greatly. 

Passed through a prism, the electric light, like the sun, is decomposed 
and gives a spectrum. Wollaston, and more especially Fraunhofer, have 
found that the spectrum of the electric light differs from that of other 
lights and of the sunlight by the presence of several very bright lines, 
one of which more especially is of almost dazzling brilliancy as compared 
with the rest of the spectrum. Wheatstone has found that by using 
electrodes of different metals, the spectrum and the lines are modified. 
According to Despretz the bright lines are fixed, and independent of the 
intensity of the current. 

Masson has recently studied the electric light in great detail, and has 
experimented upon the light of the electric machine, that of the voltaic 
arc, and that of Ituhmkorff’s coil. He has found the same colours in 
the electric spectrum as in the solar spectrum, but traversed by very 
brilliant luminous bands of the same shade as that of the colour in 
which they occur. The number and position of these bands do not 
depend on the intensity of the light, but, as we have seen, upon the 
substances between which the voltaic arc is formed. 

With carbon the lines are remarkable for their number and brilliancy; 
with zinc the spectrum is characterised by a very marked apple-green 
tint; silver produces a very intense green ; with lead a violet tint pre¬ 
dominates, and so oh with other metals. 

Bunsen, in experimenting with 48 couples, and removing the charcoals 
to a distance of a quarter of an inch, has found that the intensity of the 
electric light is equal to that of 572 candles. 

Fizeau and Foucault have compared the chemical effects of the solar 
and the electric lights, by investigating their action on iodized silver 
plates. Representing the intensity of the sunlight at mid-day at 1000, 
these physicists found that that of 46 Bunsen’s elements was 235, while 
that of 80 elements was only 238. It follows that the intensity does 
not increase to any material extent with the number of the couples; but 
experiment shows that it increases considerably with their surface. For 


692 


DYNAMICAL ELECTRICITY. 


[ 722 - 

with a battery of 46 elements, each consisting of 3 elements, with their 
zinc and copper respectively united so as to form one element of triple 
surface (715), the intensity was 385, the battery working for an hour; 
that is to say, more than a third of the intensity of the solar light. 

Despretz observes that too great precautions cannot be taken against 
the effects of the electric light when they attain a certain intensity. 
The light of 100 couples, he says, may produce very painful affections of 
the eyes. With 600, a single moment’s exposure to the light is suffi¬ 
cient to produce very violent headaches and pains in the eye, and the 
whole frame is affected as by a powerful sunstroke. 

Mr. Way has obtained a very bright light by passing the electric 
current along a stream of mercury. The light is produced by the incan¬ 
descence of the mercury vapour, it has a somewhat flickering character, 
and a greenish tinge. 

Attempts have been made to apply the electric light to the illu¬ 
mination of rooms, and even of streets; but partly the cost, and partly the 
difficulty of producing with it a uniform illumination, inasmuch as the 
shadows are thrown into too sharp relief, have hitherto been great 
obstacles to its use. Yet it is advantageously applied in special cases, 
such as the photoelectric microscope, illuminations in theatres, etc. 

722. Mechanical effects of the battery.— Under this head may 
be included the motion of solids and liquids effected by the current. An 
example of the former is found in the voltaic arc, in which there is a 
passage of the molecules of carbon from the positive to the negative pole 
(718). 

To the mechanical effects of the battery some physicists have referred 
the following experiment, due to Porret. Having divided a glass vessel 
into two compartments by a porous diaphragm consisting of bladder, he 
poured water into the two compartments to the same height, and im¬ 
mersed two electrodes of platinum in connection with a battery of 80 
elements. As the water became decomposed, part of the liquid was 
carried in the direction of the current, through the diaphragm, from the 
positive to the negative compartment, where the level rose above that 
in the other compartment. A solution of blue vitriol is best for these 
experiments, because then the disturbing influence of the disengagement 
of gas at the negative electrode is avoided. 

According to Wertheim, the elasticity of metallic wires is diminished 
by the current, and not by the heat alone, but by the electricity: he 
has also found that the cohesion is diminished by the passage of a 
current. 

To the mechanical effects of the current may be assigned the sounds 
produced in soft iron when submitted to the magnetic action of a dis¬ 
continuous current, a phenomenon which will be subsequently described. 


CHEMICAL EFFECTS. 


693 


- 724 ] 



Fig. 548. 


723. Chemical effects.— -These are among the most important of 
all the actions, either of the simple or compound circuit. The first 
decomposition effected by the 

battery was that of water, 
obtained in 1800 by Carlisle 
and Nicholson by means of 
a voltaic pile. Water is 
rapidly decomposed by 4 or 5 
Bunsen’s cells; the apparatus 
(fig. 548) is very convenient 
for the purpose. It consists 
of a glass vessel fixed on a 
wooden base. In the bottom 
of the vessel two platinum 
electrodes, p and n, are fitted, 
communicating by means of 
copper wires with the binding screws. The vessel is filled with water 
to which some sulphuric acid has been added to increase its conductivity, 
for pure water is a very imperfect conductor; two glass tubes filled with 
water are inverted over the electrodes, and on interposing the apparatus 
in the circuit of a battery a decomposition is rapidly set up, and gas 
bubbles rise from the surface of each pole. The volume of gas liberated 
at the negative pole is about double that at the positive, and on exa¬ 
mination the former gas is found to be hydrogen and the latter gas 
oxygen. This experiment accordingly gives at once the qualitative and 
quantitative analysis of water. 

724. Electrolysis. —To those substances which, like water, are re¬ 
solved into their elements by the voltaic current, the term electrolyte has 
been applied by Faraday, to whom the principal discoveries in this 
subject and the nomenclature are due. Electrolysis is the decomposition 
by the voltaic battery; the positive electrode is called the anode, and 
the negative electrode the kathode. The products of decomposition are 
iones ; katione , that which appears at the kathode, and anione , that which 
appears at the anode. 

By means of the battery, the compound nature of several substances 
which had previously been considered as elements has been determined. 
By means of a battery of 250 couples, Davy, shortly after the discovery 
of the decomposition of water, succeeded in decomposing the alkalies 
potass and soda, and proved that they were the oxides of the hitherto 
unknown metals potassium and sodium. The decomposition of potass 
may be demonstrated with the aid of the battery of 4 to 6 elements in the 
following manner: a small cavity is made in a piece of solid caustic 
potass, which is moistened, and a drop of mercury placed in it. The 

















694 


DYNAMICAL ELECTRICITY. 


[ 725 - 


potass is placed on a piece of platinum connected with the positive pole 
of the battery. The mercury is then touched with the negative pole. 
When the current passes, the potass is decomposed, oxygen is liberated 
at the positive pole, while the potassium liberated at the negative pole 
amalgamates with the mercury. On distilling this amalgam out of 
contact with air, the mercury passes off, leaving the potassium. 

The decomposition of binary compounds, that is, bodies containing 
two elements, is quite analogous to that of water and of potass; one of 
the elements goes to the positive, and the other to the negative pole. 
The bodies separated at the positive pole are called electronegative elements, 
because at the moment of separation they are considered to be charged 
with negative electricity, while those separated at the negative pole 
are called electropositive elements. One and the same body may be 
electronegative or electropositive, according to the body with which it is 
associated. For instance, sulphur is electronegative towards hydrogen, 
but is electropositive towards oxygen. The various elements may be 

arranged in such a series that any one in 
combination is electronegative to any fol¬ 
lowing, but electropositive towards all 
preceding ones. This is called the electro - 
chemical series , and begins with oxygen as 
the most electronegative element, termina¬ 
ting with potassium as the most electro¬ 
positive. 

The decomposition of hydrochloric acid 
MU into its constituents, chlorine and hydrogen, 
may be shown by means of the apparatus 
represented in fig. 549. Carbon electrodes 
must, however, be substituted for those 



Fig. 549. 


of platinum, which is attacked by the liberated chlorine ; a quantity 
of salt also must be added to the hydrochloric acid, in order to diminish 
the solubility of the liberated chlorine. The decomposition of iodide 
of potassium may be demonstrated by means of a single element. 
For this purpose a piece of bibulous paper is soaked with a solution 
of starch, to which iodide of potassium is added. On touching this paper 
with the electrodes a blue spot is produced at the positive pole, due 
to the action of the liberated iodine on the starch. 

725. Decomposition of salts. —Ternary salts in solution are de¬ 
composed by the battery, and then present effects varying with the 
chemical affinities, and the intensity of the current. In all cases the 
acid, or the body which is chemically equivalent to it, is electronegative 
in its action towards the other constituent. The decomposition of salts 
may be readily shown by means of the bent tube represented in fig. 549. 







CHEMICAL EFFECTS. 


695 


-726] 

This is nearly tilled with a saturated solution of a salt, say sulphate 
of sodium, coloured with tincture of violets. The platinum electrodes of 
a battery of four Bunsen’s elements are then placed in the two legs of 
the tube. After a few minutes the liquid in the positive leg, A, becomes 
of a red, and that in the negative leg, B, of a green colour, showing that 
the salt has been resolved into acid which has passed to the positive, and 
into base which has gone to the negative pole, for these are the 
effects which a free acid and a free base respectively produce on tincture 
of violets. 

In a solution of sulphate of copper, free acid and oxygen gas appear at 
the positive electrode, and metallic copper is deposited at the negative 
electrode. In like manner, with nitrate of silver, metallic silver is de¬ 
posited on the negative, while free acid and oxygen appear at the positive 
electrode. 

This decomposition of salts was formerly explained by saying that the 
add was liberated at the positive electrode and the base at the negative. Thus 
sulphate of potassium, K 2 0S0 3 , was considered to be resolved into sulphuric 
acid, S0 3 , and potass, K 3 0. This view regarded salts composed of three 
elements as different in their constitution from binary or haloid salts. 
Their electrolytic department has led to a mode of regarding the 
onstitution of salts, which brings all classes of them under one 
category. In sulphate of potassium, for instance, the electropositive 
element is potassium, while the electronegative element is a complex of 
sulphur and oxygen, which is regarded as a single group, S0 4 , and to 
which the name oxy-sulphion may be assigned. The formula of sulphate 
or potass would thus be K 2 S0 4 , and its decomposition would be quite 
analogous to that of chloride of potassium, KC1, chloride of lead, PbCl 2 , 
iodide of potassium, KI. The electronegative group S0 4 corresponds to 
chlorine or iodine. In the decomposition of sulphate of potassium the 
potassium liberated at the negative pole decomposes water, forming 
potass and liberating hydrogen. In like manner the electronegative 
constituent S0 4 , which cannot exist in the free state, decomposes into 
oxygen gas, which is liberated, and into anhydrous sulphuric acid, S0 3 , 
which immediately combines with water to form ordinary sulphuric acid 
H 2 S0 4 . In fact, where the action of the battery is strong these gases are 
liberated at the corresponding poles ; in other pases they combine in the 
liquid itself, reproducing water. The constitution of sulphate of copper, 
CuS0 4 , and of nitrate of silver, AgN0 3 , and their decomposition, will be 
readily understood from these examples. 

726. Transmissions effected by the current.— In chemical decom¬ 
positions effected by the battery there is not merely a separation of the 
elements, but a passage of the one to the positive, and of the other to the 
negative electrode. This phenomenon has been demonstrated by Davy 


DYNAMICAL ELECTRICITY. 


696 


[727- 


by means of several experiments, of which the two following are 
examples : 

i. He placed solution of sulphate of sodium in two capsules connected 
by a thread of asbestos moistened with the same solution, and immersed 
the positive electrode in one of the capsules, and the negative electrode 
in the other. The salt was decomposed, and at the expiration of some 
time all the sulphuric acid was found in the first capsule, and the soda in 
the second. 

ii. Having taken three glasses, A, B, and C, he poured into the first, 
solution of sulphate of sodium, into the second, dilute syrup of violets, 
and into the third pure water, and connected them by moistened threads 
of asbestos. The current was then passed in the direction from C 
to A. The sulphate in the vessel A was decomposed, and in the course 
of time there was nothing but soda in this glass, which formed the 
negative end, while all the acid had been transported to the glass C, 
which was positive. If, on the contrary, the currents passed from A to C, 
the soda was found in C, while all the acid remained in A ; but in both 

cases the remarkable phe¬ 
nomenon was seen that the 
syrup of violets in B neither 
became red nor green by the 
passage of the acid or base 
through its mass, a pheno¬ 
menon the explanation of 
which is based on the 
Fig. 550. hypothesis enunciated in 

the following paragraph. 

727. Grotthuss’s hypothesis. —Grotthiiss has given the following 
explanation of the chemical decompositions effected by the battery. 
Adopting the hypothesis that in every binary compound or body which 
acts as such, one of the elements is electropositive, and the other electro¬ 
negative, he assumes that under the influence of the contrary electricities 
of the electrodes, there is effected in the liquid in which thev are 
immersed, a series of successive decompositions and recompositions from 

one pole to the other. Hence 
it is only the elements of the 
terminal molecules which do 
not recombine, and remain¬ 
ing free appear at the elec- 
Fl g- 55L trodes. Water, for instance, 

is formed of one atom of oxygen and two atoms of hydrogen, the first 
gas being electronegative, and the second electropositive. Hence when 
the liquid is traversed by a sufficiently powerful current, the molecule 









ELECTROLYSIS. 


697 


- 728 ] 

a in contact with the positive pole arranges itself as shown in fig. 552, 
that is, the oxygen is attracted and the hydrogen repelled. The oxygen 
of this molecule is then given oft’ at the positive electrode, the liberated 
hydrogen immediately unites with the oxygen of the molecule b, 
the hydrogen of this with the oxygen of the molecule c, and so on, 
to the negative electrode, where the last atoms of hydrogen become free 
and appear on the poles. The same theory applies to the metallic 
oxides, to the acids and salts, and explains why in the experiment 
mentioned in the preceding paragraph, the syrup of violets in the vessel 
B becomes neither red nor green. The reason why, in the fundamental 
experiment, the hydrogen is given off at the negative pole when the 
circuit is closed will he readily understood from a consideration of this 
hypothesis. 

728. Laws of electrolysis. —The laws of electrolysis were discovered 
by Faraday ; the most important of them are as follows : 

I. Electrolysis cannot take place unless the electrolyte is a conductor. 
Hence ice is not decomposed by the battery, because it is a bad conductor. 
Other bodies, such as oxide of lead, chloride of silver, etc., are only 
electrolysed in a fused state, that is, when they can conduct the current. 

n. The electrolytic action of the current is the same in all its parts. 

III. The same quantity of electricity—that is , the same electric current 
—decomposes chemically equivalent quantities of all the bodies which it 
traverses; from which it follows, that the weiyhts of ele?nents separated in 
these electrolytes are to each other as their chemical equivalents. 

If an apparatus for decomposing water (fig. 548) and various U-shaped 
tubes containing respectively fused oxide of lead and chloride of tin are 
interposed in the same voltaic current, which must be sufficiently 
powerful, these substances will be decomposed ; the electro-negative 
elements will be separated at the positive, and the electropositive at the 
negative poles. The quantities of substances liberated are in a certain 
definite relation. Thus for every 18 parts of water decomposed in the 
voltameter there will be liberated 2 parts of hydrogen, 207 parts of lead, 
and 117 of tin at the respective negative electrodes, and 16 parts of 
oxygen, and 71 (or 2 X 35*5) parts of chloride at the corresponding positive 
electrodes. Now these numbers are exactly as the equivalents (not as 
the atomic weights) of the bodies. 

It will further be found, that in each of the cells of the battery 65 
parts of .zinc have been dissolved, for every two parts by weight of 
hydrogen liberated; that is, that for every equivalent of a substance 
decomposed in the circuit one equivalent of zinc is dissolved; and 
this is the case whatever be the number of cells. An increase in the 
number only has the effect of overcoming the great resistance which 

H H 




698 DYNAMICAL ELECTRICITY. [ 729 - 

many electrolytes offer, and of accelerating tlie decomposition. It does 
not increase the quantity of the electrolyte decomposed. 

IV. It follows from the above law, that the quantity of a body decom¬ 
posed in a given time is proportional to the intensity of the current. On this 
is founded the use of Faraday’s voltameter, in which the intensity of a 
current is ascertained from the quantity of water which it decomposes in 
a given time. It consists of a glass vessel, in which two platinum elec¬ 
trodes are fixed. In the neck of a vessel a bent delivery tube is fitted, 
and the mixed gases are collected in a graduated cylinder, so that their 
volume can be determined, which, reduced to a constant temperature and 
pressure, is a measure of their quantity. 

The use of this voltameter appears simple and convenient; and hence 
some physicists have proposed as unit of the intensity of the current, 
that intensity which in one minute yields a cubic centimeter of mixed 
gas reduced to the temperature 0° and the pressure 760mm. But there 
are several objections to the use of the voltameter. In the first place it 
does not indicate the intensity at any given moment, for in order to 
obtain measurable quantities of gas the current must be continued some 
time. Again, the voltameter gives no indications of the changes which 
take place in this time, but only shows the mean intensity. Moreover 
the voltameter itself offers a very considerable resistance, and can only 
be used in the case of strong currents; for feeble currents either do not 
decompose water, or only yield quantities of gas too small for accurate 
measurement. In addition to this the indications of the voltameter 
depend not only on the intensity of the current, but on the acidity of the 
water, and the distance and size of the electrodes. 

The silver voltameter is an instrument for measuring the intensity of the 
current, from the weight of metallic silver deposited in a given time from 
a solution of nitrate of silver of known strength. 

The current from the electrical machine, which is of very high intensity, 
is capable of traversing any electrolyte, but the quantity which it can 
decompose is extremely small as compared even with the smallest voltaic 
apparatus, and it must be concluded that the quantity developed by the 
frictional machine is very small as compared with that developed by che¬ 
mical action. 

729. Polarisation.— When platinum electrodes, which have been used 
in decomposing water, are detached from the battery, immersed in 
distilled water, and connected with a galvanometer, the existence of a 
current is indicated which has the opposite direction to that which had 
previously passed. This phenomenon is explained by supposing that 
oxygen has been condensed on the surface of the positive plate, and 
hydrogen on the surface of the negative plate, analogous to what has 
been already seen in the case of the nonconstant batteries (698). The 


grove’s gas battery. 


699 


-731] 

effect of this is to produce two different electromotors, which produce a 
current opposed in direction to the original one. and which, therefore, 
must weaken it. 

On this principle batteries may he constructed of pieces of metal of the 
same kind—for instance, platinum—which otherwise give no current. A 
piece of moistened cloth is interposed between each pair, and each end of 
this system is connected with the poles of a battery. After some time 
the apparatus has received a charge, and if separated from the battery 
can itself produce all the effects of a voltaic battery. Such batteries are 
called secondary batteries. Their action depends on an alteration of the 
surface of the metal produced by the electric current; the constituents of 
the liquid with which the cloth is moistened having become accumulated 
on the opposite members of the circuit. 

A dry pile which has become inactive may be used as a secondary 
battery. When a current is passed through it, in a direction contrary to 
that which the active battery yields, it then regains its activity. 

730. Grove’s gas battery.— On the property which metals have, of 
condensing gases on their surfaces, Grove has constructed his gas battery. 
In its simplest form it consists of two glass tubes, in each of which is 
fused a platinum electrode, provided on the outside with binding screws. 
In order to expose a greater surface these electrodes are covered with 
finely divided platinum. One of the tubes is partially filled with hydro¬ 
gen, and the other partially with oxygen, and they are inverted over 
dilute sulphuric acid, so that half the platinum is in the liquid and half 
in gas. On connecting the electrodes with a galvanometer the existence 
of a current is indicated, whose direction in the connecting wire is from 
the platinum in oxygen to that in hydrogen; so that the latter is positive 
towards the former. As the current passes through water this is decom¬ 
posed ; oxygen is separated at the positive plate, and hydrogen at the 
other. These gases unite with the gases condensed on their surface, so 
that the volume of gas in the tubes gradually diminishes, but in the ratio 
of one volume of oxygen to two volumes of hydrogen. These elements 
can be formed into a battery by joining the dissimilar plates with one 
another just as they are joined in an ordinary battery. One element of 
such a battery is sufficient to decompose iodide of potassium, and four will 
decompose water. 

731. Passive state of iron.— With polarisation is probably connected 
a very remarkable chemical phenomenon, which many metals exhibit, 
but more especially iron. When this is placed in contact with platinum 
wire and immersed in concentrated nitric acid it is unattacked, while the 
iron alone would be dissolved by the acid. This condition of iron is called 
the passive state , and upon it depends the possibility of the zinc-iron bat¬ 
tery (702). It is probable that in the above experiment a thin superficial 

h h 2 


DYNAMICAL ELECTRICITY. 


700 


[ 732 - 


layer of sesquioxide of iron is formed, which is then negative towards 
platinum. 

732. Nobili’s ring's.— When a drop of acetate of copper is placed on 
a silver plate, and the silver touched in the middle of the drop with a 
piece of zinc, there are formed around the point of contact a series of 
copper rings alternately dark and light. These are Noblit’s coloured rings. 
They may be obtained in beautiful iridescent colours by the following 
process: A solution of oxide of lead in potash is obtained by boiling 
finely powdered litharge in a solution of potash. In this solution is im¬ 
mersed a polished plate of silver or of German silver, which is connected 
with the positive electrode of a battery of eight Bunsen’s elements. With 
the negative pole is connected a fine platinum wire fused in glass, so that 
only its point projects; and this is placed in the liquid at a small distance 
from the plate. Around this point binoxide of lead is separated on the 
plate in very thin concentric layers, the thickness of which decreases from 
the middle. They show the same series of colours as Newton’s coloured 
rings in transmitted light. The binoxide of lead owes its origin to a 
secondary decomposition ; by the passage of the current some oxide of 
lead is decomposed into lead, which is deposited at the negative pole, and 
oxygen which is liberated at the positive, and this oxygen combines with 
some oxide of lead to form binoxide, which is deposited on the positive 
pole as the decomposition proceeds. 

733. Arbor Saturn! or lead tree. Arbor X>ianae.— When, in a 
solution of a salt, is immersed a metal which is more oxidisable than the 
metal of the salt, the latter is precipitated by the former, while the im¬ 
mersed metal is substituted equivalent for equivalent for the metal of the 
salt. This precipitation of one metal by another is partly attributable to 
the affinities, and partly to the action of a current which is set up as soon 
as a portion of the less oxidisable metal has been deposited. The action 
is promoted by the presence of excess of acid in the solution. 

A remarkable instance of the precipitation of one metal by another is 
the arbor Saiumi. This name is given to a series of brilliant ramifica¬ 
tions obtained by zinc in solutions of acetate of lead. A glass flask is 
filled with a clear solution of this salt, and the vessel closed with a 
cork, to which is fixed a piece of zinc in contact with some brass wires. 
The flask being closed is left to itself. At the expiration of a few days 
brilliant laminae of metallic lead are deposited on the brass wires, closely 
resembling vegetation, from which the old alchemical name is derived. 
For the same reason the name arbor Diance has been given to the metallic 
deposit produced in a similar manner by mercury in a solution of nitrate 
of silver. 


-734] 


ELECTROMETALLURGY. 


701 


ELECTROMETALLURGY. 

734. Electrometallurgy. —The decomposition of salts by the battery 
has received a most important application in electrometallurgy , or the art of 
precipitating metals from their solutions by the slow action of a galvanic 
current. This art was discovered independently by Spencer in England, 
and by Jacobi in Petersburgh. 

In order to reproduce a medal or any other object by this process a 
hollow cast must first be made, on which is deposited the metallic layer, 
which reproduces the metal in relief. If the medal is of metal the 
simplest way to form the cast is to use Arcet’s fusible alloy, which con¬ 
sists of 5 parts of lead, 8 of bismuth, and 3 of tin. Some of the melted 
alloy is poured into a shallow box, and just as it begins to solidify the 
medal is placed horizontally on it in a fixed position. When the alloy has 
become cool a slight shock is sufficient to detach the medal. A copper 
wire is then bound round the edge of the mould, by which it can be con¬ 
nected with the negative electrode of the battery, and then the edge and 
the posterior surface are covered with a thin non-conducting layer of wax, 
so that the deposit is only formed on the mould itself. 

In order to take a copper cast, a bath is filled with saturated solution 
of sulphate of copper, and two copper rods, B and D, stretched across 
(fig. 552) : one connected with the negative and the other with the 
positive pole of a Daniell’s or Grove’s element. From the rod connected 



Fig. 552 . 

with, the negative pole is suspended the mould m, and from the other a 
plate of copper, C. The current being thus closed, the sulphate of 
copper is decomposed, acid is liberated at the positive pole, while copper 
is deposited at the negative’pole on the mould suspended from the rod, 
B, t>o which indeed several moulds may be attached. At the expiration 
of 48 hours the mould is covered with a non-adherent, solid, resisting 
















702 


DYNAMICAL ELECTRICITY. 


[ 735 - 

layer of copper. In order completely to avoid adherence the mould 
ought previously to immersion to be brushed with a fine brush passed 
very lightly over a fatty body, or rapidly passed through a smoky flame, 
so as to form a very slight deposit of solid matter. 

If the cast to be reproduced is of plaster, Arcet’s alloy cannot be 
used. It must first be immersed in a bath of melted stearine, and with¬ 
drawn quickly; when withdrawn it dries almost immediately, which 
arises from a penetration of stearine into the pores of the plaster. 
When cooled it is coated with graphite, or black lead, which is rubbed 
with a brush ; a band of cartridge paper is then affixed round the edge, 
and some melted stearine is poured upon it; on cooling this gives a 
hollow cast of the original medal. This is prevented from adhering to 
the plaster by the layer of graphite; it is removed and covered with 
graphite in order to make it conduct. The mould thus prepared is 
suspended, as in the previous case, from the negative pole of the battery. 

Gutta-percha also gives very sharp moulds. The object of which the 
cast is to be taken is coated with a layer of graphite to prevent ad¬ 
herence, and then a quantity of gutta-percha having been placed in hot 
water until it is quite soft, is pressed against the object to be copied. 
On detaching the gutta-percha a very faithful hollow cast of the object 
is obtained. This cast is covered with graphite in order to make it con¬ 
duct ; being connected with the negative pole it is then suspended in a 
concentrated solution of sulphate of copper, and in about 48 hours a 
copper copy of the original object is obtained. 

The copper plate suspended from the positive pole serves a double pur¬ 
pose ; it not only closes the current, but it keeps the solution in a state of 
concentration, for the acid liberated at the positive pole dissolves the cop¬ 
per, and reproduces a quantity of sulphate of copper equal to that decom¬ 
posed by the current. 

735. Electrogilding-. —The old method of gilding was by means of 
mercury. It was effected by an amalgam of gold and mercury, which 
was applied on the metal to be gilt. The objects thus covered were 
heated in a furnace, the mercury volatilised, and the gold remained in 
a very thin layer on the objects. The same process was used for silver¬ 
ing ; but they were expensive and unhealthy methods, and have now 
been entirely replaced by electrogilding and electrosilvering. Electro¬ 
gilding only differs from the process described in the previous paragraph 
in_that the layer is thinner and adheres more firmly. Brugnatelli, a 
pupil of Volta, appears to have been the first, in 1803, to observe that a 
body could be gilt by means of the battery and an alkaline solution of 
gold; but M. de la Rive was the first who really used the battery in 
gilding. The methods both of gilding and silvering owe their present 


- 736 ] ELECTROGILDING. 703 

high state of perfection principally to the improvements of Elkington, 
Ruolz, and other physicists. 

The pieces to be gilt have to undergo three processes before gilding. 

The first; consists in heating them so as to remove the fatty matter 
which has adhered to them in previous processes. 

As the objects to be gilt are usually of copper, and their surface 
during the operation of heating becomes covered with a layer of sub¬ 
oxide or of protoxide of copper, this is removed by the second operation. 
For this purpose the objects, while still hot, are immersed in very dilute 
nitric acid, where they remain until the oxide is removed. They are 
then rubbed with a hard brush, washed in distilled water, and dried in 
gently heated sawdust. 

To remove all spots they must undergo the third process, which con¬ 
sists in rapidly immersing them in ordinary nitric acid, and then in a 
mixture of nitric acid, bay salt, and soot. 

When thus prepared the objects are attached to the negative pole of 
a battery, consisting of three or four Bunsen’s or Daniell’s elements. 
They are then immersed in a bath of gold, as previously described. 
They remain in the bath for a time which depends on the thickness of 
the desired deposit. There is great difference in the composition of the 
baths. That most in use consists of 1 grain of chloride of gold, 10 
grains of cyanide of potassium, dissolved in 200 grains of water. In 
order to keep the bath in a state of concentration, a piece of gold is 
suspended from the positive electrode, which dissolves in proportion as 
the gold dissolved in the bath is deposited on the objects attached to the 
negative pole. 

The method which has just been described can not only be used for 
gilding copper, but also for silver, bronze, brass, German silver, etc. 
But other metals, such as iron, steel, zinc, tin, and lead, are very difficult 
to gild well. To obtain a good coating they must first be covered with 
a layer of copper by means of the battery and a bath of sulphate of 
copper ; the copper with which they are coated is then gilded, as in the 
previous case. 

736. Electrosilvering’. —What has been said about gilding applies 
exactly to the process of electrosilvering. The difference is in the com¬ 
position of the bath, which consists of two parts of cyanide of silver, and 
two parts of cyanide of potassium dissolved in 250 parts of water. To 
the positive electrode is suspended a plate of silver, which prevents the 
bath from becoming poorer : the pieces to be silvered, which must be 
well cleaned, are attached to the negative pole. 


704 


DYNAMICAL ELECTRICITY. 


[ 737 - 


CHAPTER IV. 

ELECTRODYNAMICS. ATTRACTIONS AND REPULSIONS OF CURRENTS BY 

CURRENTS. 

737. Electrodynamics. —Under electrodynamics is understood the 
laws of electricity in a state of motion, or the action of electric currents 
upon each other and upon magnets, while electrostatics deals with the 
laws of electricity in a state of rest. 

The action of one electrical current upon another was first investi¬ 
gated by Ampere, shortly after the discovery of Oersted’s celebrated 
fundamental experiment (711). All the phenomena, even the most 
complicated, follow from two simple laws, just as the theorems of 
geometry from the axioms. These laws are— 

I. Two currents which are 'parallel , and in the same direction , attract 
one another. 

II. Tivo currents parallel , but in contrary directions , repel one 
another. 

In order to demonstrate these laws, the circuit which the current 
traverses must consist of two parts, one fixed and the other moveable, 
as shown in fig. 553. The fixed part consists of two brass uprights 
fastened on a wooden base. The positive electrode of a Bunsen’s battery 
of four or five elements being connected with the foot of the column on 



Fig. 553. 

the left of the figure, the current rises in this column, reaches the wire 
A, and then passes into a mercury cup, B. Here commences the moveable 
part of the circuit, which consists of a copper wire ; one end rests in the 





















ELECTRODYNAMICS. 


705 


- 738 ] 

cup B by means of a pivot, and the other dips in the second cup C, from 
which the current rises in the column on the right, which is connected 
at the top with the negative electrode of the battery. 

From the arrangement of the arrows it will be seen that the current 
flows in opposite directions in the fixed and 
in the moveable part. Now, when the latter 
is placed in the plane of the columns, as soon 
as the current is transmitted, the moveable 
part is repelled, rotating on its axis, BC, which 
proves the second law. 

To demonstrate the first law the moveable 
part of fig. 553 is removed and replaced by 
that represented in fig. 554. The current is 
then in the same direction both in the 
columns and in the moveable part; and when 
the latter is removed out of the plane of the columns, so long as the 
current passes it tends to return to it, proving that there is attraction 
between the two parts. 

738. Laws of angular currents. —I. Two rectilinear currents , the 
directions of which form an angle with each other, attract me another when 
both approach or recede from the apex of the angle. 

r 


Fig. 555. Fig. 556. 

II. They repel one another if one approaches and the other recedes from 
the apex of the angle. 

These two laws may be demonstrated by means of an apparatus 
(fig. 556) devised by M. De la Hive, which is a modification of one 

h h 3 




Fig. 554. 


































706 DYNAMICAL ELECTRICITY. [ 739 - 

invented by Ampere to show the actions of currents, and known as 
Ampere's stand. 

It consists of two brass columns fixed on a wooden base, and provided 
with horizontal arms, terminating in small mercury cups; on the base is 
a small wooden frame, on which are several windings of a stout insulated 
copper wire, through which the current passes; the object of multiplying 
the windings being to increase the action of the current on the moveable 
circuit PQ, which is astatic. The current enters by the foot of the column 
A, reaches the circuit PQ, which it traverses in the direction indicated by 
the arrows; it then returns by the columnB, reaches the multiplier, and 
emerges at C. The moveable circuit is at first so arranged that its plane 
makes an angle with that of the multiplier, and that the direction of the 
current is from the summit of the angle formed by the two wires. As soon 
as the current passes, the angle PQm diminishes, showing that the two 
currents attract each other. If, on the other hand, the wire MN (fig. 
555) be substituted for the wire PQ, the two currents being then in op¬ 
posite directions as regards the summit of the angle PQm, this angle in¬ 
creases ; an effect due to repulsion, and which consequently proves the 
second law. 

In a rectilinear current each element of the current repels the succeeding 
one, and is itself repelled. 

This is an important consequence of Ampere’s law, and may be ex¬ 
perimentally demonstrated by the following experiment, which was de¬ 
vised by Faraday. A U-shaped piece of copper wire, whose ends dip in 
two separate deep mercury cups, is suspended from one end of a delicate 
balance and suitably equipoised. When the mercury cups are connected 
with the two poles of a battery the wire rises very appreciably, and sinks 
again to its original position when the current ceases to pass. The current 
passes into the mercury and into the wire ; but from the construction of 
the apparatus the former is fixed, while the latter is moveable, and is ac¬ 
cordingly repelled. 

739. Laws of sinuous currents. — The action 
of a sinuous current is equal to that of a rectilinear 
current of the same length in projection. This prin¬ 
ciple is demonstrated by arranging a current mno, 
half sinuous and half rectilinear, near a moveable 
current ABCD (fig. 557). It will be seen that 
there is neither attraction nor repulsion, showing 
that the action of the sinuous portion mn is 
equalled by that of the rectilinear portion no. 

An application of this principle will presently 
be met with in the apparatus called solenoids , 
which are formed of the combination of a sinuous with a rectilinear current. 









- 740 ] 


DIRECTION OF CURRENTS BY CURRENTS. 


707 


DIRECTION OF CURRENTS BY CURRENTS. 

i 40. Action of an infinite current on a current perpendicular 
to its direction. — From the action exerted between two angular 
currents (738) the action of a fixed and infinite rectilinear current, PQ 
(fig. 558), on a moveable current, KH, perpendicular to its direction can 
be determined. Let OK be the perpendicular common to KH and PQ, 
which is null if the two lines PQ and KH meet. The current PQ 
flowing from Q to P in the direction of the arrows, let us first consider 
the case in which the current KH approaches the current QP. From 
the first law of angular currents (738) the portion QO of the current 


/V" 







o 

Fig. 558. 


_2 P 


0 

Fig. 559. 


PQ attracts the current KH because they both flow towards the summit 
of the angle formed by their directions. The portion PO, on the con¬ 
trary, will repel the current KH, for here the two currents are in opposite 
directions at the summit of the angle. If then mq and mp stand for 
the two forces, one attractive and the other repulsive, which act on the 
current KH, and which are necessarily of the same intensity, since they 
are symmetrically arranged in reference to the two sides of the point O, 
these two forces may be resolved into a single force, m», which tends 
to move the current KH parallel to the current QP, but in a contrary 
direction. 

On considering the case in which the current KH moves away from PQ 
(fig. 559) it will be readily seen from similar considerations that it moves 
parallel to this current, but in the same direction. 

Hence follows this general principle. A finite moveable current which 
approaches a fixed infinite current is acted on so as to move in a direction 
parallel and opposite to that of the fixed current; if the moveable current 
tends from the fixed current , it is acted on so as to move parallel to the 
current and in the same direction. 

It follows from this, that if a vertical current is moveable about an 
axis, XY, parallel to its direction (figs. 560 and 561), any horizontal 
current PQ, will have the effect of turning the moveable current about 







708 


DYNAMICAL ELECTRICITY. 


[ 741 - 


its axis, until the plane of the axis and of the current have become parallel 
to PQ ; the vertical current stopping, in reference to its axis, on the side 
from which the current PQ comes (fig. 560), or on the side towards which 






Pig. 560. 


Fig. 561. 


it is directed (fig. 561), according as the vertical current descends or ascends , 
that is, according as it approaches or moves from the horizontal axis. 

It also follows from this principle that a system of two vertical cur¬ 
rents rotating about a vertical axis (figs. 562 and 563) is directed by a 
horizontal current PQ in a plane parallel to this current, when one of the 



X 



X 



\ 



i 1 



I 

p 

Y 


Q p 

Y 


a 


Fig. 562. Fig. 563. 

vertical currents is ascending and the other descending (fig. 562), but 
that if they are both ascending or both descending (fig. 563) they are not 
directed. 

741. Action of an infinite rectilinear current on a rectan¬ 
gular or circular current.— It is easy to see that a horizontal infinite 
current exercises the same directive action on a rectangular current move- 
able about a vertical axis (fig. 564), as what has been above stated. 
For, from the direction of the currents indicated by the others, the part 
QY acts by attraction not only on the horizontal portion YD (law of 
angular currents ), but also on the vertical portion AD (law of perpendicu¬ 
lar currents). The same action evidently takes place between the part 
PY and the parts CY and BC. Hence, the fixed current PQ tends to 
direct the moveable rectangular current ABCD into a position parallel to PQ, 
and such that in the wires CD and PQ the direction of the two currents is the 
same. 


















ROTATION OF CURRENTS BY CURRENTS. 


709 


- 742 ] 

This principle is readily demonstrated by placing the circuit ABCD on 
the apparatus with two supports (fig. 556), so that at first it makes an 
angle with the plane of the supports. On passing below the circuit, a 
somewhat powerful current in the same plane as the supports, the move- 
able part passes into that plane. It is best to use the circuit in fig. 571, 
which is astatic, while that of fig. 564 is not. 



P 


Q 


Fig. 565. 



What has been said about the rectangular current in fig. 562 applies 
also to the circular current of fig. 565, and is demonstrated by the 
same experiments. 


ROTATION OF CURRENTS BY CURRENTS. 

742. Rotation of a finite horizontal current by an infinite 
horizontal rectangular current. — The attractions and repulsions 
which angular currents exert on one another may readily be transformed 
into a continuous circular motion. Let OA (fig. 566) be a current 



moveable about the point O in a horizontal plane, and let PQ be a fixed 
infinite current also horizontal. As these two currents flow in the 
direction of the arrows, it follows that in the position OA, the moveable 
current is attracted by the current PQ, for they are in the same direc¬ 
tion. Having reached the position OA' the moveable current is attracted 
















710 


DYNAMICAL ELECTRICITY. 


[ 743 - 

by the part NQ of the fixed current, and repelled by the part PN. 
Similarly in the position OA" it is attracted by MQ and repelled by PM, 
and so on; from which follows a continuous rotatory motion in the 
direction AA'A"A /// . If the moveable current, instead of being directed 
from 0 towards A, were directed from A towards O, it is easy to see that 
the rotation would take place in the contrary direction. Hence, by the 
action of a fixed infinite current, PQ, the moveable current OA tends 
to a continuous motion in a direction opposite that of the fixed current. 

If, both currents being horizontal, the fixed current were circular 
instead of being rectilinear, it is easily seen that its effect would still be 
to produce a continuous circular motion. For, let ABC (fig. 567) be a 
fixed circular current, and mn a rectilinear current moveable about the 
axis, n, both currents being horizontal. These currents, flowing in the 
direction of the arrows, would attract one another in the angle wAC, for 
they both flow towards the summit (738). In the angle wAB, on the 
contrary, they repel one another, for one goes towards the summit and 
the other moves from it. Both effects coincide in moving the wire mn 
in the same direction ACB. 

743. Rotation of a vertical current by a horizontal circular 
current. —A horizontal circular current, acting on a rectilinear vertical 
current, also imparts to it a continuous rotatory motion. In order to 
show this, the apparatus represented in fig. 668 is used. 



Fig. 568. 


It consists of a copper vessel, round which are rolled several coils of 
insulated copper wire, through which a current passes. In the centre of 
the vessel is a brass support, a, terminated by a small cup containing 
mercury. In this dips a pivot supporting a copper wire, bb, bent at its 
extremities in two vertical branches, which are soldered to a very light 
copper ring immersed in acidulated water contained in the vessel. The 
current of a battery entering through the wire m, reaches the wire A, and 
having made several circuits, terminates at B, which is connected by a 
wire underneath with the lower part of the column a. Ascending in 








- 744 ] ROTATION OF MAGNETS BY CURRENTS. 711 

this column, it passes by the wires bb into the copper ring, into the 
acidulated water, and into the sides of the vessel, whence it returns to 
the battery by the strip D. The current being thus closed, the circuit 
bb and the ring tend to turn in a direction contrary to that of the fixed 
current, a motion due to the action of the circular current on the current 
in the vertical branches bb ; for, as follows from the two laws of angular 
currents, the branch b on the right is attracted by the portion A of the 
fixed current, and the branch b on the left is attracted in the contrary 
direction by the opposite part, and these two motions coincide to give 
the ring a continuous rotatory motion in the same direction. The action 
of the circular current on the horizontal part of the circuit bb would 
manifestly tend to turn it in the same direction; but from its distance 
it may evidently be neglected. 

744. Rotation of magnets by currents* —Faraday has proved that 
currents impart the same rotatory motion to magnets which they do to 
currents. This may be shown by means of the apparatus represented in 



Fig. 569. Fig. 570. 


fig. 569. It consists of a large glass vessel, almost filled with mercury. 
In the centre of this is immersed a magnet about 8 inches in length, 
which projects a little above the surface of the mercury; it is loaded at 
its lower end with a platinum cylinder, represented at ab on the right of 
the apparatus. At the top t)f the magnet is a small copper cup contain¬ 
ing mercury; the current passes into this cup by the rod C. As soon as 
the current ascending in the column A, passes into the magnet, thence 
into the mercury, and emerges by the column D, the magnet begins to 
rotate round its own axis with a velocity depending on its magnetic 
power, and on the intensity of the current. 

This rotatory motion is readily intelligible on Ampere’s theory of 
magnetism, which will be subsequently explained (755), according to 

















712 


DYNAMICAL ELECTRICITY. 


[ 745 - 

which, magnets are traversed on their surface by an infinity of circular 
currents in the same direction, in planes perpendicular to the axis of 
the magnet. At the moment at which the current passes from the 
magnet into the mercury, it is divided on the surface of the mercury 
into an infinity of rectilinear currents proceeding from the axis of the 
magnet to the circumference of the glass. Now each of these currents 
acts on the currents of the magnet in the same manner as, in fig. 
567, the rectilinear current mn acts upon the circular current CAB; 
that is to say, that the circle CAB representing one of the currents 
of the magnet, there is attraction in the angle wAC, and repulsion in 
the angle wAB, and consequently rotation of the magnet round its 
axis. The action of the current merely affects the upper part of the 
magnet, and if the north pole is uppermost, as in the figure, the rota¬ 
tion is from west to east. If the north pole is below or the direction 
of the current be altered, the rotation of the magnet is in the opposite 
direction. 

Instead of making the magnet rotate on its axis, it may be caused to 
rotate round a line parallel to its axis by arranging the experiment as 
shown in fig. 570. 

ACTION OE THE EARTH AND OF MAGNETS ON CURRENTS. 

745. Directive action of magnets on currents. —Not only do 
currents act upon magnets, but magnets also act upon currents. In 
Oersted’s fundamental experiment (fig. 533), the magnet being move- 



able while the current is fixed, the former is directed and sets at right 
angles with the current. If, on the contrary, the magnet is fixed and 
















- 746 ] ACTION OF THE EARTH AND MAGNETS ON CURRENTS. 713 


the current moveable, the latter is directed and sets across the direction 
of the magnet. This may be illustrated by the apparatus represented in 
fig. 571. The circuit which the current traverses is moveable, and 
below its lower branch a powerful bar magnet is placed, the circuit 
immediately begins to turn, and stops after some oscillations in a plane 
perpendicular to the axis of the magnet. 

For demonstrating the action of magnets upon currents, and indeed 
for establishing the fundamental laws of electrodynamics, a small appa¬ 
ratus, known as De la Rive’s floating battery , is well adapted. It consists 
of a small Daniell’s element, contained in a glass tube attached to a 
cork, so that it can float freely on water. The plates are connected with 
minute mercury cups on the cork float; and with these can be connected 
either circular or rectangular wires, coils, or solenoids; and they are then 
traversed by a current, and can be subjected to the action either of magnets 
or of currents. 

746. Rotation of currents by magnets. —Not merely can currents be 
directed by magnets, but they may also be made to rotate, as is seen from the 
following experiment, devised by Faraday, 
fig. 572. On a base with levelling screws, 
and resting on an ivory support, is a copper 
rod BD. It is surmounted in part of its 
length by a magnetised bundle AB and at 
the top is a mercury cup. A copper circuit 
EF, balanced on a steel point, rests in the 
cup, and the other ends of the circuit, which 
terminate in steel points, dip in an annular 
reservoir full of mercury. 

The apparatus being thus arranged, the 
current from 4 or 5 Bunsen’s elements 
enters at the binding screw b; it thence 
ascends in the rod D, redescends by the two 
branches, reaches the mercury by the steel 
points, whence it passes by the framework, 
which is of copper, to the battery by the 
binding screw a. If now the magnetised 
bundle be raised, the circuit EF^ rotates 
either in one direction or the other accord¬ 
ing to the pole by which it is influenced. 

This rotation is due to currents assumed to 
circulate round magnets, currents which 
act on the vertical branches EF, in the 
same way as the circular current on the Fig. 572. 

arm in fig. 568. 

In this experiment the magnetised bundle may be replaced by a solenoid 


















714 


DYNAMICAL ELECTRICITY. 


[747- 

(750) or by an electromagnet, in which case the two binding screws in 
the base of the apparatus on the left give entrance to the current which 
is to traverse the solenoid as the electromagnet. 

747. Directive action of the earth on vertical currents. —The 
earth, which exercises a directive action on magnets (601), acts also 
upon currents, giving them, in some cases, a fixed direction, in others a 
continuous rotatory motion, according as their currents are arranged in a 
vertical or horizontal direction. 

The first of these two actions may be thus enunciated : Every vertical 
current moveable about an axis parallel to itself \ places itself under the 
directive action of the earth in a plane perpendicular to the magnetic meri¬ 
dian, and stops, after some oscillations, on the east of its axis of rotation 
when it is descending , and on the west when it is ascending. 

This may be demonstrated by means of the apparatus represented in 
fig. 574, which consists of two copper vessels of somewhat different 
diameters. The larger, a, about 13 inches in diameter, has an aperture 



Fig. 574. 


in the centre, through which passes a brass support, b, insulated from the 
vessel a, but communicating with the vessel K. This column terminates 
in a small cup, in which a light wooden rod rests on a pivot. At one 
end of this rod a fine wire is coiled, each end of which dips in acidulated 
water, with which the two vessels are respectively filled. 

The current arriving by the wire m passes to a strip of copper, which 
is connected underneath the base of the apparatus with the bottom of 
the column b. Ascending in this column the current reaches the vessel 
K, and the acidulated water which it contains; it ascends from thence 
in the wire c , redescends by the wire e, and traversing the acidulated 












715 


- 749 ] ACTION OF THE EARTH ON HORIZONTAL CURRENTS. 

water, it reaches the sides of the vessel a, and so back to the battery 
through the wire n. 

The current being thus closed, the wire e moves round the column 
b, and stops to the east of it, when it descends, as is the case in the 
figure; but if it ascends, which is effected by transmitting the current 
by the wire n, the wire e stops to the west of the column b, in a 
position directly opposite to that which it assumes when it is descending. 

If the rod with a single wire, in fig. 574, be replaced by one with 
two wires, as in fig. 573, the rod will not move, for as each wire tends 
to place itself on the east of the columns, b, two equal and contrary 
effects are produced, which counterbalance one another. 

748. Action of tlie earth on horizontal currents moveahle 
about a vertical axis, —The action of the earth on horizontal currents 
is not directive, but gives them a continuous rotatory motion from the east 
to the west when the horizontal current moves away from the axis of rotation, 
and from the west to the east when it is directed towards this axis. 



Fig. 574. 


This may be illustrated by means of the apparatus represented in 
fig. 575, which only differs from that of fig. 574 in having but one 
vessel. The current ascending by the column a, traverses the two 
wires cc, and descends by the wires bb, from which it regains the pile. 
The circuit bccb then begins a continuous rotation, either from the 
east to the west, or from the west to the east, according as in the wires 
cc the current goes from the centre, as is the case in the figure; or 
according as it goes towards it, which is the case when the current 
enters by the wire m instead of by n. But we have seen (747) that the 
action on the earth on the vertical wires bb is destroyed ; hence the 
rotation is that produced by the action on the hoiizontal branches cc. 
This rotatory action of the terrestrial current on horizontal currents is a 
consequence of the rotation of a finite horizontal by an infinite horizon¬ 
tal current (742). 

749. Directive action of the earth on closed currents move¬ 
able about a vertical axis, —If the current on which the earth acts 








716 


DYNAMICAL ELECTRICITY. 


[ 750 - 


is closed, whether it be rectangular or circular, the result is not a con¬ 
tinuous rotation, but a directive action, as in the case of vertical 
currents (746), in virtue of which the current places itself in a plane 
perpendicular to the magnetic meridian , so that , for an observer looking at 
the north, it is descending on the east of its axis of rotation , and ascending 
on the west. 

This property, which can be shown by means of the apparatus 
represented in fig. 576, is a consequence of what has been said 

about horizontal and ver¬ 
tical currents. For in the 
closed circuit, BDA, the cur¬ 
rent in the upper and lower 
parts tends to turn in oppo¬ 
site directions, from the law 
of horizontal currents (747) ; 
and hence is in equilibrium, 
while in the lateral parts the 
current on the one side tends 
towards the east, and on the 
other side to the west, from 
the law of vertical currents. 

From the directive action 
of the earth on currents, 
it is necessary, in most ex¬ 
periments, to obviate this 
action. This is effected by arrangingthe moveable circuit symmetrically 
about its axis of rotation, so that the directive action of the earth tends 
to turn them in opposite directions, and hence destroys them. This 
condition is fulfilled in the circuits represented in figs. 555 and 556. 
Hence these currents are called astatic currents. 

SOLENOIDS. 

750. Structure of a solenoid.— A solenoid is a system of equal 
and parallel circular currents formed of the same piece of covered 
copper wire, and coiled in the form of a helix or spiral, as represented 
in fig. 577. A solenoid, however, is only complete when part of 

the wire BC passes in the direction 
ax * s * n interior of the 

r _ u fi 1) A A A A A A A V rP ? B helix. With this arrangement, when 

the circuit is traversed by a current, 
Fig. 577. it follows from what has been said 

about sinuous currents (739) that the 
action of a solenoid in a longitudinal direction AB is counterbalanced bv 



Fig. 576. 
















SOLENOIDS. 


717 


<2 





at 

100000 

uX 

luroOOO 

ooo 


Fig. 578. 


- 753 ] 

that of the rectilinear current BC. This action is accordingly null in 
the direction of the length, and the action of a solenoid in a direction 
perpendicular to its axis is exactly equal to that of a series of equal parallel 
currents. 

751. Action of currents on solenoids.— What has been said of the 
action of fixed rectilinear currents on finite, rectangular, or circular cur¬ 
rents (741), applies evidently to each of the circuits of a solenoid, and 
hence a rectilineal current must tend to direct these circuits parallel to 
itself. To demonstrate this fact experimentally, a solenoid is constructed 
as shown in fig. 578, so that it can be suspended by two pivots in the cups 
A and B of the apparatus represented 
fig. 556. The solenoid is then move- 
able about a vertical axis, and if 
beneath it a rectilinear current be 
passed which at the same time tra¬ 
verses the wires of the solenoid, the 
latter is seen to turn and set at right 
angles to the lower current, that is, 
in such a position that its circuits are 
parallel to the fixed current; and further, in the lower part of each of 
the circuits the current is in the same direction as in the rectilinear 
wire. 

If, instead of passing a rectilinear current below the solenoid, it is 
passed vertically on the side, an attraction or repulsion will take place, 
according, as in the vertical wire, and in the nearest part of the solenoid, 
the two currents are in the same or in a contrary direction. 

752. Directive action of the earth on solenoids. —If a solenoid be 
suspended in two cups, A and B, Ampere’s stand (fig. 556), not in the 
direction of the magnetic meridian, and a current be passed through the 
solenoid, the latter will begin to move, and will finally set in such a posi¬ 
tion that its axis is in the direction of the magnetic meridian. If the 
solenoid be removed it will, after a few oscillations, return, so that its 
axis is in the magnetic meridian. Further it will be found that in the 
lower half of the coils of which the solenoid consists, the direction of the 
current is from east to west, in other words the current is descending on 
that side of the coil turned towards the east, and ascending on the west. 
The directive action of the earth on solenoids is accordingly a consequence 
of that which it exerts on circular currents. In this experiment the 
solenoid is directed like a magnetic needle, and the north pole , as in mag¬ 
nets, is that end which points towards the north, and the south pole that 
which points towards the south. This experiment may be well made by 
means of a solenoid fitted on a De la Rive’s floating battery. 

753. Mutual actions of magnets and solenoids.— Exactly the 






718 


DYNAMICAL ELECTRICITY. 


[ 754 - 

same phenomena of attraction and repulsion exist between solenoids and 
magnets as between magnets. For if to a moveable solenoid traversed by 
a current, one of the poles of a magnet be presented, attraction or repulsion 
will take place, according as the poles of the magnet and of the solenoid 
are of contrary or of the same name. The same phenomenon takes place 
when a solenoid traversed by a current and held in the hand is presented 
to a moveable magnetic needle. Hence the law of attractions and re¬ 
pulsions applies exactly to the case of the mutual action of solenoids and 
of magnets. 

754. Mutual actions of solenoids. —When two solenoids traversed 
by a powerful current are allowed to act on each other, one of them being 
held in the hand, and the other being moveable about a vertical axis, as 
shown in figure 579, attraction and repulsion will take place just as in 



the case of two magnets. These phenomena are readily explained by 
reference to what has been said about the mutual action of the currents 
bearing in mind the direction of the currents in the extremities presented 
to each other. 

755. Ampere’s theory of magnetism. —Ampere has propounded a 
most ingenious theory, based on the analogy which exists between sole¬ 
noids and magnets, by which all magnetic phenomena may be referred to 
electrodynamical principles. 

Instead of attributing magnetic phenomena to the existence of two 
fluids (595), Ampere assumes that each individual molecule of a magnetic 
substance is traversed by a closed electric current. It is further assumed 
that these molecular currents are free to move about their centres of 
gravity. The coercive force, however, which is little or nothing in soft 














THEORY OF MAGNETISM. 


719 


-756] 

iron, but considerable in steel, opposes this motion, and tends to keep them 
in any position in which they happen to be. When the magnetic sub¬ 
stance is not magnetised, these molecular currents, under the influence of 
their mutual attractions, occupy such positions that their total action on 
any external substance is null. Magnetisation consists in givingto these 
molecular currents a parallel direction, and the stronger the magnetising 
force the more perfect the parallelism. The limit of magnetisation is 
attained when the currents are completely parallel. 

The resultant of the actions of all the molecular currents is equivalent 
to that of a single current which traverses the outside of a magnet. 
For by inspection of fig. 

580, in which the mole¬ 
cular currents are repre¬ 
sented, by a series of small 
internal circles in the two A 
ends of a cylindrical bar, 
it will be seen that the 
adjacent part of the cur¬ 
rents oppose one another, 
and cannot exercise any 
external electrodynamic 
action. This is not the 580# 

case with the surface; there the molecular currents at ah are not neutra¬ 
lised by other currents, and as the points abc are infinitely near, they form 
a series of elements in the same direction situated in planes perpendicular 
to the axis of the magnet, and which constitute a true solenoid. 

The direction of these currents in magnets can be ascertained by con¬ 
sidering the suspended solenoid, fig. 579. If we suppose it traversed by 
a current, and in equilibrium in the magnetic meridian, it will set in such 
a position that in the lower half of each coil the current flows from east 
to west. We may then establish the following rule. At the north pole of 
a magnet the direction of the Amperian currents is opposite that of the hands 
of a watch , and at the south pole the direction is the same , that of the hands. 

756. Terrestrial current. —In order to explain on this supposition 
terrestrial magnetic effects, the existence of electrical currents is assumed 
which continually circulate round our globe from east to west, perpen¬ 
dicular to the magnetic meridian. 

The resultant of their action is a single current traversing the magne¬ 
tic equator from east to west. These currents are supposed to be thermo¬ 
electric currents due to the variations of temperature caused by the 
successive influence of the sun on the different parts of the globe from 
east to west. 

These currents direct magnetic needles, and impart a natural magneti- 



720 


DYNAMICAL ELECTRICITY. 


[757- 

sation to iron minerals. Lastly, they cause the action of the earth on 
horizontal and vertical currents, an effect readily explained from what 
has been said about the action of an infinite horizontal current on 
horizontal and vertical currents. 


CHAPTER V. 

MAGNETISATION BY CURRENTS. ELECTROMAGNETS. ELECTRIC 
TELEGRAPHS. 

757. Magnetisation by currents.— From the influence which cur¬ 
rents exert upon magnets, turning the north pole tn the left and the 
south pole to the right, it is natural to think that by acting upon 
magnetic substances in the natural state the currents would tend to 
separate the two magnetic fluids. In fact, when a wire traversed by a 
current is immersed in iron filings, they adhere to it in large quantities, 
but become detached as soon as the current ceases, while there is no 
action or any other non-magnetic metal. 

The action of currents on magnetic substances is well seen in an ex¬ 
periment due to Ampere, which consists in coiling an insulated copper 
wire round a glass tube, in which there is an unmagnetised steel bar. If 
a current be passed through the wire, even for a short time, the bar 
becomes strongly magnetised. 

If, as we have already seen (686), the discharge of a Leyden jar be 
transmitted through the wire by connecting one end with the outer 
coating, and the other with the inner coating, the bar is also magnet¬ 
ised. Hence both voltaic and frictional electricity can be used for 
magnetising. 

If in this experiment the wire be coiled on the tube in such a manner 
that when it is held vertically, the downward direction of the coils is 
from right to left on the side next the observer, this constitutes a right- 
handed or dextrorsal spiral or helix (fig. 581), of which the ordinary screw 



Fig. 581 . 

is an example. In a left-handed or sinistrorsal helix the coiling is in the 
opposite direction, that is from left to right (fig. 582). 

In a right-handed spiral the north pole is at the end at which the 
current emerges, and the south pole at the end at which it enters; the 









ELECTROMAGNETS. 


721 


- 758 ] 

reverse is the case in a left-handed spiral. But whatever the direction 
of the coiling the polarity is easily found by the following rule : If a 
person swimpiing in the current look at the axis of the spiral , the north pole 



Fig. 582. 



is always on his left. If the wire he not coiled regularly, but its direction 
be reversed, at each change of direction a consequent point is formed in 
the magnet. 

The nature of the tube on which the helix is coiled is not without 
influence. Wood and glass are of no effect, but a thick cylinder of copper 
may completely destroy the action of the current. The same is the case 
with iron, silver, and tin. 

In order, however, to magnetise a steel bar by means of electricity, it 
need not be placed in a tube, as shown in figs. 581 and 582. It 


is sufficient to coil round it a 
copper wire covered with silk, in 
order to insulate the circuits 
from one another. The action of 
the current is thus multiplied, 
and a feeble current is sufficient 
to produce a powerful charge of 
magnetism. 

758. Electromagnets. — Elec¬ 
tromagnets are bars of soft iron 
which, under the influence of a 
voltaic current, become magnets ; 
but this magnetism is only tem¬ 
porary, for the coercive force of 
perfectly soft iron is null, and the 
two magnetic fluids neutralise 
each other as soon as the current 
ceases to pass through the wire. 
Tf >, ,vever, the iron is not quite 
it retains more or less 
of magnetism. The elec- 
; rnets have the horse-shoe 
as shown in fig. 583, and 
>er wire, covered with silk 
;ton, is rolled several times 
them on the two branches 


Fig. 583. 

so as to form two bobbins, A and B. 



















DYNAMICAL ELECTRICITY. 


722 


[ 758 - 


The winding must be in opposite directions on the two bobbins, in order 
that the two ends of the horse-shoe may be of opposite polarity. 

Electromagnets, instead of being made in one piece, are frequently 
constructed of two cylinders, jointly screwed to a stout piece of the same 
metal. Such are the electromagnets in Morse’s telegraph (763), the 
electromagnetic motor (766). One limb is provided with a left-handed, 
and the other a right-handed helix. 

The results at which various experimenters have arrived as regards the 
force of electromagnets are often greatly divergent, which is partly due 
to the different senses they have attached to the motion of electro-magnetic 
force. For this may mean (I.) the induction current which the de¬ 
velopment and disappearance of the magnetism of an iron core indicates 
in a spiral which surrounds it; this is the excited magnetism , or (II.) the 
free magnetism measured by the action on a magnetic needle, oscillating 
at a distance, (III.) the attractive force or the force with which an 
armature is held at a distance from the electromagnet; (IV.) the lifting 
power measured by the force with which an armature is held in direct 
contact with the pole. 

The most important results which have been arrived at are the 
following: 

(i. and ii.) The temporary magnetic moment is proportional to the 
intensity of the current. This only applies when the currents are not very 
powerful, and to stout bars; for each bar there is, as Muller has found, a 
maximum of magnetisation which cannot be exceeded. It is independent 
of the nature of the wire , its thickness , and of the width of the coils; as 
regards the latter, provided the diameter of the spiral is small as com¬ 
pared with its length. 

(iii.) The temporary magnetic moment of an iron bar is within certain 
limits proportional to the number of windings. The product of the intensity 
into the number of turns is usually spoken of as the magnetising power of 
the spiral. The greatest magnetising power is obtained when the 
resistance in the magnetising spiral is equal to the sum of the other 
resistances in the circuit, those of the battery included, and the length 
and diameter of the wire must be so arranged as to satisfy these con¬ 
ditions. 

(iv.) The temporary magnetic moment is proportional to the square 
root of the diameter of the magnet. 

(v.) The magnetism is solid and in hollow cylinders of the same 
diameters is the same, provided in the latter case there is sufficient iron 
for the development of the magnetism. 

(vi.) The attraction of an armature by an electromagnet is proportional 
to the square of the intensity of the current so long as the magnetic 
moment does not attain its maximum. Two unequally strong electro- 


- 759 ] ELECTROMAGNETS. 723 

magnets attract each other with a force proportional to the square of the 
sums of both currents. 

(vii.) For powerful currents the length of the branches of an electro¬ 
magnet is without influence on the weight which it can support. 

As regards the quality of the iron used for the electromagnet it must 
be pure, and be made as soft as possible by being reheated and cooled a 
great many times; it is polished by means of a file so as to avoid twist¬ 
ing. If this is not the case the bar retains, even alter the passage of the 
current, a quantity of magnetism which is called the remanent magnetism. 
A bundle of soft iron wires loses its magnetism more rapidly than a 
massive bar of the same size. 

Wiedemann has proved that an analogy exists between the phenomena 
of magnetism and those of torsion which extends even into details. 
Agitations during the twisting of a wire increase the torsion, just as they 
increase the magnetism of a wire while under the influence of the cur¬ 
rent. The permanent torsion of iron wires is diminished by their magne¬ 
tisation, as the permanent magnetism of steel bars is by their torsion; a 
twisted wire loses some of its torsion by heat, as a magnet loses some of 
its power. 

We shall presently see the numerous applications which have been 
made of electromagnets in electric telegraphs, in electro-magnetic motors, 
in electric clocks, and in the study of diamagnetic phenomena. 

759. Vibratory motion and sounds produced by currents.— 
When a rod of soft iron is magnetised by a strong electric current, it 
gives a very distinct sound, which, however, is only produced at the 
moment of closing or opening the current. This phenomenon, which 
was first observed by Page in America, and by Delezenne in France, has 
been particularly investigated by Pe la Rive, who has attributed it to a 
vibratory motion of the molecules of iron in consequence of a rapid 
succession of magnetisations and demagnetisations. 

When the current is broken and closed at very short intervals, De la 
Rive has observed, that whatever be the shape or magnitude of the iron 
bars, two soimds may always be distinguished: one, which is musical, 
corresponds to that which the rod would give by vibrating transversely ; 
the other, which consists in a series of harsh sounds, corresponding to the 
interruptions of the current, is compared by De la Rive to the noise of 
rain falling on a metal roof. The most marked sound, says he, is that 
obtained by stretching on a sounding board pieces of soft iron wire, well 
annealed, from 1 to 2mm. in diameter, and 1 to 2 yards long. These 
wires being placed in the axis of one or more bobbins traversed by 
powerful currents, send forth a number of sounds, which produce a 
surprising effect, and much resemble that of a number of church bells 
heard at a distance. 


724 


DYNAMICAL ELECTRICITY. 


[760- 

Wertheim has obtained the same sounds by passing a discontinuous 
current, not through the bobbins surrounding the iron wires, but through 
the wires themselves. The musical sound is then stronger and 'more 
sonorous in general than in the previous experiment. The hypothesis of 
a molecular movement in the iron wires at the moment of their magne¬ 
tisation, and of their demagnetisation, is confirmed by the researches of 
Wertheim, who has found that their elasticity is then diminished. 
During magnetisation the volume of a magnet does not vary. This 
has been established by placing the bar to be magnetised, with its helix, 
in a sort of water thermometer, consisting of a flask provided with a 
capillary tube. On magnetising no alteration in the position of the water 
.is observed. But the dimensions vary, the diameter is somewhat lessened, 
and the length increased ; according to Joule to the extent of about gij—, 
if the bar is magnetised to saturation. 

ELECTRIC TELEGRAPH. 

700. Electric telegraphs. —These are apparatus by which signals can 
be transmitted to considerable distances by means of voltaic currents 
propagated in metallic wires. Towards the end of the last century, and 
at the beginning of the present, many philosophers proposed to cor¬ 
respond at a distance by means of the effects produced by electrical 
machines when propagated in insulated conducting wires. In 1811, 
Soemmering invented a telegraph in which he used the decomposition of 
water for giving signals. In 1820, at a time when the electromagnet 
was unknown, Ampere proposed to correspond by means of magnetic 
needles, above which a current was sent, as many wires and needles 
being used as letters were required. In 1834, Gauss and Weber con¬ 
structed an electromagnetic telegraph, in which a voltaic current trans¬ 
mitted by a wire acted on a magnetised bar; the oscillations of which 
under its influence were observed by a telescope. They succeeded in 
thus sending signals from the Observatory to the Physical Cabinet in 
Gottingen, a distance of a mile and a quarter, and to them belongs the 
honour of having first demonstrated experimentally the possibility of 
electrical communication at a considerable distance. In 1837, Steinheil 
in Munich, and Wheatstone in London, constructed telegraphs in which 
several wires each acted on a single needle: the current in the first case 
being produced by an electromagnetic machine, and in the second by a 
constant battery. 

Every electric telegraph consists essentially of three parts: 1, a 
circuit consisting of a metallic connection between two places, and an 
electromotor for producing the current; 2, a communicator for sending 
the signals from the one station; and, 3, an indicator for receiving them 


ELECTRIC TELEGRAPH. 


- 760 ] 


725 


at tlie other station. The manner in which these objects, more espe¬ 
cially the last two, are effected can he greatly varied, and we shall limit 
ourselves to a description of the three principal methods. 

The electromotor generally used in England is a modification of 
Wollaston’s battery. It consists of a trough divided into compartments, 
in each of which is an amalgamated zinc plate and a copper plate ; these 



plates are. usually about 4£ inches in height by 3£ in breadth. The 
compartments are filled with sand, which is moistened with dilute sul¬ 
phuric acid. This battery is inexpensive and easily worked, only requiring 
from time to time the addition of a little acid; but it has very low 
electro-motive force and considerable resistance, and when it has been at 
work for some time, the effects of polarisation begin to be perceived. 
On the telegraphs of the South Eastern Railway, the platinised graphite 
(703) battery invented by Mr. C. V. Walker is used with success. In 
France, Daniell’s battery is used for telegraphic purposes. 

The connection between two stations is made by means of galvanised 































































72G 


DYNAMICAL ELECTRICITY. 


[ 760 - 

iron wire suspended by porcelain supports, which insulate and protect 
them against the rain, either on posts or against the sides of buildings. 
In towns, wires, covered with gutta-percha, are placed in tubes laid in the 
ground. Submarine cables are formed of copper wires for the sake of 
the greater conductivity. These wires are coated with gutta-percha, 
round which is a coating of tarred hemp, the whole being surrounded by 
an iron cable, which gives it strength to resist the tension at the moment 



of laying the cable, and to enable it to resist the action of submarine 
currents. 

At the station which sends the despatch, the line is connected with the 
positive pole of a battery, the current passes by the line to the other 
station, and if there were a second return line, it would traverse it in the 
opposite direction to return to the negative pole. In 1837, Steinheil 
made the very important discovery that the earth might be used for the 
return conductor, thereby saving the expense of the second line. For 
this purpose the end of the conductor at the one station and the negative 
pole of the battery at the other are connected with large copper plates, 
















































ELECTRIC TELEGRAPH. 


727 



- 761 ] 

which are sunk to some depth in the ground. The action is then the 
same as if the earth acted as a return wire. 

761. Wheatstone’s and Cooke’s single needle telegraph.— This 
consists essentially of a vertical multiplier with an astatic needle, the 
arrangement of which is seen in fig. 585, while fig. 584 gives a 
front view of the case in which the apparatus is placed. A (fig. 585) is 
the bobbin consisting of about 400 feet of fine copper wire, wound in a 
frame in two connected coils. Instead of an astatic needle, Mr. Walker 
has found it advantageous to use a single needle formed of several pieces 
of very thin steel strongly magnetised ; it works within the bobbin, and 
a light index joined to it by a horizontal axis indicates the motion of the 
needle on the dial. 

The signs are made 1>y transmitting the current in different directions 
through the multiplier, by which the needle is deflected either to the 
right or left, according to the will of the operator. The instrument by 
which this is effected is a commutator or key, G; its construction is 


Fig. 686. 

shown in fig. 585, while fig. 586 shows on a large scale how two stations 
are connected. It consists of a cylinder of boxwood with a handle, which 
projects in front of the case (fig. 584). On its circumference parallel to 
the axis are seven brass strips (fig. 586), the spaces between which are 
insulated by ivory; these strips are connected at the end by metallic 






728 


DYNAMICAL ELECTRICITY- 


[ 762 - 

wires, also insulated from eacli other, in the following manner: a with 
b and c;,/with d , and e with g. Four springs press against the cylinder ; 
x and y are connected with the poles of the battery, m, with the earth 
plate, and n with one end of the multiplier, N. 

When not at work the cylinder and the handle are in a vertical posi¬ 
tion, as seen on the left of the diagram. The circuit is thus open , for 
the pole springs, x and y, are not connected with the metal of the com¬ 
mutator. But if, as in G', the key is turned to the right, the battery is 
brought into the circuit, and the current passes in the following direction 
-(- pole x'a'b'n'Wq, conductor qMnbacmEp, earth p'JL’m'e'g'y' — pole. 
The coils N and N' are so arranged that by the current the motion of the 
needle corresponds to the motion of the handle. By turning the handle 
to the left the current would have the following direction: + pole 
x'df'm' E'P, earth ~P'~EmcabnNq, conductor q'Wn'b'a'y' — pole, and thus 
the needle would be deflected in the opposite direction. 

The signs are given by differently combined deflections of the needle, 
as represented in the alphabet on the dial (fig. 585). \ denotes a deflec¬ 
tion of the upper end of the needle to the left, and / a deflection to the 
right; A, for instance, is indicated by two deflections to the left, and N 
by two to the right. Some of the marks on the alphabet are only half 
as long as the others; this indicates that the shortest of the connected 
marks must first be signalled. Thus, E is expressed by right-left-left, 
and L by right-left-right-left, etc. 

These signs are somewhat complicated, and require great practice; 
usually not more than 12 to 20 words can be sent in a minute. Hence 
the single needle telegraph is in most cases replaced by the double 
needle one, which is constructed on the same principle, but there are 
two needles and two wires instead of one. 

762. Dial telegraphs. —Of these many kinds exist. Figs. 588 and 
589 represent a lecture-model of one form, constructed by M. Froment, 
and which well serves to illustrate the principle. It consists of two 
parts : the manipulator for transmitting signals (fig. 588), and the indicator 
(fig. 589) for receiving them. The first apparatus is connected with a 
battery, Q, and the two apparatus are in communication by means of 
metallic wires, one of which, AOD (fig. 588), goes from the departure to 
the arrival station, and the other, HKLI (fig. 589), from the arrival to 
the departure. In practice, the latter is replaced by the earth circuit. 
Each apparatus is furnished with a dial with 25 of the letters of the 
alphabet, on which a needle moves. The needle at the departure station' 
is moved by hand, that of the arrival by electricity. 

The path of the current and its effects are as follows: From the 
battery it passes through a copper wire, A (fig. 588), into a brass spring 
N, which presses against a metal wheel, K, then by a second spring, M, 


ELECTRIC TELEGRAPH. 


729 


- 762 ] 

into the wire, 0, which joins the other station. Thence the current 
passes into the bobbin of an electromagnet, b, not fully shown in fig. 
589, but of which fig. 587 represents a section, 
showing the anterior part of the apparatus. 

This electromagnet is fixed horizontally at 
one end, and at the other it attracts an arma¬ 
ture of soft iron, a, which forms part of a bent 
lever, moveable about its axis, o, while a spring, 
r, attracts the lever in the opposite direction. 

When the current passes, the electromagnet 
attracts the lever aC, which by a rod, i, acts 
on a second lever, d, fixed to a horizontal 
axis, itself connected with a fork F. When 
the current is broken the spring r draws the 
lever «C, and therewith all the connected 
pieces; a backward and forward motion is 
produced, which is communicated to the fork, F, which transmits it to a 
toothed wheel, G, on the axis of which is the needle. From the arrange¬ 
ment of its teeth, the wheel G is always moved in the same direction by 
the fork. 

To explain the intermittent action of the magnet, we must refer to 
fig. 588. The toothed wheel, R, has 26 teeth, of which 25 correspond 
to letters of the alphabet, and the last to the interval reserved be¬ 
tween the letters A and Z. When holding the knob P in the hand 
the wheel R is turned, the end of the plate N from its curvature is always 
in contact with the teeth; the plate M, on the contrary, terminates in a 
catch cut so that contact is alternately made and broken. Hence the 
connections with the battery having been made, if the needle P is 
advanced through four letters, for example, the current passes four times 
in N and M, and is four times broken. The electromagnet of the arrival 
station will then have attracted four times, and have ceased to do so 
four times. Lastly, the wheel G will have turned by four teeth, and as 
each tooth corresponds to a letter, the needle of the arrival station will 
have passed through exactly the same number of letters as that of the 
departure station. The piece S, represented in the two figures, is a 
copper plate, moveable on a hinge, which serves to interrupt or to close 
the current at will. 

From this explanation it will be readily intelligible how communi¬ 
cations are made between different places. Suppose, for example, that 
the first apparatus being at London and the second at Brighton, there 
being metallic connection between the two towns, it is desired to send 
the word signal to the latter town: as the needles correspond on each 
apparatus to the interval retained between A and Z, the person sending 

11 3 



Fig. 587. 








730 


DYNAMICAL ELECTRICITY 


[762 



Fig. 588. Fig. 589 














































































































































morse’s telegraph. 


731 


- 763 ] 

the despatch moves the needle P to the letter S, where it- stops for a very 
short time ; as the needle at Brighton accurately reproduces the motion 
of the London needle it stops at the same letter, and the person who 
receives the despatch notes this letter. The one at London always con¬ 
tinuing to turn in the same direction, stops at the letter I, the second 
needle immediately stops at the same letter ; and continuing in the same 
manner with the letters G, N, A, L, all the word is soon transmitted to 
Brighton. The attention of the observer at the arrival station is attracted 
by means of an electric alarum. Each station further must be provided 
with the two apparatus (figs. 588 and 589), without which it would be 
impossible to answer. 

763. Morse’s telegraph. —The telegraphs hitherto described leave 
no trace of the despatches sent, and if any errors have been made in 
copying the signals there is no means of remedying them. These incon¬ 
veniences are not met with in the case of the writing telegraphs , in which 
the signs themselves are printed on a strip of paper at the time at which 
they are transmitted. 

Of the numerous printing and writing telegraphs which have been 
devised, that of Mr. Morse, first brought into use in North America, is 
best known. It has been almost universally adopted on the continent. 
In this instrument there are three distinct parts: the indicator , the 
communicator , and the relay ; figs. 590, 591, and 592 represent these 
apparatus. 

Indicator. We will first describe the indicator (fig. 590), leaving out 
of sight for the moment the accessory pieces, G and T, placed on the 
right of the figure. The current which enters the indicator by the wire, 
C, passes into an electromagnet, E, which, when the current is closed, 
attracts an armature of soft iron, A, fixed at the end of a horizontal lever 
moveable about an axis, x ; when the current is open the lever is raised 
by a spring, r. By means of two screws, m and v , the amplitude of the 
oscillations is regulated. At the other end of the lever there is a pencil, 
o, which writes the signals. For this purpose a long band of strong 
paper, pp, rolled round a drum, R, passes between two copper rollers 
with a rough surface, u, and turning in contrary directions. Drawn in the 
direction of the arrows, the band of paper becomes rolled on a second 
drum, Q, which is turned by hand. A clockwork motion placed in the 
box, BD, works the rollers, between which the band of paper passes. 

The paper being thus set in motion, whenever the electromagnet 
works, the point o strikes the paper, and, without perforating it, produces 
an indentation, the shape of which depends on the time during which 
the point is in contact with the paper. If it only strikes it instan¬ 
taneously, it makes a dot (.) ; but if the contact has any duration a line 



732 DYNAMICAL ELECTRICITY. [ 763 - 

of corresponding length is produced. Hence, by varying the length of 
contact of the transmitting key at one station, a combination of dots or 


Fig. 590. 

points may be produced at another station, and it is only necessary to 
give a definite meaning to these combinations. For instance— 

A line and a point (—.) represent the letter A. 

A line and three points (—. . .) „ „ B. 

Three points (. . .) „ „ C. 

A line and two points (—. .) „ „ D. 

In this manner words and phrases can be arranged, care being taken to 
leave a space between each letter. 

Communicator or key. This consists of a small mahogany base, which ‘ 
acts as support for a metallic lever ab (fig. 591), moveable in its middle 
on a horizontal axis. The extremity a of this lever is always pressed 
upwards by a spring beneath, so that it is only by pressing with the 
finger on the key B that the lever sinks and strikes the button x . Bound 
the base there are three binding screws ; one connected with the wire P ; 
which comes from the positive pole of the battery ; the second connected 
with L, the wire of the line; and the^ third with the wire A, which 
passes to the indicator, for of course two places in communication are 
each provided with an indicator and communicator. 










morse’s telegraph. 


733 


-763] 

These details known, there are two cases to be considered: 1. The 
communicator is arranged so as to receive a despatch from a distant 
post; the extremity b is then depressed, as represented in the drawing, 
so that the current which arrives by the wire of the line L, and ascends 
in the metallic piece m, redescends in the wire A, which leads it to the 



Fig. 591. 


indicator of the post at which the apparatus is placed. 2. A despatch 
is to be transmitted; in this case the key B is pressed so that the lever 
comes in contact with the button x. The current of the local battery, 
which comes by the wire P, ascending then in the lever, redescends by 
m and joins the wire L, which conducts it to the post to which the 
despatch is addressed. According to the length of time during which B 
is pressed, a dot or a line is produced in the receiver to which the 
current proceeds. 

jRelay. In describing the receiver we have assumed that the current 
of the line coming by the wire C (fig. 590) entered directly into the 



■III 

Fig. 592. 


electromagnet, and worked the armature A, producing a despatch j but 
when the current has traversed a distance of a few miles its intensity has 












734 


DYNAMICAL ELECTRICITY. 


[763- 

diminished so greatly that it cannot act upon the electromagnet with 
sufficient force to print a despatch. Hence it is necessary to have re¬ 
course to a relay, that is, to an auxiliary electromagnet which is still 
traversed by the current of the line, but which serves to introduce 
into the communicator the current of a local battery of 4 or 5 elements 
placed at the station, and only used to print the signals transmitted by 
the wire. 

For this purpose the current entering the relay by the binding screw 
L (fig. 592) passes into an electromagnet E, whence it passes into the 
earth by the binding screw T. Now, each time that the current of the 
line passes into the relay, the electromagnet attracts an armature, A, 
fixed at the bottom of a.vertical lever/?, which oscillates about a hori¬ 
zontal axis. 

At each oscillation the top of the lever p strikes against a button, n, 
and at this moment the current of the local battery which enters by the 
binding screw, c, ascends the column m, passes into the lever p, descends 
by the rod o, which transmits it to the screw Z : thence it enters the 
electromagnet of the indicator, whence it emerges by the wire Z, to 
return to the local battery from which it started. Then when the current 
of the line is open, the electromagnet of the relay does not act, and the 
lever/?, drawn by a spring r, leaves the button n, as shown in the draw¬ 
ing, and the local current no longer passes. Thus the relay transmits 
to the indicator exactly the same phases of passage and intermittence as 
those effected by the manipulator in the post which sends the despatch. 

With a general battery of 25 Daniell’s elements the current is strong 
enough at upwards of 90 miles from its starting-point to work a relay. 
For a longer distance a new current must be taken, as will be seen in 
the paragraph on the change of current (p. 735). 

Working of the three apparatus. The three principal pieces of Morse’s 
apparatus being thus known, the following is the actual path of the current. 

The current of the line coming by the wire L passes at first to the 
piece T intended to serve as lightning conductor, when from the influence 
of atmospheric electricity in time of storm, the conducting wires become 
charged with so much electricity as to give dangerous sparks. This 
apparatus consists of two copper discs, d and f provided with teeth on 
the sides opposite each other, but not touching. The disc d is connected 
with the earth by a metallic plate at the back of the stand which supports 
this lightning conductor, while the disc / is in the current. The latter 
coming by the line L enters the lightning conductor by the binding 
screw fixed at the lower part of the stand on the left; then rises in a 
commutator, n , which conducts it to a button, c, whence it reaches the 
disc/ by a metallic plate at the back of the stand. There the elec¬ 
tricity, acting inductively on the disc d, emerges by the points without 


- 764 ] bain’s electrochemical telegraph. 735 

danger to those about the apparatus. Moreover, from the disc f } the 
current passes into a very fine iron wire insulated on a tube e. As the 
wire is melted, when the current is too intense, the electricity does not 
pass into the apparatus, which still further removes any danger. 

Lastly, the current proceeds from the foot of the support s to a screw 
on the right, which conducts it to a small galvanometer, G, serving to 
indicate by the deflection of the needle whether the current passes. 
From this galvanometer the current proceeds to a communicator (fig. 
591) which it enters at L, whence it emerges at A to go to the relay 
(fig. 592). Entering this at L it works the electromagnet, and establishes 
the communication necessary for the passage of the current of the local 
battery, as has been said in speaking of the relay. 

Change of current. To complete this description of Morse’s apparatus 
it must be observed that in general the current which arrives at L, after 
having traversed 6 miles, has not sufficient force to register the despatch, 
nor to proceed to a new distant point. Hence, in each telegraphic 
station a new current must be taken, that of the 'postal battery , which 
consists of 20 to 30 Daniell’s elements; and is not identical with the 
local battery. 

This new current enters at P (fig. 590), reaches a binding screw which 
conducts it to the column H, and thence only proceeds further when the 
armature A sinks. A small contact placed under the lever touches then 
the button v; the current proceeds from the column H to the metallic 
mass BD, whence by a binding screw and a wire, not represented in the 
figure, it reaches lastly the wire of the line, which sends it to the follow¬ 
ing post, and so on from one post to another. 

764. Bain’s electrochemical telegraph.— If a strip of paper be 
soaked in an aqueous solution of ferrocyanide of potassium and con¬ 
nected with the negative pole of a battery, and if the other face be 
touched with a steel pointer connected with the positive pole, a blue 
mark due to the formation of some Prussian blue will be formed about 
the iron, so long as the current passes. The first telegraph based on this 
principle was invented by Mr. Bain. The alphabet is the same as Morse’s, 
but the despatch is first composed at the departure station on a long 
strip of ordinary paper. It is perforated successively by small round and 
elongated holes, which correspond respectively to the dots and marks. 
This strip of paper is interposed between a small metal wheel and a 
metal spring, both forming part of the circuit. The wheel in turning 
carries with it the paper strip, all parts of which pass successively 
between the wheel and the plate. If the strip were not perforated it 
would, not being a conductor, constantly offer a resistance to the passage 
of the current; but in consequence of the holes, every time one of them 
passes there is contact between the wheel and the plate. Thus the 


736 DYNAMICAL ELECTRICITY. [ 765 - 

current. works the relay of the post to which it is sent, and traces in 
blue, on a paper disc impregnated with ferrocyanide, the same series of 
points and marks as those on the perforated paper. 

765. Electrical clocks.— Electrical clocks are clockwork machines, 
in which an electromagnet, by means of an electric current regularly 
interrupted, is both the motor and the regulator. Fig. 593 represents 
the face of such a clock, and fig. 594 the mechanism, which works the 
needles. 



Fig. 593. 



Fig. 594. 


An electromagnet, B, attracts an armature of soft iron, P, moveable 
on a pivot, a. The armature P transmits its oscillating motion to a lever, 
s, which, by means of a ratchet, n, turns the wheel, A. This, by the 
pinion D, turns the wheel C, which by a series of wheels and pinions, 
moves the hands. The small one marks the hours, the large one the 
minutes; but as the latter does not move regularly, but by sudden starts 
from second to second, it follows that it may also be used to indicate the 
seconds. 

It is obvious that the regularity of the motion of the hands depends, 
on the regularity of the oscillations of the piece P. For this purpose, 
the oscillations of the current before passing into the electromagnet B, 
are regulated by a standard clock, which itself has been previously regu¬ 
lated by a seconds pendulum. At each oscillation of the pendulum the 
current is open and closed, and thus the armature P beats seconds exactly. 

To illustrate the use of these electrical clocks, suppose that on the 
railway from London to Birmingham each station has an electric dock, 






















ELECTRICAL CLOCKS. 


737 


-766] 


and that from the London station a conducting wire passes to all the 
clocks on the line V>iar as Birmingham. When the current passes in 
this wire all the clocks will simultaneously indicate the same hour, the 
same minute, and the same second; for electricity travels at the rate of 
about 190,000 miles in a second, so that it takes an inappreciable time 
to go from London to Birmingham. 

766. Electromagnetic machines. —Numerous attempts have been 
made to apply electromagnetism as a motive force in machines. Fig. 
595 represents a machine of this kind constructed by M. Froment. It 



Fig. 595. 


consists of four powerful electromagnets ABC I) fixed on an iron 
frame, X. Between these electromagnets is a system of two iron wheels 
moveable on the same horizontal axis, with eight soft iron armatures, M, 
on their circumference. 

The current arrives at K, ascends in the wire E, and reaches a metallic 























738 


DYNAMICAL ELECTRICITY. 


[ 767 - 

arc, 0, which serves to pass the current successively into each electro¬ 
magnet, so that the attractions exerted on the armatures M shall always 
be in the same direction. Now this can only be the case provided the 
current is broken in each electromagnet just when an armature comes in 
front of the axis of the bobbin. To produce this interruption the arc 0 
has three branches, e, each terminating with a steel spring, to which a 
small sheave is attached. Two of these establish the communication 
respectively with an electromagnet, and the third with two. On a 
central wheel, a , there are cogs, on which the sheaves alternately rest. 
Whenever one of them rests on a cog, the current passes into the corre¬ 
sponding electromagnet, but ceases to pass when there is no longer con¬ 
tact. On emerging from the electromagnets the current passes to the 
negative pole of the battery by the wi''e H. 

In this manner, the armatures M being successively attracted by the 
four electromagnets, the system of wheels which carries them assumes 
a rapid rotatory motion, which by the wheel P and an endless band is 
transmitted to a sheave Q, which sends it finally to any machine, a 
grinding mill for example. 

In his workshops M. Froment has an electromotive engine of one- 
horse power. But as yet these machines have not been applied in 
manufactures, for the expense of the acids and the zinc which they use 
very far exceeds that of the coal in steam-engines of the same force. Until 
some cheaper source of electricity shall have been discovered there is no 
expectationthat they can be applied at all advantageously. 


CHAPTER VI. 

INDUCTION. 

7G7. Induction by currents. —We have already seen (645J that 
under the name induction is meant the action which electrified bodies 
exert at a distance on bodies in the natural state. Hitherto we have 
only had to deal with electrostatical induction ; we shall now see that 
dynamical electricity produces analogous effects. 

Faraday discovered this class of phenomena in 1832, and he gave the 
name of currents of induction or induced currents to instantaneous currents 
developed in metallic conductors under the influence of metallic con¬ 
ductors traversed by electric currents, or by the influence of powerful 
magnets, or even by the magnetic action of the earth ; and the currents 
which give rise to them he has called inducing currents. 




INDUCTION. 


739 


- 768 ] 

The inductive action of currents at the moment of opening or closing 
may he shown by means of a bobbin with two wires. This consists (fig. 
596) of a cylinder of wood or of cardboard, on which a quantity of silk- 
covered No. 16 copper wire is coiled; on this is coiled a considerably 



Fig. 596. 


greater length of fine copper wire, about No. 35, also insulated by being 
covered with silk. This latter coil, which is called the secondary coil, is 
connected by its ends with two binding screws, a, b, from which wires 
pass to a galvanometer, while the thicker wire, the primary coil, is con¬ 
nected by its extremities with two binding screws, c and d. One of 
these, d, being connected with one pole of a battery, when a wire from 
the other pole is connected with c, the current passes in the primary coil, 
and in this alone. The following phenomena are then observed :— 

i. At the moment at which the thick wire is traversed by the current 
the galvanometer by the deflection of the needle indicates the existence 
in the secondary coil of a current inverse to that in the primary coil, that 
is in the contrary direction ; this is only instantaneous, for the needle 
immediately reverts to zero, and remains so long as the inducing current 
passes through cd. 

ii. At the moment at which the current is opened, that is, when the 
wire cd ceases to be traversed by a current, there is again produced in 
the wire ab an induced current instantaneous like the first, but direct , 
that is, in the same direction as the inducing current. 

768. Production of induced currents toy continuous ones.— 
Induced currents are also produced when a primary coil traversed by 
a current is approached to or removed from a secondary one: this may 
be shown by the following apparatus, fig. 597, in which B is a hollow 
coil consisting of a great length of fine wire, and A a coil consisting of 
a shorter and thicker wire, and of such dimensions that it can be placed 
in the secondary coil. The coil A being traversed by a current, if it is 


















740' 


DYNAMICAL ELECTRICITY. 


[769- 

suddenly placed in the coil B, a galvanometer connected with the latter 
indicates by the direction of its deflection the existence in it of an 
inverse current; this is only instantaneous, the needle rapidly returns to 
zero, and remains so long as the small bobbin is in the large one. If it 



is rapidly withdrawn, the galvanometer shows that the wire is traversed 
by a direct current. If instead of rapidly introducing or replacing the 
primary coil this is done slowly, the galvanometer only indicates a weak 
current, and which is the feebler the slower the motion. 

If instead of varying the distance of the inducing current its intensity 
be varied, that is either increased by bringing additional battery power 
into the circuit, or diminished by increasing the resistance, an induced 
current is produced in the secondary wire which is inverse if the intensity 
of the inducing current increases and direct if it diminishes. 

769. Conditions of induction. Xienz’s law.— From the experi¬ 
ments which have been described in the previous paragraphs the follow¬ 
ing principles may be deduced. 

I. The distance remaining the same a continuous and constant current 
does not induce any current in an adjacent conductor. 

II. A current at the moment of being closed produces in an adjacent con¬ 
ductor an inverse current. 

III. A current at the moment it ceases produces a direct current. 





































INDUCTION. 


741 


-770] 

IV. A current ivhich is removed or whose intensity diminishes, gives rise 
to a direct induced current . 

V. A current which is approached or whose intensity increases gives rise 
to an inverse induced current. 

VI. On the induction produced between a closed circuit and a current 
in activity when their relative distance varies, Lenz has based the 
following law, which is known as Lenz's law : 

If the relative position of two conductors A and B be changed, of which 
A is traversed by a current, a current is induced in B in such a direction, 
that by its electrodynamic action on the current in A, it would have imparted 
to the conductors a motion of the contrary kind to that by which the 
inducing action was produced. 

Thus, for instance, in V, when a current is approached to a conductor, an 
inverse current is produced; but two conductors traversed by currents in 
opposite directions, repel one another according to the received law of elec¬ 
trodynamics. Inversely when a current is moved away from a conductor 
a current of the same direction is produced; but two currents in the same 
direction attract one another. 

770. Inductive action of the Leyden discharge.— Figure 598 re¬ 
presents an apparatus devised by Matteucci, which is very well adapted 



-VVJAROIH. S .— =“ 


Fig. 598. 

for showing the development of induced currents produced either by the 
discharge of a Leyden jar or by the passage of a voltaic current. 

It consists of two glass plates about 12 inches diameter, fixed verti¬ 
cally on the two supports A and B. These supports are on moveable 
feet, and can either be approached or removed at will. On the anterior 
face of the plate A are coiled about 30 yards of copper wire, C, a milli¬ 
meter in diameter. The two ends of this wire pass through the plate, 
one in the centre, the other near the edge, terminating in two binding 









742 


DYNAMICAL ELECTRICITY. 


[ 771 - 

screws, like those represented in m and n , on the plate B. To these 
binding screws are attached two copper wires, c and d, through which 
the inducing current is passed. 

On the face of the plate B, which is towards A, is enrolled a spiral 
of much finer copper wire than the wire C. Its extremities terminate 
in the binding screws m and w, on which are fixed two wires, h and t, 
intended to transmit the induced current. The two wires on the plates 
are not only covered with silk, but each circuit is insulated from the 
next one by a thick layer of shellac varnish, a condition necessary in 
experimenting with statical electricity, which is always more difficult 
to insulate than that of the voltaic current, in consequence of its greater 
tension. 

In order to show the production of the induced current by the dis¬ 
charge of a Leyden jar, one end of the wire C is connected with the 
outer coating, and the other end with the knob of the Leyden jar, as 
shown in the figure. When the spark passes, the electricity traversing 
the wire C acts by induction on the neutral fluid of the wire on the 
plate B, and produces an instantaneous current in this wire. A person 
holding two copper handles connected with the wires i and h, receives a 
shock, the intensity of which is greater in proportion as the plates A and 
B are nearer. This experiment proves that frictional electricity can give 
rise to induced currents as well as voltaic electricity. 

The above apparatus can also be used to show the production of in¬ 
duced currents by the influence of voltaic currents. For this purpose 
the current of a battery is passed through the inducing wire C, while 
the ends of the other wire, h and i, are connected with a galvanometer. 
At the moment at which the current commences or finishes, or when the 
distance of the two conductors is varied, the same phenomena are ob¬ 
served as in the case of the apparatus (771). 

771. Induction by magnets.— It has been seen that the influence of 
a current magnetises a steel bar; in like manner a magnet can produce 
induced currents in metallic circuits. Faraday has shown this by means 
of a coil with a single wire of 200 to 300 yards in length. The two 
extremities of the wire being connected with the galvanometer, as shown 
in fig. 599, a strongly magnetised bar is suddenly inserted in the bobbin, 
and the following phenomena are observed : 

i. At the moment at which the magnet is introduced, the galvano¬ 
meter indicates in the wire the existence of a cnrrent, the direction of 
which is opposed to that which circulates round the magnet, considering 
the latter as a solenoid on Ampere’s theory (755). 

ii. When the bar is withdrawn, the needle of the galvanometer, 
which has returned to zero, indicates the existence of a direct current. 

The inductive action of magnets may also be illustrated by the follow- 


INDUCTION. 


743 



The same inductive effects are produced in the wires of an electro¬ 
magnet, if a strong magnet he made to rotate rapidly in front of the 
extremities of the wire in such a manner that its poles act successively 
by influence on the two branches of the electromagnet: or also by form¬ 
ing two coils round a horse-shoe magnet, and passing a plate of soft 
iron rapidly in front of the poles of the magnet; the soft iron becoming 
magnetic reacts by influence on the magnet, and induced currents are 
produced in the wire alternately in different directions. 

The inductive action of magnets is a striking confirmation of Ampere’s 
theory of magnetism. For as in this theory all magnets are solenoids, 
all the experiments which have been mentioned may be explained by 
the inductive action of currents which traverse the surface of magnets ; 
the induction of magnets is in short an induction of currents. And it is 
a useful exercise to see how on this view the inductive action of magnets 
falls under Lenz’s law (709). 

772. Inductive action of magnets on bodies in motion.— Arago 
was the first to observe, in 1824, that the number of oscillations which 
a magnetised needle makes in a given time, under the influence of the 
earth’s magnetism, is very much lessened by the proximity of certain 


- 772 ] 

ing experiment: a bar of soft iron is placed in the above bobbin and a 
strong magnet suddenly brought in contact with it; the needle of the 
galvanometer is deflected, but returns to zero when the magnet is 
stationary, and is deflected in the opposite direction when it is removed. 
The induction is here produced by the magnetisation of the soft iron bar 
in the interior of the bobbin under the influence of the magnet. 


Fig. 5C9. 







744. 


DYNAMICAL ELECTRICITY 


[772 


metallic masses, and especially of copper, which may reduce the number 
from 300 to 4. This observation led Arago in 1825, to an equally un¬ 
expected fact; that of the rotative action which a plate of copper in 
motion exercises on a magnet. 

This phenomenon may be shown by means of the apparatus represented 
in fig. 600. It consists of a copper disc, M, moveable about a vertical 



Fig. 600. 


axis. On this axis is a sheave, B, round which is coiled an endless cord 
passing also round the sheave A. By turning this with the hand, the 
disc M may be rotated with great rapidity. Above the disc is a glass 
plate, on which is a small pivot supporting a magnetic needle, ah. If the 
disc be now moved with a slow and uniform velocity, the needle is de¬ 
flected in the direction of the motion, and stops from 20° to 30° out of 
the direction of the magnetic meridian, according to the velocity of the 
rotation of the disc. But if this velocity increases, the needle is ulti¬ 
mately deflected more than 90°; it is then carried along, describes an 
entire revolution, and follows the motion of the disc until this stops. 

Babbage and Herschel modified Arago’s experiment by causing a 
horse-shoe magnet placed vertically to rotate below a copper disc sus¬ 
pended on silk threads without torsion; the disc rotated in the same 
direction as the magnets. 

The effect decreases with the distance of the disc, and varies with its 
nature. The maximum effect is produced with metals; with wood, 
glass, water, etc., it disappears. Babbage and Herschel have found that 
representing this action on copper at 100, the action on other metals is 
as follows: zinc 95, tin 46, lead 25, antimony 9, bismuth 2. Lastly, 
the effect is enfeebled if the disc presents breaks in the continuity, espe- 








INDUCTION. 


745 


-772] 

cially in tlie direction of the radii; but the same physicists have ob¬ 
served, that it virtually regains the same intensity if these breaks have 
been soldered with any metal. 

Faraday made an experiment the reverse of Arago’s first observation; 
since the presence of a metal at rest stops the oscillations of a magnetic 
needle, the neighbourhood of a magnet at rest ought to stop the motion 
of a rotating mass of metal. Faraday suspended a cube of copper to a 
twisted thread, which was placed between the poles of a powerful 
electromagnet. When the thread was left to itself it began to spin 
round with great velocity, but stopped the moment a powerful current 
passed through the electromagnet. 

Faraday was the first to give an explanation of all these phenomena 
of magnetism by rotation. They depend on the circumstance that a 
magnet or a solenoid can induce currents in a solid mass of metal. 
In the above case the magnet induces currents in the disc, when the 
latter is rotated; and conversely when the magnet is rotated while the 
disc is primarily at rest. Now these induced currents by their electro¬ 
dynamic action tend to destroy the motion which gave rise to them; 
they are simple illustrations of Lenz’s law; they act just in the same way 
as friction would do. 

i. For instance, let AB (fig. 601) be a needle oscillating over a copper 
disc, and suppose that in one of its oscillations it 
goes in the direction of the arrows from N to M. In 
approaching the point M, for instance, it developes 
there a current in the opposite direction, and which 
therefore repels it; in moving away from N it pro¬ 
duces currents which are of the same kind, and 
which therefore attract, and both these actions 
concur in bringing it to rest. 

ii. Suppose the metallic mass turns from N to¬ 
wards M, and that the magnet is fixed: the magnet will repel by induc¬ 
tion points such as N which are approaching A, and will attract M which 
is moving away j hence the motion of the metal stops, as in Faraday’s 
experiment. 

iii. If in Arago’s experiment the disc is moving from N to M; N ap¬ 
proaches A and repels it while M moving away attracts it j hence it moves 
in the same direction as the disc. 

If this explanation is true all circumstances which favour induction 
will increase the dynamic reaction, and those which diminish the former 
will also lessen the latter. We know that induction is greater in good 
conductors, and that it does not take place in insulating substances; but 
we have seen that the needle is moved with a force which is less, the 
less the conducting powers of the disc, and it is not moved when the disc 

K K 



DYNAMICAL ELECTRICITY. 


746 


[773 


is of glass. Dove has found that there is no induction on a tube split 
lengthwise in which a coil is introduced. 

In order to bring the oscillations of the needle of a galvanometer the 
%ire is coiled upon a copper frame. Such an arrangement is called a 
damper , and in practice it is frequently used. 

773. Induction by the action of the earth.— Faraday discovered 
that terrestrial magnetism can develope induced currents in metallic 
bodies in motion, acting like a powerful magnet placed in the interior of 
the earth in the direction of the dipping needle, or, according to the 
theory of Ampere, like a series of electrical currents directed from east 
to west parallel to the magnetic equator. He first proved this by placing 
a long helix of copper wire covered with silk, in the plane of the mag¬ 
netic meridian parallel to the dipping needle, by turning this helix 180° 
round an axis in its middle he observed that at each turn a galvano¬ 
meter connected with the two ends of the helix was deflected. The 
apparatus depicted in fig. 602, and known as Delezentie’s circle , serves 



Fig. 602 . 


for showing the existence of terrestrial induced currents. It consists of a 
wooden ring, RS, about two feet in diameter, fixed to an axis oi, about 
which it can be turned by means of a handle, M. The axis oi is itself 
fixed in a frame, PQ, moveable about a horizontal axis. By needles fixed 
to these two axes the inclination towards the horizon of the frame PQ 
and therefore of the axis oa , is indicated on a dial, b, while a second dial 
c, gives the angular displacement of the ring. This ring has a groove, in 
which is coiled a large quantity of insulated copper wire. The two ends of 
the wire terminate in a commutator analogous to that in Clarke’s apparatus 















INDUCTION. 


747 


-774] 

(779), the object of which is to pass the current always in the same 
sense, although its direction changes at each semi revolution of the ring. 
On each of the rings of the commutator are two brass plates, which suc¬ 
cessively transmit the current to two wires in contact with the galvano¬ 
meter. The axis oa being in the magnetic meridian, and the ring RS at 
right angles to the direction XY of the dipping needle, if it is slowly 
rotated the needle of the galvanometer is deflected, and by its deflec¬ 
tion indicates in the wire coiled on the ring an induced current whose 
intensity increases until it has been turned through 90°; the deviation 
then decreases, and is zero when the ring has made a semi revolution. If 
the rotation continues the current reappears but in a contrary direction, 
and attains a second maximum at 270°; becoming null again after 
a complete turn. When the axis oa is parallel to the dip there is no 
current. 

774. Induction of a current on itself. Extra current,— If a 

j closed circuit traversed by a voltaic current be opened, a scarcely per¬ 
ceptible spark is obtained, if the wire joining the two poles be short. 
Further, if the observer himself form part of the circuit by holding a 
pole in each hand, no shock is perceived unless the current is very 
intense. If, on the contrary, the wire is long, and especially if it makes a 
great number of turns, so as to form a bobbin with very close folds, the 
spark, which is inappreciable when the current is closed, acquires a great 
intensity when it is opened, and an observer in the circuit receives a 
shock which is the stronger the greater the number of turns. 

Faraday has referred this strengthening of the current when it is 
broken, by an inductive action which the current in each coil exerts 
upon the adjacent coils; an action in virtue of which there is produced 
in the bobbin a direct induced current, that is, one in the same direction 
as the principal one. This is known as the extra current. 

To show the existence of this current, at the moment of opening, 
Faraday has arranged the experiment as seen in fig. 603. Two wires 
from the poles of a battery are connected with two binding screws D 
and F, with which are also connected the two ends of a bobbin B with a 
long fine wire. On the path of the wires at the points A and 0 are two 
other wires which are connected with a galvanometer G. Henee the 
current from the pole E branches at A into two currents, one which 
traverses the galvanometer, the other the bobbin, and both joining the 
negative pole E'. 

The needle of the galvanometer being then deflected by the current 
which goes from A to C, it is brought back to zero, and kept there by 
an obstacle which prevents it from turning in the direction Ga, but 
leaves it free in the opposite direction. On breaking contact at E, it is 
seen that the moment the circuit is open the needle is deflected in the 

k k 2 





748 


DYNAMICAL ELECTRICITY. 


[ 775 - 


direction G«'; showing a current contrary to that which passed during 
the existence of the current, that is from C to A. But the battery current 
having ceased, the only remaining one is the current AFBDCA, and 



Fig. 603. 

since in the part CA the current goes from C to A, it must traverse the 
entire circuit in the direction AFBDG, that is the same as the principal 
current. This current, which thus appears when the circuit is opened, 
is the extra cwrent. 

775. Extra current on opening: and on closing:. —The coils of the 
spiral act inductively on each other, not merely on opening but also on 
closing the current. Here in accordance with the general law of induc¬ 
tion, each spire acting on each succeeding one, induces a current in the 
opposite direction to its own, that is an inverse current; this, which is 
the extra current on closing or the inverse extra current , being of contrary 
direction to the principal one, diminishes its intensity, and lessens or 
suppresses the spark on closing. 

When, however, the current is opened, each spire then acts induc¬ 
tively on each succeeding one, producing a current in the same direction 
as its own, and which therefore greatly heightens the intensity of the 
principal current. This is the extra current on opening, or direct extra 
current. 

To observe the direct extra current, the conductor on which its effect 
is to be traced may be introduced into the circuit, by being connected in 
any suitable manner with the binding screws A and C in the place of the 
galvanometer. 

It can thus be shown that the direct extra current gives violent shocks, 
bright sparks, decomposes water, melts platinum wire, and magnetises 
steel needles. Abria has found that the intensity of the extra current 






INDUCED CURRENTS. 


749 


- 777 ] 

is about 0-72 of the principal current. The shock produced by the 
current may be tried by attaching the ends of the wire to two files, which 
are held in the hands. On moving the point of one file over the teeth of 
the other a series of shocks is obtained, due to the alternate opening and 
closing of the current. 

The above effects acquire greater intensity when a bar of soft iron is 
introduced into the bobbin, or, what is the same thing, when the current 
is passed through the bobbin of an electromagnet; and still more is this 
the case if the core, instead of being massive, consists of a bundle of 
straight wires. Faraday explains this strengthening action of soft iron 
as follows : If inside the spiral there is an iron bar, when on opening the 
circuit the principal current disappears, the magnetism which it evokes 
in the bar disappears too ; but the disappearance of this magnetism acts 
like the disappearance of the electrical current, the disappearing mag¬ 
netism induces a current in the same direction as the disappearing prin¬ 
cipal current, the effect of which is thus heightened. 

In the experiments j ust described the effects of the two extra currents 
accompany those of the principal current. Edlund has devised an 
ingenious arrangement of apparatus by which the action of the principal 
current on the measuring instruments can be completely avoided, so that 
only that of the extra current remains. In this way he has arrived at 
the following laws: 

i. The intensity of the currents used being the same, the extra-currents 
obtained on opening and closing have the same electromotive force. 

ii. The electromotive force of the extra-current is proportional to the 
intensity of the primary current. 

776. Induced currents of different orders.— Spite of their instan¬ 
taneous character, induced currents can themselves, by their action on 
closed circuits, give rise to new induced currents, these again to others, 
and so on, producing induced currents of different orders. 

These currents, discovered by Henry, may be obtained by causing to 
act on each other a series of bobbins, each formed of a copper wire covered 
with silk, and coiled spirally in one plane, like that represented in the 
plate A, in fig. 597. The currents thus produced are alternately in op¬ 
posite directions, and their intensity decreases in proportion as they are of 
a higher order. 

777. Properties of induced currents. —Notwithstanding their 
instantaneous character, it appears from the preceding experiments 
that induced currents have all the properties of ordinary currents. 
They produce violent physiological, luminous, calorific, and chemical 
effects, and finally give rise to new induced currents. They also deflect 
the magnetic needle, and magnetise steel bars when they are passed 
through a copper wire coiled in a helix round the bars. 


750 


DYNAMICAL ELECTRICITY. 


[ 778 - 

The intensity of the shock produced by induced currents renders 
their effects comparable to those of electricity in a state of tension. But 
as they act on the galvanometer the electricity is present both in a 
state of tension and in the dynamical condition. 

The direct induced current and the inverse induced current have been 
compared as to three of their actions: the violence of the shock, the 
deflection of the galvanometer, and the magnetising action on steel 
bars. In these respects they differ greatly: they are about equal in 
their action on the galvanometer; but while the shock of the direct 
current is very powerful, that of the inverse current is scarcely percepti¬ 
ble. The same difference prevails with reference to the magnetising 
force. The direct current magnetises to saturation, while the inverse 
current does not magnetise. 

778. X>aws of induced currents.— In his special treatise on induc¬ 
tion, Matteucci has deduced from his own researches, and from those of 
Faraday, Lenz, Dove, Abria, Weber, Marianini, and Felici, the following 
laws in reference to induced currents : 

i. The intensity of induced currents is proportional to that of the inducing 
currents. 

ii. This intensity is proportional to the product of the length of the inducing 
and induced currents. 

iii. The electromotive force developed by a given quantity of elec¬ 
tricity is the same whatever be the nature , section , or shape of the inducing 
circuit. 

iv. The electromotive force developed by the induction of a current 
on any given conducting circuit is independent of the nature of the con¬ 
ductor. 

v. The development of induction is independent of the nature of the 
insulating body interposed between the induced and inducing circuit. 

This latter law is in disaccord with the experiments of Faraday, on 
the induction of statical electricity (648). 


APPARATUS POUNDED ON INDUCTION. 

779. IVffagrneto-electrical apparatus.— After the discovery of mag¬ 
neto-electrical induction, several attempts were made to produce an 
uninterrupted series of sparks by means of a magnet. Apparatus for 
this purpose were devised by Pixii and Ritchie, and subsequently by 
Saxton, Ettingshausen, and Clarke. Fig. 604 represents that invented 
by Clarke. It consists of a powerful horse-shoe magnetic battery, A, 
fixed against a vertical wooden support. In front of this there are two 
bobbins BB', moveable round a horizontal axis. These bobbins are coiled 


APPARATUS FOUNDED ON INDUCTION. 


751 


-779J 

on two cylinders of soft iron joined at one end by a plate of soft iron, V, 
and at the other by a similar plate of brass. These two plates are fixed 
on a copper axis, terminated at one end by a commutator, qi, and at 
the other by a pulley, which is moved by an endless band passing round 
a large wheel, which is turned by a handle. 



Fig. 604. 


Each bobbin consists of about 1,500 turns of very fine copper wire 
covered with silk. One end of the wire of the bobbin B is connected on 
the axis of rotation with one of the wires of the bobbin B', and the two 
other ends terminate in a copper ferrule or washer, q, which is fixed to 
the axis, but is insulated by a cylindrical envelope of ivory. In order 
that in each wire the induced current may be in the same direction, it 
is coiled on the two bobbins in different directions, that is, one is 
right-handed the other left-handed. 

When now the electromagnet turns, its two branches become alter¬ 
nately magnetised in contrary directions under the influence of the 
magnet A, and in each wire an induced current is produced, the direction 
of which changes at each half turn. 













752 


DYNAMICAL ELECTRICITY. 


[779- 

Let us follow one of the bobbins, B for instance, while it makes a 
complete revolution in front of the poles a and b of the magnet ; calling 
the poles of the electromagnet successively a' and V. Let us further con¬ 
sider the latter when it passes in front of the north pole of the magnetic 
battery (fig. 606). The iron has then a south pole in which as we know the 
Amperian currents move like the hands of a watch. The contrary seems 
to be represented by fig. 606, but it must be remembered that the bobbins 


Fig. 606. Big. 607. 



are seen here as they are in fig. 604 ; and hence it is, when viewed at the 
end which grazes the magnet, that the Amperian currents seem to turn like 
the hands of a watch. These currents act inductively on the wire of the 
bobbin, producing a current in the same direction, for the bobbin moves 
away from the pole a , its soft iron is demagnetised, and the Ampdrian 
currents cease (769). The intensity of the induced current in the bobbin 
decreases, until the right line joining the axes of the two bobbins is 
perpendicular to that which joins the poles a and b of the bar. There 
is now no magnetism in the bar, but quickly approaching the pole b , its 
soft iron is then magnetised in the opposite direction, that is it becomes a 































APPARATUS FOUNDED ON INDUCTION. 


753 


- 780 ] 

north pole (fig. 607). The Amperian currents are then in the direction of 
the arrow a'; and as they are commencing, they develope in the wire of the 
bobbin an inverse current (769), which is in the same direction as that 
developed in the first quarter of the revolution. Moreover, this second 
current adds itself to the first, for while the bobbin moves away from «, 
it approaches b. Hence during the lower half revolution from a to b, 
the wire was successively traversed by two induced currents in the 
same direction, and if the rotatory motion is sufficiently rapid, we 
might admit during this half revolution, the existence of a single current 
of the wire. 

The same reasoning applied to the figures 608 and 609 will show that 
during the upper half revolution the wire of the bobbin B is still 
traversed by a single current, but in the opposite direction to that of the 
lower half revolution. What has been said about the bobbin B applies 
obviously to the bobbin B'; yet as one of these is right-handed and the 
other left-handed, during each upper or lower half revolution the 
currents are constantly in the same direction in the two bobbins. At 
each successive half revolution, they both change, but are in the same 
direction as regards each other. 



Fig. 610 . 

780. Commutator. —The object of this apparatus (fig. 610) of which 
fig. 611 is a section, is to bring the two alternative currents always in 
the same direction. It consists of an insulating cylinder of ivory or 


















754 DYNAMICAL ELECTRICITY. [ 780 - 

ebony, J, in the axis of which is a copper cylinder K, of smaller diameter, 
fixed to the armature, V, and turning with the bobbins. On the ivory 
cylinder is first a brass ferrule, q, and in front of it two half ferrules, o 
and o', also of brass and completely insulated from one another. The half 

ferrule o is connected 
with the ferrule q, by a 
tongue x. On the sides 
of a Mock of wood, M, 
there are two brass 
plates, m n, on which 
are screwed two elastic 
springs, b and «?, which 
press successively on 
the half ferrules o and 
o', when rotation takes 
place. 

We have already 
seen that the two ends of the wire of the bobbin, those in the same 
direction, terminate in the metallic axis k , and therefore on the half 
ferrule o '; while the two other ends, both in the same direction, are joined 
to the ferrule q and therefore to the half ferrule o. Finally the pieces o o r 
are constantly poles of alternating currents which are developed in the 
bobbins, and as these are alternately in contrary directions, the pieces 
o and o' are alternately positive and negative. Now taking the case in 
which the half ferrule o' is positive, the current descends by the plate b , 
follows the plate m, arrives at n by the joining wire p, ascends in e, and 
is closed by contact with the piece o • then when in consequence of 
rotation o takes the place of o', the current retains the same direction, 
for as it is then reversed in the bobbins, o has become positive, and o' 
negative, and so forth as long as the bobbin is turned. 

With the two springs b and c alone, the opposite currents from the 
two pieces o and o' could not unite ; this is effected by means of a third 
spring, a (fig. 604), and of two appendices, t, only one of which is visible 
in the figure. These two pieces are insulated from one another on an 
ivory cylinder, but communicate respectively with the pieces o and o'. 
As often as the plate a touches one of these pieces it is connected with 
the spring b, and the current is closed, for it passes from b to a, and then 
reaches the spring c by the plate n. On the contrary, as long as the 
spring a does not touch one of these appendices the current is broken. 

For physiological effects the use of the plate a , greatly increases the 
intensity of the shocks. For this purpose two long spirals of copper wire 
with handles p and p', are fixed at n and m. Holding the handles in the 
hands so long as the plate a does not touch the appendices i, the current 

























APPARATUS FOUNDED ON INDUCTION. 


755, 


- 780 ] 

passes through the body of the experimenter, but without appreciable 
effect ; while each time that the plate a touches one of the appendices i, 
the current, as we have seen above, is closed by the pieces b, a, and c, and 
ceasing then to pass through the wires np, mp' } there is produced in this 
and through the body a direct extra current which produces a violent 
shock. 

This is renewed at each semi-revolution of the electromagnet, and its 
intensity increases with the velocity of the rotation. The muscles con¬ 
tract with such force that they do not obey the will, and the two hands 
cannot be detached. With a well-constructed apparatus of large 
dimensions a continuance of the shock is unendurable; the person re¬ 
ceiving it is prostrated, rolls on the ground, and is soon completely at the 
mercy of the operator. 

All the effects of voltaic currents may be produced by the induced 
currents of Clarke’s machine. Figure 605 shows how the apparatus is 



Fig. 612. Fig. 613. 


to be arranged for the decomposition of water. The spring is sup¬ 
pressed, the current being closed by the two wires which represent the 
electrodes. 

For physiological and chemical effects, the wire rolled on the bobbins 
is fine, and each about 500 to 600 yards in length. For physical effects, 
on the contrary, the wire is thick, and they are about 25 to 35 yards on 
each bobbin. Figures 612 and 613 represent the arrangement of the 
bobbins and the commutator in each case. The first represents the in¬ 
flammation of ether, and the second the incandescence of a metallic wire, 
o, in which the current from the plate, o, to the plate c, always passes 
in the same direction. 

Pixii’s and Saxton’s electromagnetic machine differs from Clarke’s in 
having the electromagnet fixed while the magnet rotates. 

Wheatstone has recently devised a compendious form of the magneto¬ 
electrical machine, for the purpose of using the induced spark in firing 
mines (689). 


75 G 


DYNAMICAL ELECTRICITY. 


[ 781 - 

781. IVXagneto-electrical machine.— The principle of Clarke’s ap¬ 
paratus has received in the last few years a remarkable extension in 
large magneto-electrical machines, by means of which mechanical 
work is transformed into powerful electric currents by the inductive 
action of magnets on bobbins in motion. 



Fig. 614. 


The first machine of this kind was invented by Nollet, in Brussels, in 
1850; this has been greatly improved by Van Malderen, who has also 
applied it to electrical illumination. 



















MAGNETO-ELECTRICAL MACHINE. 


757 


- 781 ] 

This machine is represented in fig 614, as it stands in a workshop 
at the Hotel des Invalides, in Paris, where it was constructed. One of 
these machines was exhibited in the International Exhibition of 1862. It 
consists of a cast-iron frame, 5^ feet in height, on the circumference of 
which 8 series of five powerful horse-shoe magnetic batteries, A, A, A . . 
are arranged in a parallel order on wooden cross pieces. These batteries, 
each of which can support from 120 to 130 pounds, are so arranged, that 
if they are considered either parallel to the axis of the frame, or in a 
plane perpendicular to this axis, opposite poles always face one another. 
In each series, the outside batteries consist of three magnetised plates, 
while the three middle ones have six plates, because they act by both 
faces, while the first only act by one. 

On a horizontal iron axis going from one end to the other of the frame, 
four bronze wheels are fixed, each corresponding to the intervals between 
the magnetic batteries of two vertical series. There are 16 bobbins on 
the circumference of each of these, that is, as many as there are magnetic 
poles in each vertical series of magnets. These bobbins, represented in 
figure 616, differ from those of Clarke’s apparatus in having, instead of a 
single wire, 12 wires each, 11£ yards in length, by which the resistance 
is diminished. The coils of these bobbins are insulated by means of 
bitumen dissolved in oil of turpentine. These are not rolled upon 
solid cylinders of iron, but on two iron tubes, slit longitudinally, so as to 
render the magnetisation and demagnetisation more rapid when the 
bobbins pass in front of the poles of the magnet. Further, the discs of 
copper which terminate the bobbins are divided in the direction of the 
radius, in order to prevent the formation of induced currents in these 
discs. The four wheels being respectively provided with 16 bobbins 
each, there are altogether 64 bobbins arranged in 16 horizontal series of 
four, as seen at D, on the left of the frame. The length of the wire on 
each bobbin being 12 times 11 \ yards, or 138 yards j the total length in 
the whole apparatus is 64 times 138 yards, or 8832 yards. 

The wires are coiled on all the bobbins in the same direction, and not 
only on the same wheel, but on all four, all wires are connected with one 
another. For this purpose the bobbins are joined, as shown in figure 
615 j on the first wheel the twelve wires of the first bobbin, x , are con¬ 
nected on a piece of mahogany fixed on the front face of the wheel, with 
a plate of copper, m, connected by a wire, 0, with the centre of the axis, 
which supports the wheels. At the other end, on the other face of the 
wheel, the same wires are soldered to a plate indicated by a dotted line 
which connects them with the bobbin y; from this they are connected 
with the bobbin 3 by a plate i, and so on, for the bobbins t, u ... up to 
the last, v. The wires of this bobbin terminate in a plate, w, which 
traverses the first wheel, and is soldered to the wires of the first bobbin 


758 


DYNAMICAL ELECTRICITY. 


[ 781 - 


of the next wheel, on which the same series of connections is repeated; 
these wires pass to the third wheel, thence to the fourth, and so on, to 
the end of the axis. 

The bobbins being thus arranged, one after another, like the elements 
of a battery connected in a series (715), the electricity has a high 
tension. But the bobbins may also be arranged by connecting the plates 
alternately, not with each other, but with two metallic rings, in such a 



Fig. 615. 


Fig. 616. 


manner that all the ends of the same name are connected with the same 
ring. Each of these rings is then a pole, and this arrangement may be 
used where a high degree of tension is not required. 

From these explanations it will be easy to understand the manner in 
which electricity is produced and propagated in this apparatus. An 
endless band receiving its motion from a steam engine passes round a 
pulley fixed at the end of the axis which supports the wheels and the 
bobbins, and moves the whole system with any desired rapidity. Expe¬ 
rience has shown that to obtain the greatest degree of light, the most 
suitable velocity is 235 revolutions in a minute. During this rotation, if 
we at first consider a single bobbin, the tube of soft iron on which it is 
coiled, in passing in front of the poles of the magnet, undergoes at its 
two ends an opposite induction, the effects of which are added, but 
change from one pole to another. As these tubes, during one rotation, 
pass successively in front of sixteen poles alternately of different names, 
they are magnetised eight times in one direction, and eight times in the 
opposite direction. In the same time there are thus produced in the 
bobbin eight direct induced currents, and eight inverse induced currents; 
in all, sixteen currents in each revolution. With a velocity of 235 turns 
in a minute, the number of currents in the same time is 235 X 19=37560 
alternately in opposite directions. The same phenomenon is produced 
with each of the 64 bobbins; but as they are all coiled in the same 
direction, and are connected with each other, their effects accumulate, 
and there is the same number of currents, but they are more intense. 


MAGNETO-ELECTRICAL MACHINE. 


759 


- 781 ] 

To utilise these currents in producing an intense electric light, the 
communications are made as shown in figure 617. On the posterior side 
the last bobbin, x of the fourth wheel terminates by a wire, G, on the 
axis MN, which supports the wheels: the current is thus conducted to 
the axis, and thence over all the machine, so that it can be taken from t 
any desired point. In the front the first bobbin, x , of the first wheel 
communicates by the wire O, not with the axis itself, but with a steel 
cylinder, c, fitted in the axis, from which, however, it is insulated by an 
ivory collar. The screw e , to which the wire 0 is attached, is likewise 
insulated by a piece of ivory. From the cylinder c the current passes to 
a fixed metallic piece, K, from which it passes to the wire H, which 



transmits it to the binding screw, a, of fig. 614. The binding screw b 
communicates with the framework, and therefore with the wire of the 
last bobbin, x' (fig. 617). From the two binding screws, a and b, the 
current is conducted by means of two copper wires to two charcoals, 
the distance of which is regulated by means of an apparatus analogous in 
principle to that already described (720). 

In this machine the currents are not rectified so as to be in the same 
direction, hence each carbon is alternately positive and negative, and in 
fact they are consumed with equal rapidity. Experiment has shown 
that when these currents are applied to produce the electric light, it is 
not necessary they should be in the same direction ; but when they are 
to be used for electrometallurgy or for magnetising they must be rectified, 
which is effected by means of a suitable commutator. 

The light produced by the magneto-electrical machine is very intense •, 
with a machine of four wheels the light obtained is equal to that of 150 
Carcel lamps. A machine [of six wheels gives a light equal to 200 
Carcel lamps. 

Serrin has constructed a new regulator for this light, which, like the 
older ones, brings the charcoals together in proportion as they become 
used j and further removes them when they are in contact. It contains 
























DYNAMICAL ELECTRICITY. 


760 


[ 782 - 


no clockwork motion, and is worked by the weight of one of its 
pieces. 

This light, which requires no other expenditure than that of a single 
horse power to turn the coils when there are not more than four of them, 
. is advantageously used for signalling by night on large vessels, and for 
lighthouses. 

One of these, constructed by Holmes, is now in use at the South 
Foreland lighthouse. 

782. Siemens’ armature. —Siemens has devised an armature or bobbin 
for magneto-electrical machines in which the insulated wire is wound 
longitudinally on the core, instead of transversely, as is usually the case. 

It consists of a soft iron cylinder AB (fig. 618) from one foot to three feet 
in length, according to circumstances. 



Fig. 618 . 


r A deep groove is cut on the outer length of this core and on the ends, in 
which is coiled the insulated wire as in a multiplier. To the two ends 
of the cylinder brass discs E and D are secured. With E is connected a 
commutator C, consisting of two pieces of steel insulated from each other, 
and connected respectively with the two ends of the wire. On the other 
disc is a pulley round which passes a cord, so that the bobbin moves very 
rapidly on the two pivots. 

When a voltaic current circulates in the wire, the two cylindrical 
segments, A and B, are immediately magnetised, one with one polarity 
and the other with the opposite. On the other hand, if, instead of 
passing a voltaic current through the wire of the bobbin, the bobbin 
itself be made to rotate rapidly between the opposite poles of magnetised 
masses as the segments A and B become alternately magnetised and demag¬ 
netised, their induction produces in the wire a series of currents alter¬ 
nately positive’and negative, as in Clarke’s apparatus (779). When these 
currents are collected in a commutator which adjusts them, that is, sends 
all the positive currents on one spring and all the negative on another, 
these springs become electrodes, from one of which positive electricity 
starts and from the other negative. If these springs are connected by a 
conductor, the same effects are obtained as when the two poles of a 
battery are united. 

Siemens has constructed magneto-electrical machines in which this 
armature is utilised. It has the great advantage that a large number of 







wild’s magneto-electrical machine. 


7G1 


- 783 ] 


small magnets may be used instead of one large one. As, weight for 
weight, the latter possess greater magnetic force than the former, they 
can be made more economically. And as the armature is always 



Fig. 619. 

very near the magnets it receives greater momentum, and is more rapidly 
changed. 

783. Wild s magneto-electrical machine. —Mr. ild has recently 













762 DYNAMICAL ELECTRICITY. [ 783 - 

constructed a magneto-electrical machine, in which Siemens’ armature is 
used along with a new’principle—that of the multiplication of the current. 
Instead of utilising directly the current produced by the induction of 
magnet, Mr. Wild passes it into a strong electromagnet, and by the 
induction of this latter a more energetic current is obtained. 

This machine consists first of a battery of 12 to 16 magnets, each ol 
which weighs about 3 pounds, and can support about 20 pounds. Between 
the poles of the magnets two soft iron keepers, CC, are arranged, separated 





Fig. 620. Fig. 621. 

by a brass plate 0. These three pieces are joined by bolts, and the whole 
compound keeper is perforated longitudinally by a cylindrical cavity, in 
which works a Siemens’ armature n, about 2 inches in diameter. The wire 
of this armature terminates in a commutator, which leads the positive 
and negative currents to two binding screws, a and b. This commutator 
is represented on a larger scale in figure 621. At the other end is a pulley 
by which the armature can be turned at the rate of 25 turns in a second. 
The wire on the armature is 20 yards long. 

Below the support for the magnets and their armatures are two large 
electromagnets BB. Each consists of a rectangular soft iron plate, 
36 inches in length by 26 in breadth and 1£ inches thick, on which are 
coiled about 1600 feet of insulated copper wire. The wires of these 
electromagnets are joined at one end, so as to form a single circuit of 
3200 feet. One of the other ends is connected with the binding screw 
a and the other with b. At the top the two plates are joined by a 
transverse plate of iron so as to form a single electromagnet. 

At the bottom of the electromagnets BB are two iron armatures 
separated by a brass plate O, and in the entire length is a cylindrical 
channel in which works a Siemens’ armature as above; this armature, 
however, is above a yard in length, nearly 6 inches in diameter, and its 
wire is 100 feet long. The ends are connected with a commutator, from 
























— 784 ] ladd’s dynamomagnetic machine. 763 

which the adjusted currents pass to two wires r and s. The armature 
m is rotated at the rate of 1700 turns in a minute. 

Fig. 620 shows on a larger scale a cross section of the bobbin, m, of 
the armatures, CC, and of the plates, AA, on which is coiled the wire of 
the electromagnets BB. 

These details being premised, the following is the working of 
the machine. When the armatures a and m are rotated by means 
of a steam engine with the velocity mentioned, the magnets produce in 
the first armature induced currents which, adjusted by the commutator, 
pass into the electromagnet, BB, and magnetise it. But as these impart 
to the lower armatures, CC, opposite polarities, the induction of these 
latter produces in the armature m, a series of positive and negative 
currents far more powerful than those of the upper armature ; so that 
when these are adjusted by a commutator and directed by the wires rand 
s, very powerful effects are obtained. 

These effects are still further intensified if, as Mr. Wild has done, the 
adjusted current of the armature m, is passed into a second electric 
magnet whose armatures surround a third and larger Siemens’ armature 
turning with the two others. A current is thus obtained which melts an 
iron wire a foot long and more than 2 inches in diameter. 

784. Iiadd's dynamomagnetic machine. —Mr. Ladd, philosophical 
instrument maker in Regent Street, has invented a very remarkable 
dynamomagnetic machine. Like that of Wild it consists of two 
Siemens’ armatures, rotating with great velocity, and of two iron plates 
A A (fig. 622), surrounded by an insulated copper wire. Ladd’s machine 
differs from that of Wild in the following respects. 

1. There are no permanent magnets; 2nd, the electromagnets BB are 
not joined so as to form a single electromagnet, but are two distinct 
electromagnets, each having at the end two armatures, CC', in which 
are contained Siemens’ armatures m and n ; the current of the armature 
n passing the electromagnets reverts to itself in this armature. This 
return of the current upon itself is an essential feature of the machine, 
it is an application of a principle announced simultaneously by Mr. 
Wheatstone and by Mr. Siemens. The wire of the armature m is in¬ 
dependent, and passes into the apparatus which is to utilise the current, 
for instance two carbon points, 1). 

The machine being thus arranged, no effect is produced so long as the 
armatures CC' are not magnetised, but if a voltaic current be passed 
once for all through the electromagnets BB, it magnetises the plates AA 
and their keepers, which by their reciprocal action retain a quantity of 
remanent magnetism sufficient to work the machine. If, then, the 
armatures m and n be rotated by means of two bands passing round a 
common drum, the magnetism of the armatures CC' acting upon the 
armature n, excites induction currents, which, adjusted by a commutator, 


764 


DYNAMICAL ELECTRICITY. 


[ 784 - 

passes into the electromagnets BB', and more strongly magnetises the 
armatures CO'. These in their turn leacting more powerfully on the 
armature n , strengthen the current; we thus see, that n and B continually 
and mutually strengthen each other as the velocity of the rotation increases. 
Hence as the iron of the armature, m, becomes more and more strongly 
magnetised under the influence of the electromagnets BB, a gradually 
more intense induced current is developed in this armature, which is 
directed, adjusted or not, according to the use for 'which it is designed. 


Fig. 622 . 

In a machine which Mr. Ladd exhibited at the Paris Exhibition of 
1867 the plates AA were "only 24 inches in length by 12 inches in 
diameter. With these small dimensions the current is equal to 25 to 30 
Bunsen’s cells. It can work the electric light and keep incandescent 
a platinum wire a metre in length and 0*5 mm. in diameter. 

The above form of the machine is worked by power. Mr. Ladd has 
devised a more compact form, which may be worked by hand. This is 
represented in fig. 622. The two armatures of the former are combined 
in one, and the coils are wound on it at right angles to each other, as 
shown in the figure. The current from this can raise to white heat 
18 inches of platinum wire OOl in. thickness, and with an inductorium 
containing 3 inches on the secondary wire 2 in. sparks can be obtained. 














ruhmkorff’s coil. 


765 


- 785 ] 

Both Ladd’s and Wild’s machines are liable to the objection of re¬ 
quiring to be rotated at a rate which cannot be kept up during 
several hours. The armatures become heated by the repeated develop¬ 
ment of induction currents, the magnetism is weakened, and therewith 
the intensity of the current. Before they can be applied industrially, 
their velocity must be reduced, either by multiplying the number of 
Siemens’ armatures or modifying their arrangement. 



Fig. 623. 


In any case they furnish a remarkable instance of the transformation 
of mechanical force into electricity, light and heat (247, 291) 

785. Xnductorium. Ruhmkorff’s coil.— These are arrangements for 
producing induced currents, in which a current is induced by the action 
of an electric current, whose circuit is alternately opened and closed in 
rapid succession. These instruments, known as inductoriums or induction 
coils, present considerable variety in their construction, but all consist 
essentially of a hollow cylinder, in which is a bar of soft iron, or bundle 
of iron wires, with two helices coiled round it, one connected with the 
poles of a battery, the current of which is alternately opened and closed 
by a self-acting arrangement, and the other serving for the development 
of the induced current. By means of these apparatus, with a current of 
three or four Grove’s cells, physical, chemical, and physiological effects are 
produced equal to and superior to those obtainable with electrical ma¬ 
chines and even the most powerful Leyden batteries. 

Of all the forms those constructed by Ruhmkorff are the most powerful. 
Fig. 624 is a representation of one, the coil of which is about 14 inches 
in length. The primary or inducing wire is of copper, and is about 2mm. 












766 


DYNAMICAL ELECTRICITY. 


[ 785 - 


in diameter, and 4 or 5 yards in length. It is coiled directly on a cylin¬ 
der of cardboard, which forms the nucleus of the apparatus, and is enclosed 
in an insulating cylinder of glass, or of caoutchouc. On these is coiled 
the secondary or induced wire, which is also of copper, and is about fmm. 
in diameter. A great point in these apparatus is the insulation. The 



Pig. 624. 

wires are not merely insulated by being in the first case covered with silk, 
but each individual coil is separated from the rest by a layer of melted 
shellac. The length of the secondary wire varies greatly; in some of 
RuhmkorfFs largest sizes it is as much as 60 miles. With these great 
lengths the wire is thinner, about |mm. The thinner the wire the greater 
the tension of the induced electricity. 

The following is the working of the apparatus. The current arriving 
by the wire P at a binding screw, a , passes thence into the commutator, 
C, to be afterwards described (fig. 625), thence by the binding screw, b, 
it enters the primary wire, where it acts inductively on the secondary 
wire ; having traversed the primary wire it emerges by the wire s. 

* Following the direction of the 


arrows, it will be seen that the 
current ascends in the binding 
screw, i, reaches an oscillating 
piece of iron, o, called the ham¬ 
mer , descends by the anvil, h , 
and passes into a copper plate, 
K, which takes it to the com¬ 
mutator, C. It goes from there 
to the binding screw, c, and 
finally to the negative pole of 
the battery by the wire N. 

Fig. 625. The current in the primary 

wire only acts inductively on 
the secondary wire (767), when it opens or closes, and hence it must be 





















CONDENSER. 


767 


- 786 ] 

constantly interrupted. This is effected by means of the oscillating 
hammer o (fig. 625). In the centre of the bobbin is a bundle of soft iron 
wires, forming together a cylinder a little larger than the bobbin, and 
thus projecting at the end as seen at A. When the current passes in the 
primary wire, this hammer o is attracted; but, immediately, there being 
no contact between o and k, the current is broken, the magnetisation 
ceases, and the hammer falls; the current again passing, the same series 
of phenomena recommences, so that the hammer oscillates with great 
rapidity. 

786. Condenser. —In proportion as the current passes thus inter¬ 
mittently in the primary wire of the bobbin, at each interruption an in¬ 
duced current, alternately direct and inverse, is produced in the secondary 
wire. But as this is perfectly insulated, the current acquires such an 
intensity as to produce very powerful effects. Fizeau has increased this 
intensity by interposing a condenser in the induced circuit. As con¬ 
structed by Ruhmkorff, for his largest apparatus, this consists of 150 sheets 
of tinfoil about 18 inches square, so that the total surface is about 75 square 
yards. These sheets being joined are coiled on two sides of a sheet of 
oiled silk, which insulates them, forming thus two armatures, they are 
then coiled several times round each other, so that the whole can be 
placed below the helix in the base of the apparatus. One of these arma¬ 
tures, the positive, is connected with the binding screw, i, which receives 
the current on emerging from the bobbin; and the other, the negative, is 
connected with the binding screw, m, which communicates by the plate 
K with the commutator C, and with the battery. 

To understand the effect of the condenser, it must be observed that at 
each break of the inducing current an extra current is produced in the 
same direction, which, continuing in a certain manner, prolongs its dura¬ 
tion. It is this extra current which produces the spark that passes at 
each break between the hammer and the anvil; when the current is 
strong this spark rapidly alters the surfaces of the hammer and anvil, 
though they are of platinum. By interposing the condenser in the 
inducing circuit, the extra current, instead of producing so strong a spark, 
darts into the condenser; the positive electricity in the armature con¬ 
nected with i, and the negative in the armature connected with m. But 
the opposite electricities combiuing quickly by the thick wire, by the 
battery and the circuit CK m, give rise to a current contrary to that of 
the battery, which instantaneously demagnetises the bundle of soft iron; 
the induced current is thus shorter and more intense. The binding 
screws m and n on the base of the apparatus are for receiving this extra 
current. 

The commutator or key serves to break contact or send the current in 
either direction. The section in fig. 626 is entirely of brass, excepting 


708 DYNAMICAL ELECTRICITY. [ 787 - 

the core A, which is ebonite ; on the two sides are two brass plates C C'. 
Against these press two elastic brass springs, joined to two binding 

screws, a and c, with which are also con¬ 
nected the electrodes of the battery. The 
current arriving at a ascends in C, thence by 
a screw y, it attains the binding screw b and 
the bobbin ; then returning by the plate K> 
which is connected with the hammer, the 
current goes to C' by the screw a, descends 
to c, and rejoins the battery by the wire 
N. If by means of the milled head the key 
is turned 180 degrees, it is easy to see that 
Fig. 626. exactly the opposite takes place ; the cur¬ 

rent reaches the hammer by the plate K, and emerges at b. Finally, if it 
is only turned through 90 degrees, the elastic plates rest on the ebony A, 
instead of on the plates C C', and the current is broken. 

The two wires from the bobbin at o and o' (fig. 624) are the two ends 
of the secondary wire. They are connected with the thicker wires P P' 
so that the induced current can be sent in any desired direction. With 
large coils the hammer cannot be used, for the surfaces become so much 
heated as to melt. But M. Foucault has recently invented a mercury 
interrupter which is free from this inconvenience, and which is an impor¬ 
tant improvement. 

787. Effects produced by RubmkorfTs coil. —The high degree of 
tension which the electricity of induction coil machines possesses has 
long been known, and many luminous and calorific effects have been 
obtained by their means. But it is only since the improvements which 
Ruhmkorff has introduced into his coil, that it has been possible to 
utilise all the tension of induced currents, and to show that these currents 
possess the properties of statical as well as dynamical electricity. 

Induced currents are produced in the coil at each opening and breaking 
of contact. But these currents are not equal either in duration or in 
tension. The direct current or that en opening, is of shorter duration, 
but more tension ; that of closing of longer duration but less tension. 
Hence if the two ends P and P' of the fine wire (figs. 624 and 625) are 
connected, as there are two equal and contrary quantities of electricity in 
the wire the two currents neutralise each other. If a galvanometer is 
placed in the circuit, only a very feeble deflection is produced in the direc¬ 
tion of the direct current. This is not the case if the two extremities P and 
P' of the wire are separated. As the resistance of the air is then opposed 
to the passage of the currents, that which has most tension, that is, the 
direct one, passes in excess, and the more so the greater the distance of 









-787 J effects of ruhmkorff’s COIL. 769 

P and P up to a certain limit, at which neither pass. There are then at 
P and P' nothing but tensions alternately in contrary directions. 

The effects of the coil, like those of the battery, may be classed under 
the heads physiological, chemical , calorific, luminous, mechanical , with this 
difference, that they are enormously more intense. 

The physiological effects of Ruhmkorff’s coil are very powerful; in fact, 
the shocks are so violent that many experimenters have been suddenly 
prostrated by them. A rabbit may be killed with two of Bunsen’s ele¬ 
ments, and a somewhat larger number of couples would kill a man. 

The calorific effects are also easily observed ; it is simply necessary to 
interpose a very fine iron wire between the two ends P and P' of the 
induced wire ; this iron wire is immediately melted, and burns with a 
bright light. A curious phenomenon may here be observed, namely, 
that when each of the wires P and P' terminates in a very fine iron wire, 
and these two are brought near each other, the wire corresponding to 
the negative pole alone melts, indicating that the tension is greater at 
the negative than at the positive pole. 

The chemical effects are very varied, inasmuch as the apparatus pro¬ 
duces both dynamical electricity and electricity in a high state of tension. 
Thus, according to the shape and distance of the platinum electrodes 
immersed in water, and to the degree of acidulation of the water, either 
luminous effects may be produced in water without decomposition, or 
the water may be decomposed and the mixed gases separated at the two 
poles, or the decomposition may take place and the mixed gases separate 
either at a single pole or at both poles. 

Gases may also be decomposed or combined by the continued action of 
the spark from the coil. Becquerel and Fremy 
have found that if the current of a RuhmkorfFs 
coil be passed through a hermetically sealed tube 
containing air, as shown in fig. 627, nitrogen and 
oxygen combine to form nitrous acid. 

The luminous effects of Ruhmkorft’s coil are 
also very remarkable, and vary according as they 
take place in air, in vacuo, or in very rarefied 
vapours. In air the coil produces a very bright 
loud spark, which, with the largest sized coils, has 
a length of 18 inches. In vacuo the effects are 
also remarkable. The experiment is made by 
connecting the two wires of the coil P and P' with the two rods of the 
electrical egg (fig. 508) used for producing in vacuo the luminous affects 
of the electrical machine. A vacuum having been produced up to 1 or 2 
millimeters, a beautiful luminous trail is produced from one knob to the 
other, which is virtually constant, and has the same intensity as that 
















770 


DYNAMICAL ELECTRICITY. 


[ 787 - 

obtained with a powerful electrical machine when the plate is rapidly 
turned. This experiment is shown on the small scale in fig. 633. 
Figure 631 represents a remarkable deviation which light undergoes when 
the hand is presented to the egg. 



Fig. 628. 

The positive pole of the current shows the greatest brilliancy; its 
light is of a fiery red, while that of the negative pole is of a feeble violet 
colour ; moreover, the latter extends along all the length of the negative 
rod, which is not the case with the positive pole. 

The coil also produces mechanical effects so powerful that with the 
largest apparatus glass plates two inches thick have been perforated. 
This result, however, is not obtained by a single charge, but by several 
successive charges. 

The experiment is arranged as shown in fig. 628. The two poles of 
the induced current correspond to the binding screws a and b ; by means 
of a copper wire, the pole a is connected with the lower part of an 
apparatus for piercing glass like that already described (fig. 513), then 
the pole is attached to the upper conductor by a wire d. The latter is 
insulated in a large glass tube r, filled with shellac, which is run in while 
in a state of fusion. Between the two conductors is the glass to be 
perforated, V. When this presents too great a resistance, there is danger 
lest the spark pass in the coil itself, perforating the insulating layer 
which separates the wire, and then the coil is destroyed. To avoid this 
two wires e and c connect the poles of the coil with two metallic rods 
whose distance from each other can be regulated. If then the spark 
cannot penetrate through the glass, it bursts across, and the coil is not- 
injured. 

The coil can also be used to charge Leyden jars. With a large coil 







EFFECTS OF RUHMKORFF’S COIL. 


771 


-787] 

giving sparks of 6 to 8 inches, and using 6 Bunsen’s elements with a 
large surface, Ruhmkorff charged large batteries of 6 jars each, having 
about 3 square yards of coated surface. 

The experiment with a single Leyden jar (fig. 629) is made as follows. 
The armatures of the latter are in connection with the poles of the coil by 



Fig. 629. 


the wires d and i f and these same pole3 are also connected by means of 
the wires e and c, with the two horizontal rods of a universal discharger 
(fig. 502). The jar is then being constantly charged by the wires i and d, 



Fig. 630. 


sometimes in one direction and sometimes in another, and as constantly 
discharged by the wires e and c ; the discharge from m to n taking place 
as a spark two or three inches in length, very luminous, and producing a 

l l 2 



















DYNAMICAL ELECTRICITY. 


772 


[ 788 - 


deafening sound ; they are not the sparks of the electrical machine, but 
rather true lightning discharges. 

To charge a battery the form of the experiment is somewhat varied ; 
the external coating being connected with one pole of the coil by the 
wire d, and the internal coating with the other by the rods m, n, and 
the wire c. The rods m and n are not, however, in contact. If they 
were, as the two currents, the inverse and direct, pass equally, the battery 
would not be charged ; while from the distance between m and n the 
direct current, that of opening, which has higher tension, passes alone, 
and it is this which charges the battery. 

788. Stratification of the electric light. —M. Quet has observed, in 
studying the electric light which Ruhmkorft’s coil gives in a vacuum, 
that if some of the vapour of turpentine, wood spirit, alcohol, or bisul- 



Fig. 631. Fig. 632. Fig. 633. 


phide of carbon, etc., be introduced into the vessel before exhaustion the 
aspect of the light is totally modified. It appears then like a series of 
alternately bright and dark zones, forming a pile of electric light between 
the two poles (fig. 632). 

In this experiment it follows from the discontinuity of the current of 





















geissler’s TUBES 


773 


- 789 ] 

induction, that the light is not continuous, hut consists of a series of dis¬ 
charges which are nearer each other in proportion as the hammer a (fig. 
625) oscillates more rapidly. The zones appear to possess a rapid 
gyratory and undulatory motion. M. Quet considers this as an optical 
illusion; for if the hammer is slowly moved by the hand, the zones 
appear very distinct and fixed. 

The light of the positive pole is most frequently red, and that of the 
negative pole violet. The tint varies, however, with the vapour or gas 
in the globe. 

M. Despretz has observed that the phenomena obtained by Ruhmkorff 
and by Quet, with a continuous current, are also reproduced with an 
ordinary continuous current, with this important difference, that the 
continuous current requires a considerable number of couples, while the 
discontinuous current of the coil only requires a single element. It is 
remarkable that the luminous effects of this coil are very little increased 
by an increase in the number of elements. 

789. Geissler’s tubes.— The brilliancy and beauty of the stratifi¬ 
cation of the electric light are most remarkable when the discharge of 
the RuhmkorfFs coil takes place in glass tubes containing a highly rare¬ 
fied vapour or gas. These phenomena, which have been investigated by 
Masson, Grove, Gassiot, Pliicker, etc., are produced by means of sealed 
glass tubes constructed by Geissler, of Bonn. These tubes are filled with 
different gases or vapours, and are then exhausted, so that the pressure 
does not exceed half a millimeter. At the ends of the tubes two platinum 
wires are soldered into the glass. 

When the two platinum wires are connected with the ends of a Ruhm- 
korff’s coil, magnificent lustrous striae, separated by dark bands, are 
produced all through the tube. These striae vary in shape, colour, and 



Fig. 634. 


lustre with the degree of the vacuum, the nature of the gas or vapour, 
and the dimensions of the tube. The phenomenon has occasionally a 
still more brilliant aspect from the fluorescence which the electric dis¬ 
charge excites in the glass. 

Fig. 634 represents the striae given by hydrogen under half a milli- 







DYNAMICAL ELECTRICITY. 


774 


[ 789 - 


meter of pressure ; in the bulbs the light is white, in the capillary parts 
it is red. 

Fig. 635 shows the striae in carbonic acid under a quarter of a milli¬ 
meter pressure; the colour is greenish, and the striae have not the same 
form as in hydrogen. In nitrogen the light is orange yellow. 



Fig. 635. 

Pliicker has found that the light in Geissler’s tubes does not depend 
on the substance of the electrodes, but simply on the nature of the gas 
or vapour in the tube. He has found that the lights furnished by hydro¬ 
gen, nitrogen, carbonic oxide, etc., give different spectra when they are 
decomposed by a prism. The discharge of the coil which passes through 
a highly rarefied gas would not pass through a perfect vacuum, and the 
presence of a ponderable substance is absolutely necessary for the passage 
of electricity. f 

By the aid of a powerful magnet Pliicker tried the action of mag¬ 
netism on the electric discharge in a Geissler’s tube, as Davy had done 
with the ordinary voltaic arc, and obtained many curious results, one of 
which may be mentioned. He found that 
< where the discharge is perpendicular to the 
line of the poles, it is separated into two 
distinct parts, which can be referred to the 
different action exerted by the electromagnet 
on the two extra currents produced in the dis¬ 
charge. 

The light of Geissler’s tubes has been re¬ 
cently applied to medical purposes. A long 
capillary tube is soldered to two bulbs pro¬ 
vided with platinum wires; this tube is bent 
in the middle, so that the two branches 
touch, and their extremities are twisted, as 
shown at a in fig. 636. This tube contains a 
highly rarefied gas, like those previously described, and when the dis- 
















- 790 ] ROTATION OF INDUCED CURRENTS. 775 

charge passes, a light is produced at a, bright enough to illuminate any 
cavity of the body into which the tube is introduced. 

790. Rotation of induced currents by magnets.— De la Rive 
has recently devised an experiment which shows in a most ingenious 
manner, that magnets act on the light in Geissler’s tubes in accordance 
with the laws with which they act on any other moveable conductor. 

This apparatus consists of a glass globe or electrical egg, provided at 
one end with two stopcocks, one of which can be screwed on the air pump, 
and the other, which is a stopcock like that of Gay Lussac (327), serves 


Fig. 637. 

to introduce a few drops of liquid into the globe. At the other end a 
tubulure is cemented, through which passes a rod of soft iron about f 
of an inch in diameter, the top of which is about the centre of the 
globe. Except at the two ends, this bar is entirely covered with a very 
thick insulating layer of shellac, then with a glass tube also coated with 
shellac, and finally with another glass tube uniformly coated with a 







776 


DYNAMICAL ELECTRICITY. 


[791- 

layer of wax. This insulating layer must be at least § of an inch thick. 
Inside the globe the insulating layer is surrounded at x with a copper 
ring connected by means of a copper wire with a binding screw, c. 

The vessel having been exhausted as completely as possible, a few 
drops of ether or of turpentine are introduced by means of the stopcock 
a ; it is again exhausted, so that the vapour remaining is highly rarefied. 
A thick disc of soft iron, o, provided with a binding screw, is then 
placed on one of the branches of a powerful electromagnet, and the 
end m of the rod mn is placed on this disc, while at the same time one 
of the ends of the secondary wire of Ruhnikorff’s coil is connected with 
the binding screw c, and the other with the knob o. If then the coil is 
worked without setting in action the electromagnet, the electricity of 
the wire s passes to the top n of the soft iron rod, and that of the second 
wire to the ring x, and a more or less irregular luminous sheaf appears 
on the inside of the globe round the rod as in the experiment of the 
electric egg. 

But if a voltaic current passes into the electromagnet the phenome¬ 
non is different; instead of starting from different points of the upper 
surface n, and the ring x, the light is condensed and emits a single 
luminous arc from n to x. Further, and this is the most remarkable 
part of the experiment, this arc turns slowly round the magnetised 
cylinder mn, sometimes in one direction, and sometimes in another, 
according to the direction of the induced current, or the direction of the 
magnetism. As soon as the magnetism ceases the luminous phenomenon 
reverts to its original appearance. 

This experiment is remarkable as having been devised a priori by 
De la Rive to explain, on the influence of terrestrial magnetism, a kind 
of rotatory motion from east to west, observed in the aurora borealis. 
The rotation of the luminous arc in the above experiment can evidently 
be referred to the rotation of currents by magnets. 

Geissler has constructed a very useful form of the above experiment, 
which is exhausted once for all. Apart from the purpose for which it 
was originally devised it is a very convenient arrangement for inves¬ 
tigating the action of magnets on currents. 

791. Heat developed by the induction of powerful magnets on 
bodies in motion.— We have already seen in Arago’s experiments (772) 
that a rotating copper disc acts at a distance on a magnetic needle, com¬ 
municating to it a rotatory motion. We shall presently see that a cube 
of copper, rotating with great velocity, is suddenly stopped by the influ¬ 
ence of the poles of two strong magnets (793). It is clear that in order 
to prevent the rotation of the needle or of the copper, a certain mechanical 
force must be consumed in overcoming the resistance which arises from 
the inductive action of the magnet. Reasoning upon the theory of the 


-7911 


HEAT DEVELOPED BY INDUCTION. 


777 


transformation of mechanical work into heat, which has occupied physi¬ 
cists in the last few years (428), it has been attempted to ascertain what 
quantity of heat is developed by the action of induced currents under 
the influence of powerful magnets. Joule, with a view of determining 
the mechanical equivalent of heat, coiled a quantity of copper wire 
round a cylinder of soft iron, and having enclosed the whole in a glass 
tube full of water, he imparted to the system a rapid rotation between 
the branches of an electromagnet. A thermometer placed in the liquid 
.served to measure the quantity of heat produced by the induced currents 
in the soft iron and the wire round it. • 

Foucault has recently made a remarkable experiment by means of the 
apparatus represented in fig. 638. It consists of a powerful electromagnet 



fixed horizontally on a table. Two pieces of soft iron, A and B, are in 
contact with the poles of the magnet, and becoming magnetic by induc¬ 
tion, they concentrate their magnetic inductive action on the two faces of 
a metallic disc, D; this disc, which is of copper, is 3 inches in diameter, 
and a quarter of an inch thick, partly projects between the pieces A and 
B, and can be moved by means of a handle and a series of toothed wheels 
with a velocity of 150 to 200 turns in a second. 

So long as the curreiit does not pass through the wire of the electro¬ 
magnet, very little resistance is experienced in turning the handle, and 
when once it has begun to rotate rapidly, and is left to itself, the rotation 
continues in virtue of the acquired velocity. But if the current passes, 
the disc and other pieces stop almost instantaneously ; and if the handle 

il3 























778 


DYNAMICAL ELECTRICITY, 


[ 792 - 

is turned considerable resistance is felt. If, spite of this, the rotation be 
continued, the force used is transformed into heat, and the disc becomes 
heated to a remarkable extent. In an experiment made by M. Foucault 


ft 



Fig. 639. 


the temperature of the disc rose from 10° to 61°, the current being’ 
formed by three of Bunsen’s elements; with six the resistance was such 
that the rotation could not long be continued. 


CHAPTER VII. 

OPTICAL EFFECTS OF POWERFUL MAGNETS. DIAMAGNETISM. 

792. Optical effects of powerful magnets.— Faraday observed in 
1845, that a powerful electromagnet exercises an action on many sub¬ 
stances, such that if a polarised ray traverses them in the direction of 
the line of the magnetic poles, the plane of polarisation is deviated either 
to the right or to the left, according to the direction of the magnetism. 

Figure 639 represents Faraday’s apparatus, as constructed by Ruhm- 
korff. It consists of two very powerful electromagnets, M and N, fixed 
on two iron supports, 00', which can be moved on a support, lv. The 
current from a battery of 10 or 11 Bunsen’s elements passes by the wire 
A to the commutator H, the bobbin M, and then to the bobbin N, by 


























OPTICAL EFFECTS OF MAGNETISM. 


779 


-793] 

the wire g, descends in the wire i, passes again to the commutator, and 
emerges at B. The two cylinders of soft iron, which are in the axis of 
the bobbins, are perforated by cylindrical holes, to allow the luminous 
rays to pass. At b and a there are two Nicol’s prisms, the first serving 
as polariser, and the second as analyser. By means of a limb this latter 
is turned round the centre of a graduated circle, P. 

The two prisms being then placed so that their principal sections are 
perpendicular to each other, the prism a completely extinguishes the 
light transmitted through the prism b. If at c, on the axis of the two 
coils, a plate be placed with parallel faces, either of ordinary or flint 
glass, light is still extinguished so long as the current does not pass; but 
when the communications are established, the light reappears. It is 
now coloured, and if the analyser be turned from left to right, according 
to the direction of the current,' the light passes through the different 
tints of the spectrum, as is the case with plates of quartz cut perpendicu¬ 
larly to the axis (585). Becquerel has shown that a large number of 
substances can also rotate the plane of polarisation under the influence 
of powerful magnets. Faraday assumes that in these experiments the 
rotation of the plane of polarisation is due to an action of the magnets 
on the luminous rays, while Biot and Becquerel ascribe the phenomena 
to an action of magnets on the transparent bodies submitted to their 
influence. 

793. Diamagnetism. —Coulomb observed, in 1802, that magnets act 
upon all bodies in a more or less marked degree $ this action was at first 
attributed to the presence of ferruginous particles. Brugmann also 
found that certain bodies, for instance, bars of bismuth, when suspended 
between the poles of a powerful magnet, do not set axially between the 
poles, that is, in the line joining the poles, but equatorially , or at right 
angles to that line. This phenomenon was explained by the assumption 
that the bodies were transversely magnetic. Faraday made the im¬ 
portant discovery in 1845 that all solids and liquids are either attracted 
or repelled by a powerful electromagnet. The bodies which are attracted 
are called magnetic or 'paramagnetic substances, and those which are 
repelled are diamagnetic bodies. Among the metals, iron, nickel, cobalt, 
manganese, platinum, cerium, osmium, and palladium are magnetic: 
while bismuth, antimony, zinc, tin, mercury, lead, silver, copper, gold, 
and arsenic are diamagnetic, bismuth being the most so and arsenic the 
least. The diamagnetic effects can only be produced by means of 
very powerful magnets, and it is by means of Faraday’s apparatus that 
they have been discovered and studied. In experimenting on the dia¬ 
magnetic effects—solids, liquids, and gases—armatures of soft iron, S 
and Q (figs. 640-2) of different shapes are screwed on the magnets, 
i. Diamagnetism of solids. If a small cube of copper, suspended by 


780 DYNAMICAL ELECTRICITY. [ 793 - 

a fine silk thread between the poles of the magnet (fig. 641). he in rapid 
rotation, between the poles of an electromagnet, it stops, the moment the 
current passes through the bobbins. If the moveable piece have the 
form of a small rectangular bar it sets equatorially, or at right angles, 
to the axis of the bobbins, if it is a diamagnetic substance, such as 
bismuth, antimony, or copper; but axially, or in the direction of the 
axis, if it is a magnetic substance, such as iron, nickel, or cobalt. 

Besides the substances enumerated above, the following are diamag¬ 
netic : rock crystal, alum, glass, phosphorus, sulphur, sugar, bread; and 
the following are magnetic: many kinds of paper and sealing-wax, 
fluorspar, graphite, charcoal, etc. 

ii. Diamagnetism of liquids. Liquids also present the phenomena of 
magnetism and of diamagnetism. In making the experiment, very thin 
glass tubes filled with th^substance are suspended between the poles 
instead of the cube m in the figure 641. If the liquids are magnetic, such 



Fig. 640. Fig. 641. Fig. 642. 

as solutions of iron or cobalt, the tubes set axially; if diamagnetic, like 
water, alcohol, ether, essence of turpentine, and most saline solutions, 
the tubes set equatorially. 

Very remarkable changes take place in the direction of magnetic and 
diamagnetic substances when they are suspended in liquids. A magnetic 
substance is indifferent in an equally strong magnetic liquid; it sets 
equatorially in a stronger magnetic substance, and axially in a substance 
which is less strongly magnetic; it sets axially in all diamagnetic liquids. 

A diamagnetic substance surrounded by a magnetic or diamagnetic 
substance sets equatorially. According to its composition, glass is some¬ 
times magnetic and sometimes diamagnetic, and as in these investiga¬ 
tions glass tubes are used for containing the liquids, I its deportment 
must first be determined, ad then taken into account in the experiment. 

The action of powerful magnets on liquids may also be observed in 
the following experiment devised by Pliicker. A solution of gold is 
placed on a watch glass between the two poles, S and Q, of a powerful 









DIAMAGNETISM. 


781 


- 793 ] 

electromagnet. When the current passes, the solution forms one or 
two enlargements, as represented in A and B (fig. 642) ; these continue 
as long as the current passes, and are produced to different extents with 
all magnetic liquids. Diamagnetic liquids present the opposite effects, as 
Pliicker observed, with mercury, in noting its curvature on a piece of 
freshly amalgamated silver placed between the two poles. 

iii. Diamagnetism of gases. Bancalari observed that the flame of a 
candle placed between the two poles in Faraday’s apparatus was strongly 
repelled (fig. 640). All flames present the same phenomenon to a diffe¬ 
rent extent. M. Quet has obtained very intense repulsive effects by 
experimenting in the same manner with the electric light obtained with 
two carbon cones in the figure 544, page 686. 

The magnetic deportment of gases may be exhibited for lecture 
purposes by inflating soap bubbles with them between the poles of the 
electromagnet, and projecting on them either the lime or the electric 
light. 

Faraday has experimented on the magnetic or diamagnetic nature of 
gases. He allowed gas mixed with a small quantity of a visible gas or 
vapour, so as to render it perceptible, to ascend between the two poles 
of a magnet, and observed their deflections from the vertical line in the 
axial or equatorial direction j in this way he found that oxygen was 
least, nitrogen more, and hydrogen most diamagnetic. With iodine 
vapour, produced by placing a little iodine on a hot plate between the 
two poles, the repulsion is strongly marked. Becquerel, who has made 
important researches on magnetism, has found that oxygen is most 
strongly magnetic of all gases, and that a cubic yard of this gas con¬ 
densed would act on a magnetic needle like 5-5 grains of iron. Faraday 
has found that oxygen, although magnetic under ordinary circumstances, 
becomes diamagnetic when the temperature is much raised, and that the 
magnetism or diamagnetism of a substance depends on the medium in 
which it is placed. A substance, for instance, which is magnetic in 
vacuo, may become diamagnetic in air. 

In the crystallised bodies which do not belong to the regular system, 
the directions in which the magnetism or diamagnetism of a body is 
most easily excited, are generally related to the crystallographic axis of 
the substance. The optic axis of the uniaxial crystals sets either axially 
or equatorially when a crystal is suspended between the poles of an 
electromagnet. Faraday has assumed from this the existence of a mag¬ 
neto-crystalline force, but it appears probable from Knoblauch’s re¬ 
searches, that the action arises from an un qual density in different 
directions, inasmuch as unequal pressure in different directions produces 
the same result. 

iv. Detonation 'produced by the rupture of a current under the influence . 


782 


DYNAMICAL ELECTRICITY. 


[ 794 - 

of a powerful electromagnet. The following experiment devised by 
Ruhmkorff is a remarkable effect of Faraday’s apparatus. When the 
two ends of a stout wire in which the current of the electromagnet 
passes, are placed between the two poles, S and Q, of figure 640, that 
is to say, when the current is closed between S and Q, this closing takes 
place without a spark and without noise, or merely a feeble noise and a 
spark. But when the two ends are separated, and the current is hence 
broken, a violent noise is heard almost as strong as the report of a 
pistol. It woilld appear to be the extra current, the intensity of which 
is greatly increased by the influence of the two poles. 


CHAPTER VIII. 

THERMOELECTRIC CURRENTS. 

794. Thermoelectricity.— In 1821, Professor Seebeck, in Berlin, 
found that by heating one of the junctions of a metallic circuit, con¬ 
sisting of two metals soldered together, an electric current was pro¬ 
duced. This phenomenon may be shown by means of the apparatus 
represented in fig. 643, which consists of a plate of copper, mn, the ends 



Fig. 643. 


of which are bent and soldered to a plate of bismuth, op. In the 
interior of the circuit is a magnetic needle moving on a pivot. When 
the apparatus is placed in the magnetic meridian, and one of the solder- 
ings gently heated, as shown in the figure, the needle is deflected in a 
manner which indicates the passage of a current from n to m, that is, 
from the heated to the cool junction in the copper. If, instead of 
beating the junction n, it is cooled by ice or by placing upon it cotton 








THERMOELECTRIC SERIES. 


783 


- 795 ] 

wool moistened with ether, the other junction remaining at the ordi¬ 
nary temperature, a current is produced, hut in the opposite direction$ 
that is to say, from n to m. In both cases the current is more energetic 
in proportion as the difference in temperature of the solderings is 
greater. 

Seebeck gives the name thermoelectric to this current, and the couple 
which produces it, to distinguish it from the hydroelectric or ordinary 
voltaic current and couple. 

795. Thermoelectric series.— If small bars of two different metals 
are soldered together at one end while the free ends are connected with 
the wires of a galvanometer, and if now the point of junction of the two 
metals be heated, a current is produced, the direction of which is indi¬ 
cated by the deflection of the needle of the galvanometer. Moreover, 
the intensity of the current calculated from the deflection of the gal¬ 
vanometer is proportional to the electromotive force of the thermoelement. 
By experimenting in this way with different metals, they may be formed 
in a list such that each metal gives rise to positive electricity when asso¬ 
ciated with one of the following, and negative electricity with one 
of those that precede ; that is, that in heating the soldering, the positive 
current goes from the positive to the negative metal across the soldering, 
just as if the soldering represented the liquid in a hydroelectrical 
element; hence out of the element, in the connecting wire in the gal¬ 
vanometer for instance, the current goes from the negative to the positive 
metal. 

Thus a couple bismuth-antimony heated at the junction would corre¬ 
spond to a couple zinc-copper, immersed in sulphuric acid. The following 
is a list drawn up from Dr. Matthiessen’s researches, which also gives 
comparative numerical values for the electromotive force. 


Bismuth.-(-25 Silver. 1*0 

Cobalt .9 Zinc. 0-2 

Potassium.5 o Cadmium. 0 3 

Nickel.5 Arsenic . 3-8 

Sodium.3 Iron. 5-2 

Lead.1'03 Bed phosphorus .... 9 6 

Tin .1 Antimony. 9-8 

Copper.1 Tellurium.179-8 

Platinum.0-7 Selenium.-• 290'0 


The meaning of the numbers in this list is that, taking the electromo¬ 
tive force of the copper-silver couple as unity, the electromotive force of 
any pair of metals is expressed by the difference of the numbers where 
the signs are the same and by the sum where the signs are different 
Thus the electromotive force of a bismuth-nickel couple would be 25 —5 














784 


DYNAMICAL ELECTRICITY. 


[ 796 - 

=20; of a cobalt-iron 9 — (—5'2)=14-2, and of an iron-antimony — 5*2 
— 9*6= —4’4. Where the positive sign is fixed, the current is from 
the other metal to silver across the soldering; and where the negative, 
from silver to that metal. 

Hence of these bodies, bismuth and selenium produce the greatest 
electromotive force ; but from the expense of this latter element, and on 
account of its low conducting power, antimony is generally substituted. 
The antimony is the negative metal but the positive pole, and the bis¬ 
muth the positive metal but the negative pole, and the current goes from 
bismuth to antimony across the junction. 

If copper wires connected with the ends of a galvanometer are sol¬ 
dered together to the ends of an antimony rod, and if one of the junctions 
is heated to 50°, the other being maintained at 0°, a certain deflection is 
observed in the galvanometer. If similarly a compound bar, consisting of 
antimony and tin soldered together, be connected with the ends of the 
galvanometer, and if the junction copper-tin, and the junction tin-anti¬ 
mony, be heated to 50°, while the junction antimony-copper is kept at 0°, 
the deflection is the same as in the previous case. Hence the electromo¬ 
tive force produced by heating the two junctions, copper-tin and tin- 
antimony, is equal to the electromotive force produced by heating the 
copper-antimony. 

Becquerel found with a number of couples where one end of the junc¬ 
tion was heated to a given temperature and the other kept at 0°, that the 
intensity of the current was proportional to the temperature at the junc¬ 
tion. If the two j unctions are at any given temperature, the intensity of 
the current is proportional to the difference of the temperature of the two 
places, provided that this does not exceed 50°. 

The direction of the current frequently changes when the tempera¬ 
ture of the couple is raised beyond a certain limit. Thus, in a copper 
and iron circuit the current goes from copper to iron through the heated 
part, provided the temperature does not exceed 300° ; at a higher tem¬ 
perature the current changos its direction, and goes from iron to copper. 

As compared with ordinary hydroelectric currents the electromotive 
force of thermocurrents is very small; thus the electromotive force of a 
bismuth-copper element with a difference of 100° C. in the temperatures 
of their junctions is according to Wheatstone and according to Neu¬ 
mann ^ that of Daniell’s element: the electromotive force of an iron- 
argentan couple with 10 to 15° difference of temperatures in their junctions 
is that of a Daniell’s according to Kohlrausch. 

796. Causes of thermoelectric currents. —The thermoelectric 
currents cannot be attributed to contact, for they can be produced in cir¬ 
cuits formed of a single metal. Nor do they arise from chemical actions, 
for Becquerel has found that they are formed in hydrogen, and even in 


- 798 ] thermoelectric couples and batteries. 785 

vacuo. The same physicist ascribes them to the unequal propagation of 
heat in the different parts of the circuit. He found that when all the 
parts of a circuit are homogeneous, no current is produced on heating, 
because the heat is equally propagated in all directions. This is the case if 
the wires of the galvanometer are connected by a second copper wire. But 
if the uniformity of this is destroyed by coiling it in a spiral, or by knot¬ 
ting it, the needle indicates by its deflection a current going from the 
heated part to that in which the homogeneity has been destroyed. If 
the ends of the galvanometer wires be coiled in spiral, and one end is 
heated and touched with the other, the current goes from the heated to 
the cooled end. 

Svanberg has found that the thermoelectro-motive force is influenced 
by the crystallisation; for instance, if the cleavage of bismuth is parallel 
to the face of contact, it is greater than if both are at right angles, and 4 
that the reverse is the case with antimony. Thermoelectric elements 
may be constructed of either two pieces of bismuth or two pieces of 
antimony, if in the one the principal cleavage is parallel to the place 
of contact, and in the other is at right angles. Hence the position of 
metals in the thermoelectric series is influenced by their crystalline 
structure. 

797. Thermoelectric couples and batteries. —From what has 
been said it will be understood that a 
thermoelectric couple consists of two me¬ 
tals soldered together, the two ends of 
which can be joined by a conductor. Fig. 

644 represents a bismuth-copper couple ; 
fig. 645 represents a couple used by M. 

Pouillet. It consists of a bar of bismuth 
bent twice at right angles, at the ends of 
which are soldered two copper strips, c, 
d ,, which terminate in two binding screws 
fixed on some insulating material. 

When several of these couples are 
joined so that the second copper of the 
first is soldered to the bismuth of the 
second, then the second copper of this 
to the bismuth of the third, and so on, this arrangement constitutes a 
thermoelectric battery, which is worked by keeping the odd solderings, 
for instance, in ice, and the even ones in water, which is kept at 
100 °. 

798. Nobili’s thermoelectric battery. —Nobili devised a form of 
thermoelectric battery in which there are a large number of elements in 



Fig. 644. 











786 


DYNAMICAL ELECTRICITY. 


[ 799 - 

a very small space. For this purpose he joined the couples of bismuth 
and antimony in such a manner, that after having formed a series of five 



Fig. 645. 

couples, as represented in fig. 647, the bismuth from b was soldered to 

the antimony of a second series 
arranged similarly; the last 
a + bismuth of this to the antimony 
of a third, and so on for four 
vertical series, containing together 
20 couples, commencing by anti- 
mony, finishing by bismuth. Thus 

.arranged, the couples are insulated 

from one another by means of 
small paper bands covered with 
Fig. 647. yarnish, and then enclosed in a 
copper frame, P (fig. 646), so 
that only the solderings appear at the two ends of the pile. Two small 
copper binding screws, m and n, insulated in an ivory ring, commu¬ 
nicate in the interior, one with the first antimony, representing the 
positive pole, and the other with the last bismuth, representing the 
negative pole. These binding screws communicate with the extre¬ 
mities of a galvanometer wire when the thermoelectric current is to be 
observed. 

799. Becquerel’s thermoelectric battery. —Becquerel has found 
that artificial sulphuret of copper heated to 200° to 300° is powerfully 
positive, and that a couple of this substance and copper has an electro¬ 
motive force nearly ten times as great as that of the bismuth and copper 
couple in fig. 644. Native sulphuret, on the contrary, is powerfully nega¬ 
tive. As the artificial sulphuret only melts at about 1035°, it may be 



Fig. 646. 


































becquerel’s thermoelectric battery. 


787 


- 799 ] 

used at very high temperatures. The metal joined with it is German 
silver (90 of copper and 10 of nickel). Fig. 648 represents the arrange¬ 
ment of a battery of 50 couples arranged in two series of 25. Fig. 650 
gives on a larger scale the view of a single couple, and fig. 649 that of 



Fig. 648. 


6 couples in two series of 3. The sulphuret is cut in the form of rectan¬ 
gular prisms, 10 centimeters in length, by 18mm. in breadth, and 12mm. 
thick. In front is a plate of German silver m, intended to protect the 
sulphuret from roasting when it is placed in a gas flame. Below there 
is a plate of German silver MM, which is bent several times so as to be 
joined to the sulphuret of the next, and so on. The couples, thus 



Fig. 649. Fig. 650. 

arranged in two series of 25, are fixed to a wooden frame supported by 
two brass columns A B, on which it can be more or less raised. Below 
the couples there is a brass trough, through which water is constantly 
flowing; arriving by the tube b and emerging by the stopcock r. The 





















788 


DYNAMICAL ELECTRICITY. 


[ 800 - 

plates of German silver are thus kept at a constant temperature. On each 
side of the trough are two long burners on the Argand principle fed by 
gas from a caoutchouc tube a. The frame being sufficiently lowered, the 
ends are kept at a temperature of 200° to 300°. For collecting the 
current, two binding screws are placed on the left of the frame, one com¬ 
municating with the first sulphuret, that is the positive pole, and the 
other with the last German silver or the negative pole. At the other 
end of the frame are two binding screws, which facilitate the arrange¬ 
ment of the couples in different ways. 

The resistance of sulphuret of copper is great, and consequently the 
current can acquire great tension. It may be used for telegraphing at a 
great distance, and passed into an electro-magnet can lift a weight of 200 
pounds. It can raise a short piece of fine iron wire to redness, and 
freely decomposes water. The electromotive force of a Daniell’s cell is 
equal to about 8 or 9 of these couples. 

800. Melloni’s thermomultiplier. —We have already noticed the 
use which Melloni has made of Nobili’s pile, in conjunction with the 
galvanometer, for measuring the most feeble alterations of tem¬ 
perature. The arrangement he used for his experiment is represented 
in fig. 651. 

On a wooden base, provided with levelling screws, a graduated copper 



rule, about a yard long, is fixed edgeways. On this rule the various 
parts composing the apparatus are placed, and their distances can be 
fixed by means of binding screws, a is a support for a Locatellf s lamp, 
or other source of heat; F and E are screws; C is a support for the 
bodies experimented on, and m is a thermoelectrical battery. Near the 
















- 801 ] PROPERTIES AND USES OF THERMOELECTRIC CURRENTS. 789 

apparatus is a galvanometer, D; this has only a comparatively few turns 
of a tolerably thick (1 mm.) copper wire; for the electromotive force of the 
thermocurrents is small, and as the internal resistance is small too, for 
it only consists of metal, it is clear that no great resistance can he intro¬ 
duced into the circuit if the current is not to he completely stopped. 
Such galvanometers are called thermomultipliers. The delicacy of this 
apparatus is so great that the heat of the hand is enough at a distance 
of a yard from the pile to deflect the needle of the galvanometer. 

In using it for measuring temperature, the relation of the deflection of 
the needle, and therrore of the intensity of the current, to the difference 
of the temperatures of the two ends, must be determined. That known, 
the temperature of the ends not exposed to the source of heat being 
known, the observed deflection gives the temperature of the other, and 
therewith the intensity of the source of heat. 

801. Properties and uses of thermoelectric currents. —Thermo¬ 
elements are well adapted to produce constant currents ; for their junc¬ 
tions, by means of melting ice and boiling water, can easily be kept at 
0° and 100° C. On this account, Ohm used them in the experimental 
establishment of his law. They can produce all the actions of the 
ordinary battery in kind, though in less degree. By means of a thermo¬ 
electrical pile consisting of 769 elements of iron and German silver, the 
ends of which differed in temperature by about 10° to 15°, Kohlrausch 
proved the presence of free positive and negative electricity at the two 
ends of the open pile respectively. He found that the density of the 
free electricity was nearly proportional to the number of elements, and 
also that the electromotive force of a single element under the above 
circumstances was about that of a single Daniell s element. On 
account of their feeble tension, thermoelectric piles produce only feeble 
chemical actions. Botto, however, with 120 platinum and iron wires, 
has decomposed water. 

Besides these, sparks can be obtained on breaking circuit, and magnetic 
and physiological effects produced as with other sources of electricity. 

In addition to their very important use in measuring small alterations 
of temperature, thermopiles have been constructed for the measurement 
of high temperatures. Pouillet’s electropyrometer consists of a gun 
barrel closed at one end by an iron plug. In this is fixed a platinum 
wire, which is stretched in the axis of the tube, and fastened at the other 
end to a binding screw fitted in a block of ebonite, which insulates it 
from the barrel. The platinum wire and the barrel are connected with 
a galvanometer, and the other end where the platinum is in contact with 
the iron, being placed in the fire, the deflection of the galvanometer is 
read off. If the fire is very hot, the end is sometimes coated with fire 
clay. 


790 


DYNAMICAL ELECTRICITY. 


[ 802 - 

The instrument is graduated by comparing its indications with those 
furnished by an air thermometer. In a similar manner, thermoelectric 
couples united to a galvanometer have been used for making observations 
on the temperature of the earth. 

802. Peltier’s experiment. —Peltier found that an electric current, 
in passing through a conductor, in some cases produces heat, in others 
cold. He obtained the greatest increase of temperature when the nega¬ 
tive current passed from a good conductor of electricity to a bad one— 
for example, from copper to zinc; and the least increase when the positive 
current passed in this direction. But when a bar of bismuth and a bar 
of antimony were soldered together, the temperature of the air sank at 
the soldering when the positive current passed from the first to the 
second metal, and rose in the opposite case. This experiment may easily 
be made by hermetically fixing in two tubulures in an air thermometer, a 
compound bar consisting of bismuth and antimony soldered together in 
such a manner that the ends project on each side. The projecting parts 
are provided with binding screws, so as to allow a current to be passed 
through. When the positive current passes from the antimony to the 
bismuth, the air in the bulb is heated, it expands, and the liquid in the 
stem sinks; but if it passes in the opposite direction the air is cooled, it 
contracts, and the liquid rises in the stem. For this experiment the 
current must neither be too strong nor too weak: it is best regulated by 
a rheostate (803). 

These experiments form an interesting illustration of the principle 
that whenever the effects of heat are reversed, heat is produced; and 
whenever the effects ordinarily produced by heat are otherwise pro¬ 
duced, cold is the result. 


CHAPTER IX. 

DETERMINATION OP ELECTRICAL CONDUCTIVITY. 1 

803. Rheostate. —The rheostate is an instrument by which the 
resistance of any given circuit can be increased or diminished without 
opening the circuit. As invented by Mr. Wheatstone, it consists of two 
parallel cylinders, one, A, of brass, the other, B, of wood (fig. 652). In 
the latter there is a spiral groove, which terminates at a in a copper 
ring, to which is fixed the end of a fine brass wire. This wire, 
which is about 40 yards long, is partially coiled on the groove; it 



RHEOSTATE. 


791 


-803] 



passes to the cylinder A, and after a ‘great number of turns on 
this cylinder, is fixed at the extremity e. Two binding screws, n 
and o, connected with the 
battery, communicate by two 
steel plates; one with the cylin¬ 
der A, the other with the ring a. 

When a current enters at o, it 
simply traverses that portion of 
the wire rolled on the cylinder 
B, where the windings are insu¬ 
lated by the grooves; passing 
thence to the cylinder A, which 
is of metal, and in contact with 
the wire, the current passes 
directly to m and n. Hence, if 
the length of the current is to be 
increased, the handle, d , must be 
turned from right to left. If, on 1 ®‘ 

the contrary, it is to be diminished, the handle is to be fixed on the 



Fig. 653. 


axis, c, and turning then from left to right, the wire is coiled on the 


















792 


DYNAMICAL ELECTRICITY. 


[ 804 - 

cylinder A. The length of the circuit is indicated in feet and inches, 
by two needles, at the end of the apparatus not seen in the figure, 
which are moved by the cylinders A and B. 

804. Sine compass.— This is another form of galvanometer for 
measuring powerful currents. Round the circular frame, M, fig. 653, 
several turns of stout insulated copper wire are coiled, the two ends of 
which, i, terminate in the binding screws at E. On a table in the centre 
of the ring there is a magnetic needle, m ; a second light needle, ?i, fixed 
to the first, serves as pointer along the graduated circle, N. Two copper 
wires, a b, from the sources of electricity to be measured, are connected 
with E. The circles M and N are supported on a foot, 0, which can 
move about a vertical axis passing through the centre of a fixed horizontal 
circle, H. 

The circle M being then placed in the magnetic meridian, and there¬ 
fore in the same plane as the needle, the current is allowed to pass. The 
needles being deflected, the circuit M is 
turned until it coincides with the vertical 
plane passing through the magnetic needle m. 
The directive action of the current is now 
exerted perpendicularly to the direction of 
the.magnetic needle, and it may be shown 
that the intensity of the current is propor¬ 
tional to the sine of the angle of deflection ; 
this angle is measured on the circle H by 
means of a vernier on the piece C. This 
piece, C, fixed to the foot O, turns it by means 
of a knob, A. The angle of deflection, and 
hence its sine, being known, the intensity of 
the current is deduced, for this intensity is 
proportional to the sine. 

To prove this, let mm' be the direction of the magnetic meridian, d the 
angle of deflection, I the intensity of the current, and T the directive 
action of the earth. If the direction and intensity of this latter force be 
represented by ak , it may be replaced by two components, ah and ac , 
fig. 654. Now, as the first has no directive action on the needle, the 
component ac must alone counterpoise the force I, that is I —ac. But 
in the triangle, ack, ac=ak. cos. cak, from which ac —T sin. d, for the 
angle cak is the completement of the angle d, and ak is equal to T ; hence 
lastly, I = T sin. d, which was to be proved. 

805. Determination of the resistance of a conductor. Reduced 
length.— If in the circuit of a constant element a tangent compass be 
interposed, a certain deflection of the needle will be produced. If, 
then, different lengths of copper wire of the same diameter be sue- 






- 806 ] BRITISH ASSOCIATION UNIT OF ELtCfRlCAL RESISTANCE. 793 


cessively interposed, corresponding deflections will in each case he 
produced. Let us suppose, that in a particular case the tangent of 
the angle of deflection (714) observed with the element and tangent 
compass alone was 1*88, and that when 5, 40, 70, and 100 yards of copper 
wire were successively placed in the circuit, the tangents of the corre¬ 
sponding deflections were 0*849, 0*172, 0*105, and 0*074. Now, in this 
experiment, the total resistance consists of two components; the re¬ 
sistance offered by the element and the tangent compass, and the resistance 
offered by the wire in each case. The former resistance may be supposed 
to be equal to the resistance of x yards of copper wire of the same dia¬ 
meter as that used, and then we have the following relations. 


Length of wire . 
x yards . 

x + 5 ,, • 

X + 40 „ . 

x + 70 „ . 

x + 100 „ 


Tangent of angle of deflection . 


1*88 

0849 


0*172 

0*105 

0*074 


If the intensities of the currents are inversely as the resistances, that 
is, as the lengths of the circuits, the proportion must prevail, 
x : x + 5 = 0*849 : 1*886; 

from which .r = 4*ll. Combining, in like manner, the other obser¬ 
vations, we get a series of numbers, the mean of which is 4 08. That is, 
the resistance offered by the element and galvanometer is equal to the 
resistance of 4*08 yards of such copper wire, and this is said to be the re¬ 
duced length of the element and galvanometer in terms of the copper wire. 

It is of great scientific and practical importance to have a unit or 
standard of comparison of resistances, and numerous such have been pro¬ 
posed. Jacobi proposed the resistance of a meter of a special copper wire 
a millimeter in diameter. Copper is however ill adapted for the purpose, 
as it is difficult to obtain pure. Matthiessen has proposed an alloy of 
gold and silver, containing two parts of gold and one of silver; its com 
ducting power is very little affected by impurities in the metals, by an¬ 
nealing or by moderate changes of temperature. 

Siemens' unit is a meter of pure mercury, having a section of a square 
millimeter. 

The Varley unit is much used in telegraphic work, is a standard mile 
of a special copper wire ~ °f an inch in diameter. Matthiessen has 
proposed instead of this a mile of pure annealed copper wire ~ in. in 
diameter. 

806. British Association unit of electrical resistance. —The great 
importance, both theoretically and practically, of having some uniform 

M M 










794 


DYNAMICAL ELECTRICITY. 


[ 806 - 


standard for the comparison of electrical resistance has for years past 
engaged the attention of a committee of the British Association, which 
includes the principal electricians in this country. Their labours have 
resulted in the adoption of a standard which has received the approval of 
men of science both in this and other countries. The following account 
of this unit, which it is proposed to call the Ohmad or BA unit, has been 
kindly furnished by the secretary to the Committee, Mr. Fleeming 
Jenkin. 

It represents a convenient multiple of the so-called absolute unit 
of electrical resistance. The word 1 absolute/ as here used, does not 
imply accuracy of construction, but is intended to express that the 
measurement of electrical resistance is made by a unit which bears a 
definite relation to the fundamental units of time, mass, and space only; 
instead of being a mere comparison with the resistance of some particular 
piece of metal arbitrarily chosen as the unit. In a similar sense a square 
foot and a cubic foot may be called absolute units of surface and capa¬ 
city, an acre and a gallon arbitrary units. 

It seems strange at first that the unit of electrical resistance can be 
measured by reference to time, mass, and space only, without reference tc 
the specific qualities of any material; but our chief knowledge of electric 
phenomena is derived from an observation of mechanical effects, and we 
need, therefore, feel no surprise at learning that those phenomena can be 
measured in purely mechanical units. The voltaic current, electro-motive 
force, and resistance, quantity, and capacity, can all be so measured in 
more than one way. The electro-magnetic measurement of current is 
determined by the following considerations. If f be the force exerted 
by a current of strength C, and length L on a pole of a magnet; m 
being the magnetic strength of that pole, and K its distance from the 

CR2 

currrent, it is found by experiment that f varies as --—., so that C = 

L m 


/K 2 

*4—. where k is some constant. Now if the unit current be that which 
k Lm 

in unit length of circuit exerts unit force on a unit pole at unit distance, 
we get h = 1, and the equation for C becomes: 


c = SE 

Lm 


( 1 ) 


and C may be measured by the expression 


/ K 2 
Lm’ 


Again, for the resistance we get 



( 2 ) 


where W is the work done in the time t by a current C flowing in a 




- 806 ] BRITISH ASSOCIATION UNIT OF ELECTRICAL RESISTANCE. 795 


circuit of the resistance r. Now, the first equation allows us to measure 
a current in terms of a forced, two lengths K and L, and a magnitude???, 
which again depends on measurements of force and length onty, so that 
we here have a current measured in mechanical units in virtue of a ma¬ 
thematical relation between the phenomena produced by the current and 
the mechanical units. It follows from the equation that the unit current 
will be that of which each unit length exerts a unit force on a unit pole 
at unit distance. The second equation, like the first, is deduced from ob¬ 
servation, the resistance of a circuit is found to be proportional to the work 
done by a current in that circuit, and inversely proportional to the square 
of the current and to the time during which it acts ; any two circuits 
W 

for which — is equal have equal resistances ; if this quantity for circuit 

A is double what it is for circuit B, then the resistance of circuit A is double 
that of circuit B. Therefore, we have exactlv the same ground for saying 
W • 

that — measures the resistance of the circuit that we have for sayino- a 5 


measures the contents of a square with sides equal to a. In equation 2, 
W, the work, is essentially a mechanical measurement, for, though 
generally observed in the form of heat, it is by Joule’s equivalent 
referred to the mechanical unit of energy or work. 


Moreover Ohm’s law C = —.(3) 

further measures electromotive force in terms of C and r, and Faraday’s 
discovery expressed by equation 

Q = C* 

where Q is the quantity of electricity conveyed by the current C in the 
time t, shows how quantity is measured in the same mathematical series. 

Although nothing can be simpler than the mathematical conceptions 
here involved, the practical measurement of resistance, or any other of 
the above magnitudes by direct reference to force, work, time, etc., in¬ 
volves much labour, so that for each kind of measurement it is necessary 
for practical use to construct a standard which affords the desired mea¬ 
sure by direct and simple comparison with the thing measured. Thus, 
a Frenchman to measure wine does not work out the cubic contents of a 
bottle, but measures the number of litres by reference to a standard litre, 
which is a simple decimal submultiple of the cubic metre. In like 
manner practical measurements of resistance are made by comparison 
with the Ohm or BA unit prepared to represent a simple decimal 
multiple (ten million times) the absolute electromagnetic unit; the 
metre, the gramme, and the second of time were taken as fundamental 
units by the committee, and one which is approximately equal to 10 7 metre 

mm2 



796 DYNAMICAL ELECTRICITY. [ 807 “ 

seconds. Great care has been taken in the determination and construction 
of the standard, which is represented by several coils of wires of various 
metal and alloys, and by tubes of mercury which have all been adjusted 
to represent one and the same standard unit, the variety of materials 
being intended as a safeguard against possible alteration in resistance 
of one or more of the coils or tubes. Certified copies of the unit, con¬ 
sisting of coils of platinum-silver wire, are issued by the Committee 
through their secretary, Mr. Fleeming Jenkin, of 6 Duke Street, Adelphi. 
Similar standards for the measurement of currents, electromotive force, 
quantity, and capacity will also be issued. 

807. Equivalent conductors. —The resistance of a conductor de¬ 
pends as we have seen (715), on its length, section, and conductivity. 
Two conductors, C and C', whose length, conductivity, and section are 
respectively X X', k k', w a/, would offer the same resistance and might 
be substituted for each other in any voltaic circuit, without altering its 

4 X X / 

intensity, provided that — = ——-: and such conductors are said to be 

KM km' 

equivalent to each other. An example will best illustrate the application 
of this principle. 

It is required to know what length of a cylindrical copper wire 4 mm. 
in diameter would be equivalent to 12 yards of copper wire 1 mm. in 
diameter. 

Let X = 12 the length of the copper wire 1 mm. in diameter, and 
the length of the other wire; then since in this case the material is the 

same, the conductivity is the same, and the equation becomes - = — . 

Now the sections of the wires are directly as the squares of the diameters, 
12 X' 

and hence we have — = — or X' = 12 x 16 = 192. That is, 192 
V 4 , ? 

yards of copper wire 4 mm. in thickness would only offer the same re¬ 
sistance as 12 yards of copper wire 1 mm. in thickness. 

How thick must an iron wire be which for the same length shall offer 
the same resistance as a copper wire 2-5 mm. in diameter ? 

Here the length being the same, the expression becomes kw = kV, or 
since the sections are as the squares of the diameters k(P = K r d n . The 
conductivity of copper is unity, and that of iron 0T38. Hence we have 
2-5 3 = d'x 0T38 or d'* = 6-25+-0-138 = 45-3mm. or d=6‘ 7mm. That 
is, any length of a copper wire 2*5mm. in diameter might be replaced by 
an iron wire of the same length, provided its diameter were 6-7mm. 

808. Determination of electrical conductivity. —The various 
methods of determining the electrical conductivity of a body consist 
essentially in determining what length of a given section of the known 
body will offer the same resistance as a known length of a metallic wire 


- 808 ] DETERMINATION OF ELECTRICAL CONDUCTIVITY. 797 

of a given section, taken as standard of comparison. A description of 
the principle of one of these methods, known as Wheatstone’s Balance, 
will give a general idea of them. 

On a base of some hard wood four stout wires are fixed, in the manner 
represented in figure 655. They are provided with binding screws at A, B, 
C, and D, and there are breaks at a, b f c, d, also provided with binding 
screws so that any resistances may be introduced there. The points A 
and 0 are connected with the terminals of a battery, while B and 1) are 
connected with a delicate galvanometer. Now it can be shown that if 
the resistances introduced at a , b , c, d, and which we will designate by 
these letters, bear a certain relation, no current will pass in the galvano¬ 
meter. 



Suppose first of all that the resistances are all equal in every re¬ 
spect ; the current arriving at A would divide, one part would traverse 
the galvanometer in the direction AcBGD, and the other in the direc¬ 
tion AfcDGB, and as both these are equal and opposite in direction no 
effect would be produced on the galvanometer; but if the resistances a 
and b are different, the tensions at B and D will be different, and accor¬ 
dingly a current will traverse the galvanometer either from B to D or 
from D to B, and the needle be deflected in a corresponding manner. If 
now one of the resistances can be varied, if, for instance, c is a rheostate, 
either by increasing or diminishing the amount of wire, the two resis¬ 
tances may be made equal, and then a current ceases to pass. We can 
then express one resistance, b, in terms of c. 

Wheatstone’s bridge, however, is more general. It can be shown that 
no current passes, provided that the four resistances bear to each other 
the ratio a : b = d : c. So that if c, for instance, is the resistance' to be 
determined, by varying the others in a suitable manner the proportion 
can always be obtained. In practice two of them are generally fixed 



DYNAMICAL ELECTRICITY. 


798 


[809- 


resistauces of known amount, and the third is a rheostate; and, where 
possible, it is most convenient to take a = b, in which case d = c. 

The following is a method of determining the internal resistance of an 
element. A circuit is formed consisting of one element, a rheostate and 
a galvanometer, and the intensity I is noted on the galvanometer. A 
second element is then joined with the first, so as to form one of double 
the size, and therefore half the resistance, and then by adding a length l 
of the rheostate wire, the intensity is brought to what it originally was. 
Then if E is the electromotive force, and R the resistance of an element, 
r, the resistance of the galvanometer and the other parts of the circuit; 
the intensity 1 in both cases is 


1 = 


hence R=2 1. 


E _ E 

R+r £R+r+/ 

809. Electrical conductivity. —We can regard conductors in two 
aspects, and consider them as endowed with a greater or less facility for 
allowing electricity to traverse them, a property which is termed conduc¬ 
tivity : or we may consider conductors interposed in a circuit as offering 
an obstacle to the passage of electricity, that is, a resistance which it must 
overcome. A good conductor offers a feeble resistance, and a bad con¬ 
ductor a great resistance. Conductivity and resistance are the inverse of 
each other. 

The conductivity of metals has been investigated by many physicists 
by methods analogous in general to that described in the preceding para¬ 
graph, and very different results have been obtained. This arises in part 
from the different degrees of purity of the specimens investigated, but 
their molecular condition has also great influence. Matthiessen finds 
the difference in conductivity between hard-drawn and annealed silver 
wire to amount to 8 5, for copper 2*2, and for gold 1-9 per cent. The 
following are results of a series of careful experiments by Matthiessen 
on the electrical conductivity of metals at 0°C. compared with silver as 
a standard. 


Silver 

. 1000 

Iron . 

. 16-8 

Copper 

. 99*9 

Tin . 

. 13*1 

Gold. 

. 80-0 

Lead . 

. 8-3 

Aluminium 

. 560 

German Silver . 

. 7-7 

Sodium 

. 37-4 

Antimony . 

. 4*6 

Zinc . 

. 29-0 

Mercury 

. 1-6 

Cadmium . 

. 23-7 

Bismuth 

. 1-2 

Potassium 

. 20-8 

Graphite 

. 007 

Platinum . 

. 180 




The conductivity of metals is diminished by an increase in temperature. 
The law of this diminution is expressed by the formula, 

(1 - at + bt 2 ) ; 







ELECTRICAL CONDUCTIVITY. 


799 


- 810 ] 

where k * and « are the conductivities at t and 0° respectively, and a and 
b are constants, which are probably the same for all pure metals. For 
ten metals investigated by Matthiessen he found that the conductivity 
is expressed by the formula 

K t =Ko (1-0-0037647^+0-00000834^). 

Liquids are infinitely worse conductors than metals. The conductivity 
of a solution of one part of chloride of sodium in 100 parts of water is 
30000000 that of copper. In general, acids have the highest, and solutions 
of alkalis and neutral salts the feeblest conductivity. Yet, in solutions, 
the conductivity does not increase in direct proportion to the quantity of 
^.lt dissolved. 

The following is a list of the conductivity of a few liquids as compared 
with that of pure silver. 


Pure silver. 

. 100,000,000-00 

Nitrate of copper, saturated solution 

8-99 

Sulphate of copper ditto 

5-42 

Chloride of sodium ditto 

31-52 

Sulphate of zinc ditto 

5-77 

Sulphuric acid, 1*10 sp. gr. 

9907 

„ „ 1-24 sp. gr. . 

132-75 

„ . „ 1-40 sp. gr. 

90-75 

Nitric acid, commercial . 

88-68 

Distilled water .... 

0-01 


Liquids and fused conductors increase in conductivity by an increase of 
temperature. This increase is expressed by the formula 

K t = K 0 (1+ at), 

and the values of K are considerable. Thus, for a saturated solution of 
sulphate of copper, it is 0*0286. 

By most physicists the conductivity of liquids has been regarded as a 
purely electrolytic conductivity that is due to chemical decomposition. 
Yet Faraday, in stating his law of electrolytic decomposition, had an¬ 
nounced that it was subject to certain restrictions in cases in which 
liquids could conduct electricity without being decomposed. Foucault 
has recently shown by delicate experiments, that liquids have a peculiar 
conductivity, a physical conductivity analogous to that of metals. This 
is, however, much less than the electrolytic conductivity, but may have 
a distinct influence on the chemical effects of currents and on Faraday’s 
law. 

810. Determination of electromotive force. Wheatstone's 

method. —In the circuit of the element whose electromotive force is to 




800 


DYNAMICAL ELECTRICITY. 


[ 811 - 


be determined, a tangent compass and a rheostate are inserted, the latter 
being so arranged that the intensity I of the current is a definite amount; 
for example, the galvanometer indicates 45°. By increasing the amount 
of the rheostate wire by the length l, a diminished intensity i (for instance 
40°) is obtained. 

A second standard element is then substituted for that under trial, and 
by arranging the rheostate, the intensity of the current is first made 
equal to I, and then, by the addition of l lengths of the rheostate, is made 

Then if E and E : are the two electromotive forces, It and R 1 their 
resistances when they have the intensity I, and l and l x the lengths 
added ; we have * 


Trial element. 

Standard element. 


1 = 5* 

R 


E 

i - 

* R +1 

Ri-Ki 


from which we have 


Hence the electromotive forces of the elements compared are directly 
as the lengths of the wire interposed. 

Another method is described by Wiedemann. The two elements are 
connected in the same circuit with a tangent galvanometer, or other 
apparatus for measuring intensity, first in such a manner that their cur¬ 
rents go in the same direction, and, secondly, that they are opposed. 
Then if the electromotive forces are E and E', their resistances It and It', 
the other resistances in the circuits r, while I 8 is the intensity, when the 
elements are in the same direction, and L , the intensity when they go in 
opposite directions, then: 



I s = 

and 

l A = 

whence 

E' = 


JcJ + Jii 

R + R' + r 
E - E' 

R *T R' -j~ r 


I, + I d 


811. Siemens’ electrical resistance thermometer. —Supposing in 
a Wheatstone’s bridge arrangement, after the ratio a : b = d : c has 
been established, the temperature of one of the coils, c for instance, be 
increased, the above ratio will no longer prevail, for the resistance of c will 
have been altered by the temperature, and if d be the rheostate the 




- 812 ] SIEMENS’ ELECTRICAL RESISTANCE THERMOMETER. 801 

length of wire must he altered so as to produce equivalence. On this 
idea Siemens has based a mode of observing the temperature of difficultly 
accessible places. He places a coil of known resistance in the particular 
locality where temperature is to be observed j it is connected by means of 
long conducting wires with the place of observation, where it forms part 
of a Wheatstone’s bridge arrangement. The resistance of the coil is 
known in terms of the rheostate, and by preliminary trials it has been as¬ 
certained t how much additional wire must be introduced to balance a 
given increase in the temperature of the resistance coil. This being known, 
and the apparatus adjusted at the ordinary temperature, when the tem¬ 
perature of the resistance coil varies, this variation in either direction is 
at once known by observing the quantity which must be brought in or 
out of the rheostate to produce equivalence. 

This apparatus has been of essential service in watching the tempera¬ 
ture of large coils of telegraph wire, which, stowed away in the hold of 
vessels, are very liable to become heated. It might also be used for the 
continuous and convenient observation of underground and submarine 
temperatures. If a coil of platinum wire were substituted for the copper, 
the apparatus could be used for watching the temperature of the interior 
of a furnace. 

- 812. Derived currents.— In fig. 656 the current from a Bunsen’s 
element traverses the wire rqpmn j let us take the case in which any two 
points of this circuit n and q are joined by a second wire, nxq. The 
current will then divide at the point q into two others, one of which 
goes in the direction qpnm , while another takes the direction qxnm. The 



two points q and n from which the second conductor starts and ends are 
called the points of derivation, the wire qpn and the wire qxn are derived 
wires. The currents which traverse these wires are called the derived or 
partial currents ; the current which travelled the circuit rqpmn before it 
branches, is the primitive current j and the name principal current is given 
to the whole of the new current which traverses the circuit when the 
derived wire has been added. The principal current is stronger than the 

mm3 






802 


DYNAMICAL ELECTRICITY. 


[ 812 - 

primitive one, because the interposition of the wire qxn lessens the total 
resistance of the circuit. The principal laws of derived currents are 

i. The sum of the intensities in the divided parts of a circuit is equal to 
the intensity of the principal current. 

ii. The intensities of the currents in the divided parts of a circuit are 
inversely as their resistances; or, what is the same, the division of a current 
into partial currents which lie between two points is directly as the respective 
conductivities of these branches. 

If the two derived wires are of the same length and the same section, 
their action would be the same as if they were juxtaposed, and they 
might be replaced by a single wire of the same length but of twice the 
section, and therefore with half the resistance. Hence the current would 
divide into two equal parts along the two conductors. 

When the two wires are of the same length but of different sections, 
the current would divide unequally, and the quantity which traversed 
each wire would be proportional to its section, just as when a river divides 
into two branches, the quantity of water which passes in each branch is 
proportional to its dimensions. Hence the resistance of the two con¬ 
ductors joined would be the same as that of a single wire of the same 
length, the section of which would be the sum of the two lengths. 

If the two conductors qpn and qxn are different, both in kind, length, 
and section, they could always be leplaced by two wires of the same 
kind and length, with such sections that their resistances would be 
equal to the two conductors; in short, they might be replaced by equiv¬ 
alent conductors. These two wires would produce in the circuit the 
same effect as a single wire, which had this common length, and whose 
section would be the sum of the sections thus calculated. The current 
divides at the junction into two parts proportional to these sections, or 
inversely as the resistances of the two wires. 

Suppose, for instance, is an iron wire 5 metres in length, and 3 mm. 

square in section, and qxn a copper wire. 

The first might be replaced by a copper wire a metre in length, whose 
section would be f x £ (taking the conductivity of copper at 7 times 
that of iron) or ~ square mm. The second wire might be replaced by 
a copper wire a metre in length with a section of § square mm. These 
two wires would present the same resistance as a copper wire a metre in 
length, and with a section of ~ 4* | = 3Y5 square millimetres. 

The principal current would divide along the wires in two portions 
which would be as — : §. 


- 813 ] 


ANIMAL ELECTRICITY. 


803 


CHAPTER X. 

ANIMAL ELECTRICITY. APPLICATION OF ELECTRICITY TO 
THERAPEUTICS. 

813. Peculiar current of animals. —It has been already shown 
that animal electricity has been the subject of discussion between physio¬ 
logists and.physicists (692). Since Galvani, numerous researches have 
been made on this subject, especially by Aldini, Humboldt, Lehot, 
Marianini, and Matteucci. 

By means of the galvanometer, Nobili first observed, in frogs prepared 
like those of Galvani (fig. 521), a current, which he named proper current 
"of the frog. For this purpose he placed the crural members of the frog 
in a capsule full of saline water, and then the lumbar nerves in a second 
capsule full of the same solution, and closed the circuit by immersing in 
each capsule one of the ends of a fine galvanometer wire. He thus ob¬ 
tained a deflection of from 10° to 30°, indicating a current from the feet 
to the head of the animal. 

Matteucci obtained analogous effects by forming piles of the thighs of 
frogs. For this purpose he took the halves of the thighs laid bare, but 
without removing the lumbar nerve, and he arranged them one upon the 
other, so that each nerve rested upon the muscular part of the next 
following one. Closing the circuit by means of the galvanometer, he 
obtained, with eight halves of thighs, a deflection of 12°. 

The same physicist also constructed batteries of frog thighs by re¬ 
moving the lumbar nerve, and causing the interior of the muscle of each 
thigh to touch the external surface of the following thigh. In the 
muscles of these animals, whether living or recently killed, he always 
observed a current, when this circuit was closed, from the interior of the 
muscle to the surface. M. Matteucci calls this current the muscular 
current , to distinguish it from the ‘proper current of the frog. In these 
animals he always met with both currents, while in other animals he 
observed nothing more than the muscular current. 

M. Dubois-Reymond has recently published researches on the muscular 
currents in man. Owing to the great resistance of the human body, it 
was necessary to use in these researches a galvanometer with 24,000 
windings. M. Dubois-Reymond observed that when the two ends of 
the galvanometer were connected with two symmetric parts of the body 
—for instance, with the two hands or the two feet—the galvanometer 
gave at first very irregular indications; but soon a current was produced, 


804 


DYNAMICAL ELECTRICITY. 


[ 814 - 

the direction of which was constant as often as the experiment was re¬ 
peated, even at distant intervals. This current had not the same intensity 
at different intervals; in the same subject the direction might change, 
but only at distant epochs; for it often remained with a constant direc¬ 
tion for several months. 

814. Electrical fish. —Electrical fish are those fish which have the 
remarkable property of giving, when touched, shocks like those of the 
Leyden jar. Of these fish there are several species, the best known of 
which are the torpedo, the gymnotus, and the silurus. The torpedo, 
which is very common in the Mediterranean, has been carefully studied 
by MM. Becquerel and Breschet in France, and by M. Matteucci in 
Italy. The gymnotus has been investigated by Humboldt and Bonpland 
in South America, and in England by Faraday, who had the opportunity 
of examining live specimens. 

The shock which they give serves both as a means of ofience and of 
defence. It is purely voluntary, and becomes gradually weaker as it is 
repeated and as these animals lose their vitality, for the electrical action 
soon exhausts them materially. 

The shock is very violent. According to Faraday the shock which 
the gymnotus gives is equal to that of a battery of 15 jars exposing a 
coating of 25 square feet, which explains how it is that horses frequently 
give way under the repeated attacks of the gymnotus. 

Numerous experiments show that these shocks are due to ordinary 
electricity. For if, touching with one hand the back of the animal, the 
belly is touched with the other, or with a metal rod, a violent shock is 
felt in the wrists and arms; while no shock is felt if the animal is 
touched with an insulating body. Further, when the back is connected 
with one end of a galvanometer wire and the belly with the other, at 
each discharge the needle is deflected, but immediately returns to zero, 
which shows that there is an instantaneous current; and, moreover, the 
direction of the needle shows that the current goes from the back to the 
belly of the fish. Lastly, if the current of a torpedo be passed through 
a helix, in the centre of which is a small steel bar, the latter is mag¬ 
netised by the passage of the discharge. 

By means of the galvanometer, Matteucci has established the follow¬ 
ing facts: 

1. When a torpedo is lively, it can give a shock in any part of its 
body; but as its vitality diminishes, the parts at which it can give a 
shock are nearer the organ which is the seat of the development of 
electricity. 

2. Any point of the back is always positive as compared with the cor¬ 
responding point of the belly. 

« 3, Of any two points at different distances from the electrical organ, 


-815] ELECTRICAL FISH. 805 

the nearest always plays the part of positive pole, and the furthest that 
of negative pole. With the belly, the reverse is the ease. 

The organ where the electricity is produced in the torpedo is double, 
and formed of two parts symmetrically situated on the two sides of the 
head, and attached to the skull bone by the internal face. These two 
parts unite in front of the nasal bones, but are separated from the skin 
by a strong aponeurosis. According to Matteucci, each of these organs 
consists of a tolerably large number of small prismatic masses, placed 
side by side, and proceeding from the external to the internal face, so 
that a section perpendicular to the apex of the prism, appears like the 
cells of a honeycomb. These prisms, perpendicular to their summits, 
are divided by diaphragms, forming a series of small cells which are 
filled with a liquid consisting essentially of 9 parts of water to 1 of 
albumen and a little common salt. 

Reasoning from the following experiment, Matteucci considers each of 
these vesicles as the elementary organ of the electrical apparatus. He 
removed from the apparatus of the torpedo a mass of these vesicles of 
the size of a pin’s head, and put it in contact with the nerves of a dead 
frog prepared in Galvani’s manner. When this mass was excited by 
pricking it with a pin, contractions were observed in the frog. 

Matteucci investigated further the influence of the brain on the dis¬ 
charge. For this purpose he laid bare the brain of a living torpedo, and 
found that the first three lobes could be irritated without the discharge 
being produced, and that when they were removed the animal still pos¬ 
sessed the faculty of giving a shock. The fourth lobe, on the contrary, 
could not be irritated without an immediate production of the discharge : 
but if it was removed, all disengagement of electricity disappeared, even if 
the other lobes remained untouched. Hence it would appear that the 
primary source of the electricity elaborated is the fourth lobe, whence 
it is transmitted by means of the nerves to the two organs described 
above, which act as multipliers. In the silurus the head appears also 
to be the seat of the electricity; but in the gymnotus it is found in the 
tail. 

Reasoning from this considerable disengagement of electricity in the 
case of certain fish, physicists have inquired whether a similar elaboration 
of electricity does not take place in other animals ; not perhaps in suf¬ 
ficient quantity to produce shocks like those of the Leyden jar, but 
sufficiently so to effect slow actions, and to serve for the essential func¬ 
tions of life, like the secretions, digestion, etc. 

815. Application of electricity to medicine. —The first appli¬ 
cations of electricity to medicine date from the discovery of the Leyden 
jar. Nollet and Boze appear to have been the first who thought of the 
application, and soon the spark and electrical frictions became a universal 


DYNAMICAL ELECTRICITY. 


80 G 


[ 815 - 


panacea ; but it must be admitted that subsequent trials did not come up 
to the hopes of the experimentalists. 

After the discovery of dynamic electricity Galvani proposed its appli¬ 
cation to medicine ; since which time many physicists and physiologists 
have been engaged upon this subject, and yet there is still much un¬ 
certainty as to the real effects of electricity, the cases in which it is to be 
applied, and the best mode of applying it. Practical men prefer the use 
of currents to that of statical electricity, and, except in a few cases, dis¬ 
continuous to continuous currents. There is, finally, a choice between 
the currents of the battery and those of induction currents; further, the 
effects of the latter differ, according as induction currents of the first or 
second order are used. 

In fact, since induction currents, although very intense, have a very 
feeble chemical action, it follows that when they traverse the organs, 
they do not produce the chemical effects of the current of the battery, 
and hence do not tend to produce the same disorganisation. Further, in 
electrifying the muscles of the face, induction currents are to be pre¬ 
ferred, for Dr. Duchenne has found that these currents only act feebly on 
the retina, while the currents of the battery act energetically on this 
organ, and may affect it dangerously, as serious accidents have shown. 
There is a difference in the action of induced currents of different orders ; 
for while the primary induced current causes lively muscular actions, but 
has little action on the cutaneous sensibility, the secondary induced 
current, on the contrary, increases the cutaneous sensibility to such a 
point, that its use ought to be proscribed to persons whose skin is very 
irritable. 

Hence electrical currents should not be applied in therapeutics with¬ 
out a thorough knowledge of their various properties. They ought to be 
used with great prudence, for their continued action may produce serious 
accidents. Matteucci, in his lectures on the physical phenomena of living 
bodies, expresses himself as follows : 1 In commencing, a feeble current 
must always be used. This precaution now seems to me the more im¬ 
portant, as I did not think it so before seeing a paralytic person seized 
with almost tetanic convulsions under the action of a current formed of 
a single element. Take care not to continue the application too long, 
especially if the current is energetic. Rather apply a frequently-inter¬ 
rupted current than a continuous one, especially if it be strong; but after 
20 or 30 shocks at most, let the patient take a few moments’ rest.’ 

Of the numerous apparatus which have been devised for applying 
interrupted currents to therapeutics, three may be described : two invented 
by Dr. Duchenne, one of which gives a primary induced current, and the 
other an induced current either of the primary or of the secondary order ; 


- 816 ] DUCHENNE’S ELECTROVOLTAIC APPARATUS. 807 

the third, invented by M. Pulvermacher, gives the ordinary current of 
the battery, but interrupted, and of great tension. 

816. Duchenne's electrovoltaic apparatus. —This consists of a 
bobbin with two wires, analogous to that already described in speaking 



Fig. 667. 

of induction currents, and inclosed in a brass case, V (fig. 657). This 
bobbin is fixed on a wooden box in which are two drawers, one of these, 
containing a compass, which acts as galvanometer, and measures the 
intensity of the induced current by the deflection of the needle, and the 
other a zinc-carbon element arranged so as to occupy as little space as 
possible. The zinc element, Z, has itself the shape of a small drawer, 
in which is a solution of common salt and a rectangular plate of well 
calcined gas coke. In the centre of the carbon is a small cavity, O, in 
which a small quantity of nitric acid is placed, which is absorbed. A 
copper plate, L, communicates with the zinc, and another, N, with the 
carbon. When the drawers are closed, their electrodes, L, and N, are 
respectively in contact with the lower ends of two binding screws, E and 
C, which are connected by means of copper wires, EF and CB, with two 
metallic plates, H and G, the first of which is moveable. When it is 
lowered the current is closed; if raised, as shown in the figure, the cur¬ 
rent is open. 

As the induced current is only formed when the inducing current 
commences or finishes, it is necessary that the latter be frequently inter¬ 
rupted. In Duchenne’s apparatus this may be effected either rapidly or 
slowly. For rapid intermittences, the current passes into a piece of soft 
iron, A, which oscillates very rapidly under the influence of a bundle of 








808 


DYNAMICAL ELECTRICITY. 


[ 817 - 

soft iron wire placed in the axis of the bobbin, and which is temporarily 
magnetised when the current passes. This oscillating motion of the piece 
A, breaks and makes the inducing current, and therefore produces the 
induced current. 

For slow interruptions, the oscillating piece is fixed by means of a small 
rod, a, then the current, instead of passing by the piece A, passes by an 
elastic plate, K, and by the metallic teeth of a wooden wheel, D, which 
are in metallic connection with I and C. By turning the handle M, 
the current is broken whenever the plate K is not in contact with a 
tooth; and as there are four teeth, there are four interruptions during 
one revolution, and hence, by a more or less rapid rotation, the number 
of interruptions, and therefore of shocks, in a given time, can be raised 
at will. 

To transmit the shocks, the ends of the induced wire are connected 
with two binding screws, to which are attached the ends of two long 
insulated copper wires, provided with metallic handles, TT. These 
handles are applied to the part of the body which is to be exposed to the 
action of the current. 

There is in the apparatus a regulator , consisting of a copper cylinder 
surrounding the bobbin, and which, by means of a graduated rod, can 
be drawn out like a drawer. The greatest intensity is obtained when 
the regulator is withdrawn so as to leave the bobbin uncovered, and the 
least when it is covered. The action of this enveloping cylinder is to be 
referred to the induction currents produced in its mass. 

817. Duchenne’s electromagnetic apparatus. —In this the in¬ 
ductive action of a powerful magnet is used to develope the current, as 
in the case of Clarke’s apparatus (779). The magnet KK (fig. 658) is in 
two branches united posteriorly by an armature of soft iron; in front of 
the other ends there is a soft iron armature, C, rotating about a horizontal 
axis, to which the motion is transmitted by means of a cog-wheel, 0, a 
Vaucanson’s chain, A, and a handle, M. 

On the two branches of the magnet a silk-covered copper wire is 
coiled, intended to experience the inductive action of the magnets; on 
this first wire a second, EE, is coiled for receiving the induced current of 
the second order. 

When C is made to rotate, it becomes magnetised at each passage in 
front of the magnets KK, and exercises an action which produces in the 
first wire an induced current of the first order, while at the same time 
this developes in the wire EE an induced current of the second order. 
These currents may be separately received by the aid of a system of 
pieces, P or Q, each of which is double, but of which only one of each 
system is seen in the figure. The current passes thence by spirals of 
copper wires to handles, YY, which are held in the hand by glass , rods, 


PULVERMACHEli’s GALVANIC CHAIN. 


809 


- 818 ] 

and can thus be applied to various parts of the body. The interruptions 
necessary for the formation of induced currents are produced by a com¬ 
mutator, B, analogous to that in Clarke’s apparatus, and by means of a 
suite of pieces, S, I, D, and F, the details of which need not be given. 


Fig. 658. 



The intensity of the shocks may be regulated by means of a screw, N, 
which alters the distance of the piece C from the magnet. The principal 
regulator consists of two copper cylinders, which surround the bobbins, 
and can be withdrawn to any extent by means of a slide, to which they 
are fixed. The shocks are least violent when the cylinders cover the 
bobbins completely, and most so when the bobbins are entirely un¬ 
covered, effects due to the induced currents developed in the mass of the 
cylinders. 

The medical action of these currents has been found to be most 
efficacious in cases of paralysis. 

818. Pulvermacher’s galvanic chain.— Pulvermacher has devised 
a battery remarkable for its great tension and the facility with which it 
is worked. Figure 659 gives a view of this battery, which has a general 
resemblance to the Voltaic pile (697) ; fig. 660 gives a few of its details. 

It consists of a series of small wooden cylinders, on which are coiled, 
side by side, but without touching, a zinc wire and a copper wire. At 
each of its ends (fig. 660) the zinc wire, ab , of the cylinder M is joined 
to the copper wire of the cylinder N, by means of two small copper 
rings fixed in the wood ; the zinc of the cylinder N is joined in the same 












810 


DYNAMICAL ELECTRICITY. 


way to the copper of the third cylinder, so that the zinc of one cylinder 
forms with the copper of the following one a couple. The whole forms 
a liind of chain held by the two hands, and it is immersed in vinegar 
diluted with water. The small cylinders of wood, being porous, imbibe 





Fig. 659. 


some liquid, and thus play the part of the acidulated discs in the Voltaic 
pile, and the chemical action which is set up between the zinc and acetic 
acid produces a current which is more intense in proportion as the couples 
are more numerous. With a chain of 120 couples very violent shocks 
are obtained. 

To break the current, which is necessary in order to produce shocks, 
Pulvermacher uses two armatures, A and 
B (fig. 659), to which are fixed the two 
ends of the pile M. The armature B only 
serves to make better contact with the 
hand; but the armature A, which has 
the same use, also serves to interrupt the 
current. It contains a small clockwork 
motion, which causes a piece to oscillate, 
so that, in the interior, contact is alter¬ 
nately made and broken between the pole 
of the battery and the side i of the armature. The rapidity of the 
oscillations, and hence the number of shocks, may be varied within 
certain limits by means of a small regulator held in the hand. The 
clockwork motion is wound up by turning a key d, which serves as 
handle for the armature. 



ELEMENTARY OUTLINES 


OF 

METEOEOLOGY AND CLIMATOLOGY. 


METEOROLOGY. 

819. Meteorology. —The phenomena which are produced in the 
atmosphere are called meteors ; and meteorology is that part of physics 
which is concerned with the study of these phenomena. 

A distinction is made between aerial meteors, such as winds, and 
hurricanes, and whirlwinds ; aqueous meteors, comprising fogs, clouds, 
rain, dew, snow, and hail ; and luminous meteors, as lightning, the rain¬ 
bow, the aurora borealis. 

Aerial Meteors. 

820. Direction and velocity of winds. — Winds are currents moving 
in the atmosphere with variable directions and velocities. There are 
eight principal directions in which they blow: north, north-east, east, 
south-east, south, south-west, west, and north-west. Mariners further divide 
each of the distances between these eight directions into four others, 
making in all 32 directions, which are called points or rhumbs. A figure 
of these 32 rhumbs on a circle in the form of a star, is known as the 
mariner's card. 

The direction of the wind is determined by means of vanes, and its 
velocity by means of the anemometer. There are several forms of this 
instrument; the most usual consists of a small vane with fans, which 
the wind turns; the velocity is deduced from the number of turns made 
in a given time, which is measured by means of an endless screw and 
wheelwork. In our climate the mean velocity is from 18 to 20 feet in a 
second. With a velocity of 6 or 7 feet, the wind is moderate ; with 30 
or 35 feet, it is fresh ; with 60 or 70 feet, it is strong ; with a velocity of 
85 to 90 feet, it is a tempest, and from 90 to 120 it is a hurricane. 




812 


METEOROLOGY. 


[ 821 - 

We have but few experimental results as to the law of the intensity of 
the force which wind exerts on surfaces exposed to its action. Smeaton 
gives a table compiled by Rouse from a considerable number of facts 
and experiments; he observes that these experiments do not deserve as 
much confidence for velocities above as for velocities below 50 miles an 
hour. The numerical values for the pressures given, this table seems to 
have been calculated on the supposition that the pressure is proportional 
to the square of the velocity of the wind ; they are approximately given 
by the formula 

/=0-002214 V 2 

where Y being the velocity of the wind in feet per second, / is the 
pressure in pounds per square foot. 

821. Causes of winds. —Winds are produced by the disturbance of 
the equilibrium in some part of the atmosphere, a disturbance always 
resulting from a difference in temperature between adjacent countries. 
Thus, if the temperature of a certain extent of ground becomes higher, 
the air in contact with it becomes heated, it expands and rises towards 
the higher regions of the atmosphere; whence it flows, producing winds 
which blow from hot to cold countries. But at the same time the equi¬ 
librium is destroyed at the surface of the earth, for the barometric pressure 
on the colder adjacent parts is greater than on that which has been heated, 
and hence a current will be produced with a velocity dependent on the 
difference between these pressures ; thus two distinct winds will be pro¬ 
duced, an upper one setting outwards from the heated region, and a lower 
one setting imvards towards it, 

822. Regular, periodical, and variable winds. — According to 
the more or less constant directions in which winds blow, they may be 
classed as regular, periodical, and variable winds. 

i. Regular winds are those which blow all the year through in a 
virtually constant direction. These winds, which are also known as the 
trade winds , are uninterruptedly observed far from the land in equatorial 
regions, blowing from the north-east to the south-west in the northern 
hemisphere, and from the south-east to the north-west in the southern 
hemisphere. They prevail on the two sides of the equator as far as 30° 
of latitude, and they blow in the same direction as the apparent motion 
of the sun, that is, from east to west. 

The air above the equator being gradually heated, rises as the sun 
passes round from east to west, and its place is supplied by the colder air 
from the north or south. The direction of the wind, however, is modified 
by this fact; that the velocity which this colder air has derived from the 
rotation of the earth, namely, the velocity of the surface of the earth at 
th6 point from which it started, is less than the velocity of the surface of 
the earth at the point at Which it has now arrived; hence the currents 


WINDS, 


- 822 ] 


813 


acquire, in reference to the equator, the constant direction which con¬ 
stitutes the trade winds. 

ii. Periodical winds are those which blow regularly in the same direction 
at the same seasons, and at the same hours of the day; the monsoon, 
simoon, and the land and sea breeze are examples of this class. The 
name monsoon is given to winds which blow for six months in one direc¬ 
tion, and for six months in another. They are principally observed in 
the Red Sea and in the Arabian Gulf, in the Bay of Bengal and in the 
Chinese Sea. These winds blow towards the continents in summer, and 
in a contrary direction in winter. The simoon is a hot wind which blows 
over the deserts of Asia and Africa, and which is characterised by its 
high temperature and by the sands which it raises in the atmosphere and 
carries with it. During the prevalence of this wind the air is darkened, 
the skin feels dry, the respiration is accelerated, and a burning thirst is 
experienced. 

This wind is known under the name of sirocco in Italy and Algiers, 
where it blows from the great desert of Sahara. In Egypt, where it 
prevails from the end of April to June, it is called kamsin. The natives 
of Africa, in order to protect themselves from the effects of the too 
rapid perspiration occasioned by this wind, cover themselves with fatty 
substances. 

The land and sea breeze is a wind which blows on the sea coast during 
the day from the sea towards the land, and during the night from the 
land to the sea. For during the day the land becomes more heated than 
the sea, in consequence of its lower specific heat and greater conduc¬ 
tivity, and hence as the superincumbent air becomes more heated than 
that upon the sea, it ascends and is replaced by a current of colder and 
denser air flowing from the sea towards the land. During the night 
the land cools more rapidly than the sea, and hence the same pheno¬ 
menon is produced in a contrary direction. The sea breeze commences 
after sunrise, increases to three o’clock in the afternoon, decreases towards 
evening, and is changed into a land breeze after sunset. These winds 
are only perceived at a slight distance from the shores. They are regular 
in the tropics, but less so in our climates; and traces of them are seen 
as far as the coasts of Greenland. The proximity of mountains also 
gives rise to periodical daily breezes. 

iii. Variable winds are those which blow sometimes in one direction 
and sometimes in another, alternately, without being subject to any law. 
In mean latitudes the direction of the winds is very variable; towards 
the poles this irregularity increases, and under the arctic zone the winds 
frequently blow from several points of the horizon at once. On the 
other hand, in approaching the torrid zone, they become more regular. 
The south-west wind prevails in the north of France, in England, and in 


814 METEOROLOGY. [ 823 - 

Germany; in the south of France the direction inclines towards the 
north, and in Spain and Italy the north wind predominates. 

823. Law of the rotation of winds. —Spite of the great irregularity 
which characterises the direction of the winds in our latitude, it has 
been ascertained that the wind has a preponderating tendency to veer 
round according to the sun’s motion, that is to pass from north, through 
north-east, east, south-east to south, and so on round in the same direc¬ 
tion from west to north; that it often makes a complete circuit in that 
direction, or more than one in succession, occupying many days in doing 
so, but that it rarely veers, and very rarely or never makes a complete 
circuit in the opposite direction. 

For a station in south latitude a contrary law of rotation prevails. 

This law, though more or less suspected for a long time, was first 
formally enunciated and explained by Dove, and is known as Dove's law 
of rotation of winds. 

824. Fogs and mists. —When aqueous vapours rising from a vessel 
of boiling water, diffuse in the colder air, they are condensed; a sort of 
cloud is formed which consists of a number of small hollow vesicles of 
water, which remain suspended in the air. These are usually spoken of 
as vapours, yet they are not so, at any rate not in the physical sense of 
the word ; for they are partially condensed vapours. 

When this condensation of aqueous vapours is not occasioned by con¬ 
tact with cold solid bodies, but takes place throughout large spaces of 
the atmosphere, they constitute fogs or mists , which, in fact, are nothing 
more than the appearance seen over a vessel of hot water. 

A chief cause of fogs consists in the moist soil being at a higher tem¬ 
perature than the air. The vapours which then ascend condense and 
become visible. In all cases, however, the air must have reached its 
point of saturation before condensation takes place. Fogs may also be 
produced when a current of hot and moist air passes over a river at a 
lower temperature than its own, for then the air being cooled, as soon as 
it is saturated, the excess of vapour present is condensed. 

The distinction between mists and fogs is one of degree rather than 
of kind. A fog is a very thick mist. 

825. Clouds. — Clouds are masses' of vapour, condensed into little 
drops or vesicles of extreme minuteness, like fogs; from which they 
only differ in occupying the higher regions of the atmosphere ; they 
always result from the condensation of vapours which rise from the 
earth. According to their appearance, they have been divided by 
Howard into four principal kinds: the nimbus, the stratus, the cumulus, 
and the cirrus. These four kinds are represented in fig. 660, and are de¬ 
signated respectively by one, two, three^ and four birds on the wing. 

The cirrus consist of small whitish clouds, which have a fibrous or 


CLOUDS, 


815 


- 825 ] 

wispy appearance, and occupy the highest regions of the atmosphere. 
The name of mares' tails , by which they are generally known, well 
describes their appearance. From the low temperature of the spaces 
which they occupy, it is more than probable that cirrus clouds consist of 
frozen particles; and hence it is that haloes, coronae, and other optical 
appearances, produced by refraction and reflection from ice crystals, 
appear almost always in these clouds and their derivatives. Their 
appearance often precedes a change of weather. 

The cumulus are rounded spherical forms which look like mountains 
piled one on the other. They are more frequent in summer than in 
winter, and after being formed in the morning, they generally disappear 
towards evening. If, on the contrary, they become more numerous, 



Fig. 661 . 


and especially if surmounted by cirrus clouds, rain or storms may be 
expected. 

Stratus clouds consist of very large and continuous horizontal sheets, 
which chiefly form at sunset, and disappear at sunrise. They are fre¬ 
quent in autumn and unusual in spring time, and are lower than the 
preceding. 

The nimbus , or rain clouds, which are sometimes classed as one of 
the fundamental varieties, are properly a combination of the three pre¬ 
ceding kinds. They affect no particular form, and are solely distinguished* 




















816 METEOROLOGY. [ 826 - 

by a uniform grey tint, and by fringed edges. They are indicated on the 
right of the figure by the presence of one bird. 

The fundamental forms pass into one another in the most varied 
manner; Howard has classed these transitional forms as cirro-cumulus , 
cirro-stratus, and cumulo-stratus, and it is often very difficult to tell from 
the appearance of a cloud which type it most resembles. The cirro- 
cumulus is most characteristically known as a ‘ mackarel sky; ’ it consists 
of small roundish masses, disposed with more or less irregularity and 
connection. It is frequent in summer, and attendant on warm and dry 
weather. Cirro-stratus appears to result from the subsidence of the fibres 
of cirrus to a horizontal position, at the same time approaching laterally. 
The form and relative position when seen in the distance frequently give 
the idea of shoals of fish. The tendency of cumulo-stratus is to spread, 
settle down into the nimbus , and finally fall as rain. 

The height of clouds varies greatly; in the mean it is from 1,300 to 
1,500 yards in winter, and from 3,300 to 4,400 yards in summer. But 
tffey often exist at greater heights; Gay-Lussac, in his balloon ascent, 
at a height of 7,650 yards, observed cirrus-clouds above him, which 
appeared still to be at a considerable height. In Ethiopia, M. d’Ab- 
badie observed storm clouds whose height was only 230 yards above the 
ground. 

In order to explain the suspension of clouds in the atmosphere, Halley 
first proposed the hypothesis of vesicular vapours. He supposed that 
clouds are formed of an infinity of extremely minute vesicles, hollow, 
like soap bubbles filled with air, which is hotter than the surrounding 
air; so that these vesicles float in the air like so many small balloons. 
This theory, which was first propounded by Saussure, has been defended 
by Kratzenstein, subsequently by Bravais and most physicists; it has, 
however, been combated by Desagueliers, and afterwards by Monge, and 
has at present many opponents. These latter assume that clouds and 
fogs consist of extremely minute droplets of water, which are retained 
in the atmosphere by the ascensional force of currents of hot air, just as 
light powders are raised by the wind. Ordinarily, clouds do not appear 
to descend, but this absence of downward motion is only apparent. In 
fact, clouds do usually fall slowly, but then the lower part is continually 
dissipated on coming in contact with the lower and more heated layers ; 
at the same time the upper part is always increasing from the condensa¬ 
tion of new vapours; so that from these two actions clouds appear to 
retain the same height. 

826. Formation of clouds.— Many causes may concur in the forma¬ 
tion of clouds, i. The low temperature of the higher region of the 
atmosphere. For owing to the solar radiation, vapours are constantly 
disengaged from the earth and from the waters, which from their 


RAIN. 


817 


-827] 

..elastic force and lower density rise in the atmosphere; meeting there 
continually colder and colder layers of air, they sink to the 'point of 
saturation and then condensing in infinitely small droplets, they give rise 
to clouds. 

ii. The hot and moist currents of air rising during the day undergo a! 
gradually feebler pressure, and thus is produced an expansion which is a 
source of intense cold, and produces a condensation of vapour. Hence it 
is thht high mountains, stopping the aerial currents, and forcing them to 
rise, are an abundant source of rain. 

iii. A hot, moist current of air mixing with a colder current, undergoes 
a cooling, which brings about a condensation of the vapour. Thus the 
hot and moist winds of the south and south-west, mixing with the colder 
air of our latitude, give rain. The winds of the north and north-east 
tend also, in mixing with our atmosphere, to condense the vapours; but 
as these winds, owing to their low temperature, are very dry, the mixture 
rarely attains saturation, and generally gives no rain. 

The formation of clouds is thus explained by Hutton. The tension 
of aqueous vapour, and therewith the quantity present in a given space 
when saturated, diminishes according to a geometric progression, while 
the temperature falls in arithmetical progression, and therefore the elas¬ 
ticity of the vapour present at any time is reduced by a fall of tempera¬ 
ture more rapidly than in direct proportion to the fall. Hence if a current 
of warm air, saturated with aqueous vapour, meet a current of cold air 
also saturated, the air acquires the mean temperature of the two, but 
can only retain a portion of the vapour in the invisible condition, and a 
cloud or mist is formed. Thus suppose two equal volumes of air at 18° 
and 6° respectively, and each saturated with vapour to be mixed, the 
mean temperature would be 12°. The elastic force of aqueous vapour at 
6° is 6‘998mm., and at 18° it is 15-357mm. (see table, page 263), the 
mean of these is llT77mm., but the actual tension at 12° is only 10 457 
mm., consequently a quantity of vapour represented by an elastic force of 
072mm. will be precipitated in the form of clouds. 

827. Rain. —When by the constant condensation of aqueous vapour 
the individual vapour vesicles become larger and heavier, and when 
finally individual vesicles unite, they form regular drops, which fall as 
rain. 

The quantity of rain which falls annually in any given place, or the 
annual rainfall, is measured by means of a rain gauge or pluviometer. 
Ordinarily it consists of a cylindrical vessel M (figs. 662 and 663), closed 
at the top by a funnel-shaped lid, in which there is a very small hole 
through which the rain falls. At the bottom of the vessel is a glass tube, 
A, in which the water rises to the same height as inside the rain gauge, 
and is measured by a scale on the side, as shown in the figures. 

N N 


818 


METEOROLOGY. 


[ 827 - 

The apparatus being placed in an exposed situation, if at the end of a 
month the height of water in the tube is 2 inches for example, it shows 
that the water has attained this height in the vessel; and, consequently, 
that a layer of two inches in depth expresses the quantity of rain which 
this extent of surface has received. 



Fig. 662. Fig. 663. 


It has been noticed that the quantity of rain indicated by the rain- 
gauge is greater as this instrument is nearer the ground. This has 
been ascribed to the fact that the rain-drops, which are generally 
colder than the layers of air which they traverse, condense the vapour in 
these layers, and, therefore, constantly increase in volume. Hence more 
rain falls on the surface of the ground than at a certain height. But it 
has been objected that the excess of the quantity of rain which falls, 
over that at a certain height, is six or seven times that which could 
arise from condensation, even during the whole course of the rain-drops 
from the clouds to the earth. The difference must, therefore, be ascribed 
to purely local causes, and it is now assumed that the difference arises 
from eddies produced in the air about the rain-gauge, which are more 
perceptible as it is higher above the ground; as these eddies disperse the 
drops which would otherwise fall into the instrument, they diminish the 
quantity of water which it receives. 

In any case it is clear that if rain-drops traverse moist air, they will 
from their temperature condense vapour and increase in volume. If, on 
the contrary, they traverse dry air, the drops tend to vaporise, and less 
rain falls than at a certain height; it might even happen that the rain 
did not reach the earth. 

Many local circumstances may affect the quantity of rain which falls 
in different countries; but, other things being equal, most rain falls in 
hot climates, for there the vaporisation is most abundant. The rain-fall 
decreases, in fact, from the equator to the poles. At London it is 23*5 





























WATERSPOUTS, 


819 


- 828 ] 

inches; at Bordeaux it is 25-8 ; at Madeira it is 27*7 ; at Havannah it is 
91’2, and at St. Domingo it is 107'6. The quantity varies with the 
seasons : in Paris, in winter, it is 4*2 inches; in spring 6*9; in summer 
6*3, and in autumn 4-8 inches. 

An inch of rain on a square yard of surface expresses a fall of 46*74 
pounds or 4*67 gallons. On an acre it corresponds to 22,622 gallons, or 
100*9935 tons. 100 tons per inch per acre is a ready way of remem¬ 
bering this. 

828. Waterspouts.— These are masses of vapour suspended in the 
lower layers of the atmosphere which they traverse, and endowed with 
a gyratory motion rapid enough to uproot trees, upset houses, and break 
and destroy everything with which they come in contact. 

These meteors, which are generally accompanied by hail and rain, 
often emit lightning and thunder, producing the sound of carriages 



Fig. 664. 


rolling over a stony road. Many of them have no gyratory motion, 
and about a quarter of those observed are produced in a calm atmo¬ 
sphere. 

When they take place on the sea they present a curious phenomenon. 
The water is disturbed, and rises in the form of a cone, while the clouds 
are depressed in the form of an inverted cone; the two cones then unite 

N N 2 

































820 


METEOROLOGY. 


[ 829 - 

and form a continuous column from the sea to the clouds (fig. 664), which 
are called watersjjouts, Even, however, on the high sea the water of 
these waterspouts is never salt, proving that they are formed of con¬ 
densed vapours, and not of sea water raised by aspiration. 

The origin of these is not known. Kaemtz assumes that they are 
due principally to two opposite winds which pass by the side of each 
other, or to a very high wind which prevails in the higher regions of 
the atmosphere. Peltier and many others ascribe to them an electrical 
origin. 

829. Influence of aqueous vapour on climate. —One of the most 
important elements in meteorology is undoubtedly the property pos¬ 
sessed by aqueous vapour of powerfully absorbing and radiating heat. 
The same physicist who discovered this property (342), has applied it 
to the explanation of some obscure points in meteorological science, and 
there can be no doubt that the knowledge of it will gradually lead to a 
clearer understanding of many inexplicable and apparently capricious 
meteorological phenomena. 

Tyndall has established the fact, that in a tube 4 feet long the atmo¬ 
spheric vapour on a day of average dryness absorbs 10 per cent, of obscure 
heat. With the earth warmed by the sun, as a source, there can be no 
doubt that at the very least 10 per cent, of its heat is intercepted within 
10 feet of the surface. If aqueous vapour be compared atom for atom 
with air, its power of absorption and radiation is more than 16,000 times 
that possessed by air. Such facts as these are sufficient to show the 
importance of the small quantity of this vapour that exists in our atmo¬ 
sphere. 

The radiative power of aqueous vapour may be the main cause of the 
torrential rains that occur in the tropics, and also of the formation of 
cumuli clouds in our own latitudes. It is this same property which 
probably causes the descent of a very fine rain, called serein. This small 
rain has more the characteristics of falling dew, as it appears a short 
time after sunset, when the sky is clear; its production has therefore 
been attributed to the cold, resulting from the radiation of the air. It 
is not the air, however, but the aqueous vapour in the air, which by its 
own radiation chills itself, so that it condenses into serein. 

The absorbent power of aqueous vapour is even of greater importance. 
Whenever the air is dry, terrestrial radiation at night is so rapid as to 
cause intense cold. Thus in the central parts of Asia, Africa, and Aus¬ 
tralia, the daily range of the thermometer is enormous; in the interior 
of the last continent a difference in temperature of no less than 40° C. 
has been recorded within 24 hours. In India, and even in Sahara, owing 
to the copious radiation, ice has been formed at night. But the heat 
aqueous vapour absorbs most largely is of the kind emitted from sources 


DEW. HOAR FROST. 


821 


- 830 ] 

of low temperature: it is to a large extent transparent to the heat emitted 
from the sun, whilst it is almost opaque to the heat radiated from the 
earth. Consequently, the solar rays penetrate our atmosphere with a loss, 
as estimated by Pouillet, of only 25 per cent., when directed vertically 
downwards, but after warming the earth they cannot retraverse the 
atmosphere. Through thus preventing the escape of terrestrial heat, the 
aqueous vapour in the air moderates the extreme chilling which is due 
to the unchecked radiation from the earth, and raises the temperature of 
that region over which it is spread. Tyndall has thus described the 
action of this substance :—‘ Aqueous vapour is a blanket more necessary 
to the vegetable life of England, than clothing is to man. Remove for 
a single summer night the .aqueous vapour from the air which over¬ 
spreads this country, and every plant capable of being destroyed by a 
freezing temperature would perish. The warmth of our fields and gardens 
would pom’ itself unrequited into space, and the sun would rise upon an 
island held fast in the iron grip of frost.’ 

830. Dew. Hoar frost. —JDeiv is merely aqueous vapour which has 
condensed on bodies during the night in the form of minute globules. 
It is occasioned by the chilling which bodies near the surface of the 
earth experience in consequence of nocturnal radiation. Their tem¬ 
perature having then sunk several degrees below that of the air, it 
frequently happens, especially in hot seasons, that this temperature is 
below that at which the atmosphere is saturated. The layer of air which 
is immediately in contact with the chilled bodies, and which virtually 
has the same temperature, then deposits a portion of the vapour which it 
contains: just as when a bottle of cold water is brought into a warm 
room, it becomes covered with moisture, owing to the condensation of 
aqueous vapour upon it. 

According to this theory, which was first propounded by Dr. Wells, 
all causes which promote the cooling of bodies increase the quantity of 
dew. These causes are the emissive power of bodies, the state of the 
sky, and the agitation of the air. Bodies which have a great radiating 
power more readily become cool, and therefore ought to condense 
more vapour. In fact, there is generally no deposit of dew on metals, 
whose radiating power is very small, especially when they are polished ; 
while the ground, sand, glass, and plants, which have a great radiating 
power, become abundantly covered with dew. 

The state of the sky also exercises a great influence on the formation 
of dew. If the sky is cloudless, the planetary spaces send to the earth an 
inappreciable quantity of heat, while the earth radiates very considerably, 
and therefore becoming very much chiiled, there is an abundant deposit 
of dew. But if there are clouds, as their temperature is far higher 
than that of the planetary spaces, they radiate in turn towards the earth, 


METEOROLOGY. 


8*22 


[ 831 - 


and as bodies on the surface of the earth only experience a feeble chilling-, 
no deposit of dew takes place. 

Wind also influences the quantity of vapour deposited. If it is feeble, 
it increases it, inasmuch as it renews the air; if it is strong, it diminishes 
it, as it heats the bodies by contact, and thus does not allow the air 
time to become cooled. Finally, the deposit of dew is more abundant 
according as the air is moister, for then it is nearer its point of satura¬ 
tion. 

Hoar f rost and rime are nothing more than dew which has been depo¬ 
sited on bodies cooled below zero, and has therefore become frozen. The 
flocculent form which the small crystals present, of which rime is formed, 
shows that the vapours solidify directly without passing through the 
liquid state. Hoar frost, like dew, is formed on bodies which radiate 
most, such as the stalks and leaves of vegetables, and is chiefly deposited 
on the parts turned towards the sky. 

831. Snow. Sleet.— Snoiu is water solidified in stellate crystals, 
variously modified, and floating in the atmosphere. These crystals arise 
from the congelation of the minute vesicles which constitute the clouds, 
when the temperature of the latter is below zero. They are more regular 
when formed in a calm atmosphere. Their form may be investigated by 
collecting them on a black surface, and viewing them through a strong 
lens. The regularity, and at the same time variety, of their forms are 
truly beautiful. Fig. 665 shows some of the forms as seen through a 
microscope. 

It snows most in countries near the poles, or which are high above the 
sea level. Towards the poles, the earth is constantly covered with snow; 
the same is the case on high mountains, where there are perpetual snows 
even in equatorial countries. 

Sleet is also solidified water, and consists of small icy needles pressed 
together in a confused manner. Its formation is ascribed to the 
sudden congelation of the minute globules of the clouds in an agitated 
atmosphere. 

832. Hail. —Hail is a mass of compact globules of ice of different 
sizes, which fall in the atmosphere. In our climates hail falls prin¬ 
cipally during spring and summer, and at the hottest times of the day : 
it raiely falls at night. The fall of hail is always preceded by a peculiar 
noise. 

Hail is generally the precursor of storms, it rarely accompanies them, 
and follows them more rarely still. Hail falls from the size of small peas 
to that of an egg or an orange. The formation of hailstones has never 
been altogether satisfactorily accounted for: nor more especially their 
great size. On Volta’s theory the hailstones are successively attracted 
by two clouds charged with opposite electricities; but if the hailstones 


- 833 ] ice. rectElation. 823 

were thus attracted, it is much more probable that the two clouds would 
be mutually attracted, and would unite. 

833. Ice. Revelation.— Ice is nothing more than an aggregate of 
snow crystals, such as are shown in fig. 665. The transparency of ice is due 
to the close contact of these crystals, which causes the individual particles 
to blend into an unbroken mass, and renders the substance optically, as 



Fig. 665. 


well as mechanically, continuous. When large masses of ice slowly 
melt away, a crystalline form is sometimes seen by the gradual disin¬ 
tegration into rude hexagonal prisms: a similar structure is frequently 
met with, but in greater perfection, in the ice caves or glaciers of cold 
regions. 

A striking experiment of Tyndall has, however, more clearly revealed 
the beautiful structure of ice. When a piece of ice is cut parallel to its 
planes of freezing, and the radiation from any luminous source, as the sun, 
a glowing fire, a gas or oil flame, is permitted to pass through it, the dis¬ 
integration of the substance proceeds in a remarkable way. By observing 
the plate of ice through a lens, numerous small crystals will be seen 
studding the interior of the block; as the heat continues these crystals 
expand, and finally assume the shape of six-rayed stars of exquisite beauty. 

This is a kind of negative crystallisation, the crystals produced being 
composed of water, and owe their formation to the molecular disturbance 
caused by the absorption of heat from the source. Nothing is easier than 
to reproduce this phenomenon, if care be taken in cutting the ice. The 
planes of freezing can be found by noting the direction of the bubbles in 
ice, which are either sparsely arranged in striae at right angles to the 
surface, or thickly collected in beds parallel to the surface of the water. 





824 METEOROLOGY. [ 834 - 

A warm and smooth metal plate should be used to level and reduce the 
ice to a slab not exceeding half an inch in thickness. 

A still more important property of ice remains to be noticed. Faraday 
discovered that when two pieces of melting ice are pressed together they 
freeze into one at their points of contact. This curious phenomenon is 
now known under the name of regelation. The cause of it has been the 
subject of much controversy, but the simplest explanation seems to be 
that given by its discoverer. The particles on the exterior of a block of 
ice are held by cohesion on one side only; when the temperature is at 
0° C., these exterior particles being partly free are the first to pass into 
the liquid state, and a film of water covers the solid. But the particles 
in the interior of the block are bounded on all sides by the solid ice, the 
force of cohesion is here a maximum, and hence the interior ice has no 
tendency to pass into a liquid even when the whole mass is at 0°. If 
the block be now split in halves, a liquid film instantly covers the frac¬ 
tured surfaces, for the force of cohesion on the broken surfaces has been 
lessened by the act. By placing the halves together, so that their 
original position shall be regained, the liquid films on the two fractured 
surfaces again become bounded by ice on both sides. The film being 
excessively thin, the force of cohesion is able to act across it: the conse¬ 
quence of this is, the liquid particles pass back into the solid state, and 
the block is reunited by regelation. Not only do ice and ice thus freeze 
together, but regelation also takes place between moist ice and any non¬ 
conducting solid body, as flannel or sawdust; a similar explanation to 
that just given has been applied here, substituting another solid for the 
ice on one side. It must be remarked, however, that many eminent 
philosophers dissent from the explanation we have given. 

Whatever may be the true cause of regelation, there can be no doubt 
that this interesting observation of Faraday’s explains many natural phe¬ 
nomena. For example, the formation of a snowball depends on the 
regelation of the snow granules composing it, and as regelation cannot 
take place at temperatures below 0° C., for then both snow and ice are drv, 
it is only possible to make a coherent snowball when the snow is melting. 

The snow bridges, also, which span wide chasms in the Alps and 
elsewhere, and over which men can walk in safety, owe their existence 
to the regelation of gradually accumulating particles of snow. 

834. Glaciers.— Tyndall has applied this regelating property of ice to 
the explanation of still grander phenomena—the formation and motion 
of glaciers, of which the following is a brief description. In elevated 
regions what is termed the snow line marks the boundary of eternal 
snow, for above this the heat of summer is unable to melt the winter’s 
snow. By the heat of the sun and the consequent percolation of water 
melted from the surface, the lower portions of the snow field are raised 


ATMOSPHERIC ELECTRICITY. 


825 


- 835 ] 

to 0° C.; at the same time this part is closely pressed together by the 
weight of the snow above, regelation therefore sets in, converting the 
loose snow into a coherent mass. 

By increasing pressure the intermingled air which renders snow opaque 
becomes ejected and transparent; ice then results. Its own gravity, and 
the pressure from behind, urges downwards the glacier, which has thus 
been formed. In its descent from the mountain the glacier behaves in 
all respects like a river, passing through narrow gorges with comparative 
velocity, and then spreading out and moving slowly as its bed widens. 
Further, just as the central portions of a river move faster than the 
sides, so Professor Forbes has ascertained, that the centre of a glacier 
moves quicker than its margin, and from the same reason (the difference 
in the friction encountered) the surface moves more rapidly than the 
bottom. To explain these facts, Forbes assumed ice to be a viscous body 
capable of flexion, and flowing like lava, but as ice has not the pro¬ 
perties of a viscous substance, the now generally accepted explanation of 
glacier motion is that supplied by the theory of regelation. According 
to this theory, the brittle ice of the glacier is crushed and broken into 
its passage through narrow channels, such as that of Trelaporte on Mont 
Blanc, and then as it emerges from the gorge which confined it, becomes 
reunited by virtue of regelation ; in this instance forming the well known 
Mer de Glace. By numerous experiments,'^Tyndall has established that 
regelation is adequate to furnish this explanation, and with complete 
success has artificially imitated, on a small scale, the moulding of glaciers 
by the crushing and subsequent regelation of ice. 

LUMINOUS METEORS. 

835. Atmospheric electricity. Franklin’s experiment. —The 

most frequent luminous phenomena, and the most remarkable for their 
effects, are those produced by the free electricity in the atmosphere. The 
first physicists who observed the electric spark compared it to the gleam 
of lightning, and its crackling to the sound of thunder. But Franklin, 
by the aid of powerful electrical batteries, first established a complete 
parallel between lightning and electricity, and he indicated, in a memoir 
published in 1749, the experiments necessary to attract electricity from 
the clouds by means of pointed rods. The experiment was tried by 
Dalibard in France; and Franklin, pending the erection of a pointed 
rod on a spire in Philadelphia, had the happy idea of flying a kite, 
provided with a metallic point, which could reach the higher regions 
of the atmosphere. In June, 1752, during stormy weather, he flew 
the kite in a field near Philadelphia. The kite was flown with 
ordinary pack-thread, at the end of which Franklin attached a key, and 

nn3 


826 


METEOROLOGY. 


[ 836 - 

to the key a silk cord, in order to insulate the apparatus; he then fixed 
the silk cord to a tree, and haying presented his hand to the key, at first 
he obtained no spark. He was beginning to despair of success, when, 
rain having fallen, the cord became a good conductor, and a spark 
passed. Franklin, in his letters, describes his emotion on witnessing 
the success of the experiment as being so great that he could not refrain 
from tears. 

Franklin, who had discovered the power of points (641), but who did 
not understand its explanation, imagined that the kite withdrew from 
the cloud its electricity ; it is, in fact, a simple case of induction, and 
depends on the inductive action which the thunder-cloud exerts upon the 

836. Apparatus to investigate the elec¬ 
tricity of the atmosphere.— The apparatus 
used to ascertain the presence of electricity in 
the atmosphere are: the electroscope, either with 
pith-balls, straw or gold leaf; the apparatus first 
used by Dalibard, and which consisted of an in¬ 
sulated iron rod, 36 yards in height; arrows dis¬ 
charged into the atmosphere, and even kites and 
captive balloons. 

To observe the electricity in fine weather, when 
the tension is generally small, an electrometer is 
used, as devised by Saussure for this kind of in¬ 
vestigation. It is an electroscope similar to that 
already described, but the rod to which the gold 
leaves are fixed is surmounted by a conductor 2 
feet in length, and terminating either in a knob 
or a point (fig. 666). To protect the apparatus 
against rain, it is covered with a metallic shield 
4 inches in diameter. The glass case is square, 
instead of being round, and a divided scale on 
its inside face indicates the divergence of the 
gold leaves or of the straws. This electrometer 
only gives signs of atmospheric electricity as 
long as it is raised in the atmosphere, so that it is 
in layers of air of which the electrical condition 
is superior to its own. 

To ascertain the electricity of the atmosphere, 
Saussure also used a copper ball, which he pro- 
Fig. 666. jected vertically with his hand. This ball was 

fixed to one end of a metallic wire, the other 
end of which was attached to a ring, which could glide along the con- 


kite and the cord. 










ATMOSPHERIC ELECTRICITY. 


827 


-837] 

ductor of the electrometer. From the divergence of the straws, or of 
the gold leaves, the electrical condition of the air at the height which 
the ball had attained could be determined. M. Becquerel, in experi¬ 
ments made on the St. Bernard, improved Saussure’s apparatus by sub¬ 
stituting for the knob an arrow, which was projected into the atmo¬ 
sphere by means of a bow. A gilt silk thread, 88 yards long, was fixed 
with one end to the arrow, while the other was attached to the stem 
of an electroscope. Peltier used a gold-leaf electroscope, at the top of 
which was a somewhat large copper globe. Provided with this in¬ 
strument, the observer stations himself in a commanding position, it 
is then quite sufficient to raise the electroscope even a foot or so to 
obtain signs of electricity. 

To observe the electricity of clouds, where the tension is very con¬ 
siderable, use is made of a long bar terminated in a point. This bar, 
which is insulated with care, is fixed to the summit of a building, and 
its lower end is connected with an electrometer, or even an electric 
chimes (fig. 487, page 620'), which announces the presence of thunder¬ 
clouds. As, however, the bar can then give dangerous shocks, a me¬ 
tallic ball must be placed near it, which is well connected with the 
ground, and which is nearer the bar than the observer himself; so 
that if a discharge should ensue, it will strike the ball and not the ob¬ 
server. Professor Richmann, of St. Petersburg, was killed in an ex¬ 
periment of this kind, by a discharge which struck him on the forehead. 

Sometimes also kites are used, provided with a point, and connected 
by means of a gilt cord with an electrometer. Captive balloons are also 
similarly used. 

A good collector of atmospheric electricity consists of a fishing rod 
with an insulating handle which projects from an upper window. At 
the summit is a bit of lighted amadou held in a metallic forceps, the 
smoke of which, being an excellent conductor, conveys the electricity of 
the air down a wire attached to the rod. A sponge moistened with 
alcohol, and set on fire, is also an excellent conductor. 

837. Ordinary electricity of the atmosphere.— By means of the 
different apparatus which have been described, it has been found that the 
presence of electricity in the atmosphere is not confined to stormy weather, 
but that the atmosphere always contains free electricity, sometimes posi¬ 
tive and sometimes negative. When the sky is cloudless the electricity 
is always positive, but it varies in intensity with the height of the locality, 
and with the time of day. The intensity is greatest in the highest and 
most isolated places. No trace of positive electricity is found in houses, 
streets, or under trees; in towns positive electricity is most perceptible in 
large open spaces, on quays, or on bridges. In all cases, positive electricity 
is only found at n certain height above the ground. On flat land, it only 


828 


METEOROLOGY. 


[ 838 - 

becomes perceptible at a height of 5 feet; above that point it increases 
according to a law which is not made out, but which seems to depend 
on the hygrometric state of the air. 

At sunrise the free positive electricity is feeble ; it increases up to 8 to 
11 o’clock, according to the season, and then attains its first maximum. 
It then decreases rapidly until a little before sunset, and again increases 
till it reaches its second maximum, a few hours after sunset; the re¬ 
mainder of the night the electricity decreases. These increasing and 
decreasing periods, which are observed all the year, are more perceptible 
when the sky is clearer, and the weather more settled. The positive 
electricity of fine weather is much stronger in winter than in summer. 

When the sky is clouded, the electricity is sometimes positive and 
sometimes negative. It often happens that the electricity changes its 
sign several times in the course of the day, owing to the passage of an 
electrified cloud. During storms, and when it rains or snows, the atmo¬ 
sphere may be positively electrified one day, and negatively the next, and 
the numbers of the two sets of days are virtually equal. 

The electricity of the ground has been found by Peltier to be always 
negative, but to different extents, according to the hygrometric state and 
temperature of the air. 

838. Causes of the atmospheric electricity.— Many hypotheses 
have been propounded to explain the origin of the atmospheric electricity. 
Some have ascribed it to the friction of the air against the ground, some 
to the vegetation of plants, or to the evaporation of water. Some, again, 
have compared the earth to a vast voltaic pile, and others to a thermo¬ 
electrical apparatus. Many of these causes may, in fact, concur in pro¬ 
ducing the phenomena. 

Volta first showed that the evaporation of water produced electricity. 
Pouillet and others have subsequently shown that no electricity is pro¬ 
duced by the evaporation of distilled water ; but if an alkali or a salt is 
dissolved, even in small quantity, the vapour is positively and the solution 
is negatively electrified. The reverse is the case if the water contains 
acid. Hence it has been assumed that as the waters which exist on the 
surface of the earth and on the sea always contain salts dissolved, the 
vapours disengaged ought to be positively and the earth negatively elec¬ 
trified. 

The development of electricity by evaporation may be observed by 
heating strongly a platinum dish, adding to it a small quantity of liquid, 
and placing it on the upper plate of the condensing electroscope (fig. 505, 
page 636), taking care to connect the lower plate with the ground. When 
the water of the capsule is evaporated, the connection with the ground 
is broken, and the upper plate raised. The gold leaves then diverge if 
the water contained salts, but remain quiescent if the water was pure. 


ATMOSPHERIC ELECTRICITY. 


829 


- 839 ] 

Reasoning from this experiment, Pouillethas ascribed the development 
of electricity by evaporation to the separation of particles of water from 
the substances dissolved ; but Reich and Riess have shown that the elec¬ 
tricity disengaged during evaporation could be attributed to the friction 
which the particles of water carried away in the current of vapour exercise 
against the sides of the vessel, just as in Armstrong’s electrical machine. 
By a recent series of experiments, Gaugain has arrived at the same result; 
and thinks it no longer allowable to ascribe the atmospheric electricity 
to any changes that take place during the tranquil evaporation of sea 
water. 

In support of the hypothesis which considers the earth as an immense 
source of voltaic electricity due to chemical actions, Becquerel has re¬ 
cently published numerous experiments to show that wdien land and 
water come in contact, electricity is always produced : the land taking a 
considerable excess of positive or negative electricity, and the water a 
corresponding excess of the opposite electricity, according to the nature 
of the salts or other compounds which the water held dissolved. This 
is a general fact which, according to M. Becquerel, is liable to no 
exception. 

Becquerel experimented with an ordinary multiplier, the wire of which 
was connected with two platinum plates immersed in the pieces of ground, 
or the water whose electrical condition he wished to investigate. lie 
thus found that when two moist pieces of ground are connected, that 
which contained the strongest solution took an excess of positive elec¬ 
tricity. He found that in the neighbourhood of a river, even at some 
distance, the land and objects placed on the surface possessed an excess 
of negative electricity, while the water and the aquatic plants which 
swam on the surface were charged with positive electricity. But accord¬ 
ing to the nature of the substances dissolved in the water, different effects 
were produced. As from Becquerel’s experiments, the waters are some¬ 
times positive and sometimes negative, and the earth in a contrary con¬ 
dition, it follows that water in evaporating must constantly send into the 
atmosphere an excess of positive or negative electricity, while the earth, 
by the vapours disengaged on its surface, allows an excess of the contrary 
electricity to escape. Now this excess of electricity ought necessarily to 
influence the distribution of the electricity in the atmosphere, and may 
serve to explain how it is that the clouds are sometimes positively and 
sometimes negatively electrified. 

839. Electricity of clouds.— In general the clouds are all electrified, 
sometimes positively and sometimes negatively, and only differ in their 
greater or less tension. The formation of positive clouds is usually 
ascribed to the vapours which are disengaged from the ground, and con¬ 
dense in the higher regions. Negative clouds are supposed to result from 


830 


METEOROLOGY. 


[ 840 - 

fogs, which, by their contact with the ground, become charged with nega¬ 
tive fluid, which they retain on rising into the atmosphere; or that, 
separated from the ground by layers of moist air, they have been 
negatively electrified by induction from the positive clouds, which have 
repelled into the ground positive electricity. 

840. Iiiglitiring;. —This, as is well known, is the dazzling light emitted 
by the electric spark when it shoots from clouds charged with electricity. 
In the lower regions of the atmosphere the light is white, but in the 
higher regions, where the air is more rarefied, it takes a violet tint; as 
does the spark of the electrical machine in a rarefied medium (681). 

The flashes of lightning are sometimes several leagues in length ; they 
generally pass through the atmosphere in a zigzag direction : a phenomenon 
ascribed to the resistance offered by the air condensed by the passage of a 
strong discharge. The spark then diverges from a white line, and takes 
the direction of least resistance. In vacuo electricity passes in a straight 
line. 

Several kinds of lightning-flashes may be distinguished—1. the zigzag 
flashes, which move with extreme velocity in the form of a line of fire 
with sharp outlines, and which entirely resemble the spark of an elec¬ 
trical machine; 2. the flashes which, instead of being linear, like the 
preceding, fill the entire horizon without having any distinct shape. This 
kind, which is most frequent, appears to be produced in the cloud 
itself, and to illuminate the mass. Another kind is called heat lightning, 
because it illuminates the summer nights without the presence of any 
clouds above the horizon, and without producing any sound. The most 
probable of the many hypotheses which have been proposed to account 
for its ori'gin, is that which supposes it to consist of ordinary lightning 
flashes, which strike across the clouds at such distances that the rolling of 
thunder cannot reach the ear of the observer. There are, further, the 
lightning flashes which appear in the form of globes of fire. These, which 
are sometimes visible for as much as ten seconds, descend from the clouds 
to the earth with such slowness that the eye can follow them. They 
often rebound on reaching the ground ; at other times they burst and 
explode with a noise like that of the report of many cannon. 

The duration of the light of the first three kinds does not amount to a 
thousandth of a second, as has been determined by Mr. Wheatstone by 
means of a rotating wheel, which was turned so rapidly that the spokes 
were invisible : on illuminating it by the lightning-flash, its duration was 
so short that whatever the velocity of rotation of the wheel, it appeared 
quite stationary; that is, its displacement is not perceptible during the 
time the lightning exists. 

841. Thunder.— The thunder is the violent report which succeeds 
lightning in stormy weather. The lightning and the thunder are always 


ATMOSPHERIC ELECTRICITY. 


831 


- 842 ] 

simultaneous, but an interval of several seconds is always observed 
between these two phenomena, which arises from the fact that sound 
only travels at the rate of about 1100 feet in a second (205), while the 
passage of light is almost instantaneous. Hence an observer will only 
hear the noise of thunder five or six seconds, for instance, after the 
lightning, according as the distance of the thunder-cloud is five or six 
times 1100 feet. The noise of thunder arises from the disturbance which 
the electric discharge produces in the air, and which may be witnessed 
in Kinnersley’s thermometer. Near the place where the lightning 
strikes, the sound is dry and of short duration. At a greater distance a 
series of reports are heard in rapid succession. At a still greater distance 
the noise, feeble at the commencement, changes into a prolonged rolling 
sound of varying intensity. Some attribute the noise of the rolling 
of thunder to the reflection of sound from the ground and from 
the clouds. Others have considered the lightning not as a single 
discharge, but as a series of discharges, each of which gives rise to a 
particular sound. But as these partial discharges proceed from points at 
different distances, and from zones of unequal density, it follows not 
only that they reach the ear of the observer successively, but that they 
bring sounds of unequal density, which occasion the duration and 
inequality of the rolling. The phenomenon has finally been ascribed to 
the zigzags of lightning themselves, assuming that the air at each 
salient angle is at its greatest compression, which would produce the 
unequal intensity of the sound. 

842. Effects of lightning. —The lightning discharge is the electric 
discharge which strikes between a thunder-cloud and the ground. The 
latter, by the induction from the electricity of the cloud, becomes 
charged with contrary electricity, and when the tendency of the two 
electricities to combine exceeds the resistance of the air, the spark 
passes, which is often expressed by saying that a thunder-bolt has fallen. 
Lightning in general strikes from above, but ascending lightning is also 
sometimes observed; probably this is the case when the clouds being 
negatively the earth is positively electrified, for all experiments show 
that at the ordinary pressure the positive fluid passes through the 
atmosphere more easily than negative electricity. 

From the first law of electric attraction, the discharge ought to fall 
first on the nearest and best-conducting objects, and, in fact, trees, 
elevated buildings, metals, are more particularly struck by the discharge. 
Hence it is imprudent to stand under trees in stormy weather, especially 
if they are good conductors, such as oaks and elms. But the danger is 
said not to be the same under resinous trees, such as pines, for they 
conduct less well. 

The effects of lightning are very varied, and of the same kind as those 


832 


METEOROLOGY. 


[ 843 - 

of batteries (679), but of far greater intensity. The lightning discharge 
kills men and animals, inflames combustible matters, melts metals, 
breaks bad conductors in pieces. When it penetrates the ground it 
melts the siliceous substance in its way, and thus produces in the 
direction of the discharge those remarkable vitrified tubes called 
fulgurites, some of which are as much as 12 yards in length. When 
it strikes bars of iron, it magnetises them, and often inverts the poles of 
compass needles. 

After the passage of lightning, a highly peculiar odour is generally 
produced, like that perceived in a room in which an electrical machine 
is being worked. This odour was first attributed to the formation of 
an oxygenised compound, to which the name ozone was given; but 
Schonbein,' in 1840, has shown that ozone is a peculiar allotrophic 
modification of oxygen. 

843. Return shock.— This is a violent and sometimes fatal shock 
which men and animals experience, even when at a great distance 
from the place where the lightning discharge passes. This is caused 
by the inductive action which the thunder-cloud exerts on bodies placed 
within the sphere of its activity. These bodies are then, like the 
ground, charged with the opposite electricity to that of the cloud; but 
when the latter is discharged by the recombination of its electricity with 
that of the ground, the induction ceases, and the bodies reverting 
rapidly from the electrical state to the neutral state, the concussion in 
question is produced, the return shock. A gradual decomposition and 
reunion of the electricity produces invisible effects; yet it appears that 
such disturbances of the electrical equilibrium are perceived by nervous 
persons. 

The return shock is always less violent than the direct one ; there is 
no instance of its having produced any inflammation, yet plenty of cases 
in which it has killed both men and animals; in such cases no broken 
limbs, wounds, or bums, are observed. 

The return shock may be imitated by placing a frog near a strong 
electrical machine in action; at each spark taken from the machine, the 
frog experiences a smart shock. 

844. Lightning conductor.— The ordinary form of this instrument 
is an iron rod, through which passes the electricity of the ground 
attracted by the opposite electricity of the thunder-clouds. It was 
invented by Franklin in 1755. 

There are two principal parts in a lightning conductor; the rod and 
the conductor. The rod is a pointed bar of iron, fixed vertically to the 
roof of the edifice to be protected ; it is from 6 to 10 feet in height, and 
its basal section is about 2 or 3 inches in diameter. The conductor is 
a bar of iron which descends from the bottom of the rod to the ground, 


ATMOSPHERIC ELECTRICITY. 


833 


- 844 ] 

which it penetrates to some distance. As, in consequence of their 
rigidity, iron bars cannot always be well adapted to the exterior of 
buildings, they are best formed of wire cords, such as are used for 
rigging and for suspension bridges. In a report made by the Academy 
of Sciences on the construction of lightning conductors, the use of 
copper instead of iron wire in these conductors is recommended, inas¬ 
much as copper is a better conductor than iron. The metallic section of 
the cords ought to be about £ a square inch, and the individual wires 
0-04 to 0-06 inch in diameter; they ought to be twisted in three strands, 
like an ordinary cord. The point of the lightning conductor ought to be 
of copper instead of platinum, for the sake of better conductivity. 
The conductor is usually led into a well, and to connect it better with 
the soil it ends in two or three ramifications. If there is no well in 
the neighbourhood, a hole is dug in the soil to a depth of 6 or 7 yards, 
and the foot of the conductor having been introduced, the hole is filled 
with wood-ashes, which conduct very well and preserve the metal from 
oxidation. 

The action of a lightning conductor depending on induction and the 
power of points (641), ^Franklin, as soon as he had established the 
identity of lightning and electricity, assumed that lightning conductors 
withdrew electricity from the clouds ; the converse is the case. When 
a storm-cloud positively electrified, for instance, rises in the atmosphere, 
it acts inductively on the earth, repels the positive and attracts the 
negative fluid, which accumulates in bodies placed on the surface of the 
soil, the more abundantly as these bodies are at a greater height. The 
tension is then greatest on the highest bodies, which are therefore most 
exposed to the electric discharge ; but if these bodies are provided with 
metallic points, like the rods of conductors, the negative fluid, withdrawn 
from the soil by the influence of the cloud, flows into the atmosphere, 
and neutralises the positive fluid of the cloud. Hence, not only does a 
lightning conductor tend to prevent the accumulation of electricity on 
the surface of the earth, but it also tends to restore the clouds to their 
natural state, both which concur in preventing lightning discharges. The 
disengagement of electricity is, however, sometimes so abundant, that 
the lightning conductor is inadequate to discharge the ground, and the 
lightning strikes; but the conductor receives the discharge, in conse¬ 
quence of its greater conductivity, and the edifice is preserved. 

Experiment has shown that, approximately, a lightning conductor 
protects a circular space around it, the radius of which is double its 
height. Thus, a building, 64 yards in length, would be preserved by two 
rods 8 yards in height, at a distance of 32 yards. 

A conductor, to be efficient, ought to satisfy the following conditions : 
i. the rod ought to be so large as not to be melted if the discharge passes; 


834 


METEOROLOGY. 


[ 845 - 

ii. it ought to terminate in a point' to give readier issue to the electri¬ 
city disengaged from the ground, hence the rod is usually provided with 
a point of platinum or of gilt copper; iii. the conductor must be conti¬ 
nuous from the point to the ground, and the connection between the rod 
and the ground must be as intimate as possible; iv. if the building which 
is provided with a lightning conductor contains metallic surfaces of any 
extent, such as zinc roofs, metal gutters, or iron work, these ought to be 
connected with the conductor. If the last two conditions are not ful¬ 
filled, there is great danger of lateral discharges ; that is to say, that the 
discharge takes place between the conductor and the edifice, and then it 
only increases the danger. 

845. Rainbow. —The rainbow is a luminous meteor which appears in 
the clouds opposite the sun when they are resolved into rain. It consists 
of seven concentric arcs, presenting successively the colours of the solar 
spectrum. Sometimes only a single bow is perceived, but there are 
usually two ; a lower one, the colours of which are very bright, and an 
external or secondary one, which is paler, and in which the order of the 
colours is reversed. In the interior rainbow the red is the highest 
colour; in the other rainbow the violet is. It is seldom that three bows 
are seen; theoretically a greater number may exist, but their colours are 
so feeble that they are not perceptible. 

The phenomenon of the rainbow is produced by the decomposition of 
the white light of the sun when it passes into the drops and by its reflec¬ 
tion from their inside face. In fact, the same phenomenon is witnessed 
in dew-drops and in jets of water ; in short, wherever solar light passes 
into drops of water under a certain angle. 

The appearance and the extent of the rainbow depend on the position 
of the observer, and on the height of the sun above the horizon ; hence 
only some of the rays refracted by the rain-drops, and reflected in their 
concavity to the eye of the spectator, are adapted to produce the pheno¬ 
menon. Those which do so are called effective rays. 

To explain this let n (fig. 667) be a drop of water, into which a solar 
ray Sa penetrates. At the point of incidence, a, part of the light is re¬ 
flected from the surface of the liquid; another, entering it, is decomposed 
and traverses the drop in the direction ah. Arrived at b, part of the light 
emerges from the rain-drop, the other part is reflected from the concave 
surface, and tends to emerge at g. At this point the light is again par¬ 
tially reflected, the remainder emerges in a direction gO, which forms 
with the incident ray S«, an angle called the angle of deviation. It is 
such rays as gO, proceeding from the side next the observer, which pro¬ 
duce on the retina the sensation of colours, provided the light is suffi¬ 
ciently intense. 

It can be shown mathematically that in the case of a series of rays 


RAINBOW. 


835 


- 845 ] 

which impinge on the same drop, and only undergo a reflection in the 
interior, the angle of deviation increases from the ray S "n, for which it is 
zero, up to a certain limit, beyond which it decreases, and that near this 
limit rays passing parallel into a drop of rain, also emerge parallel. From 
this parallelism a beam of light is produced sufficiently intense to impress 
the retina; these are the rays which emerge parallel and are efficient. 



Fig. 667. 


As the different colours which compose white light are unequally re¬ 
frangible, the maximum angle of deviation is not the same for all. For 
red rays the angle of deviation corresponding to the active rays is 42° 2', 
and for violet rays it is 40° 17'. Hence, for all drops placed so that rays 
proceeding from the sun to the drop make, with those proceeding from 
the drop to the eye, an angle of 42° 2', this organ will receive the sen¬ 
sation of red light; this will be the case with all drops situated on the 
circumference of the base of a cone, the summit of which is the spectator’s 
eye; the axis of this cone is parallel to the sun’s rays, and the angle 
formed by the two opposed generating lines is 84° 4'. This explains the 
formation of the red band in the rainbow; the angle of the cone in the 
case of the violet band is 80° 34'. 

The cones corresponding to each band have a common axis called the 
visual axis. As this right line is parallel to the rays of the sun, it follows 
that when this axis is on the horizon, the visual axis is itself horizontal, 
and the rainbow appears as a semicircle. If the sun rises, the visual axis 
sinks, and with it the rainbow. Lastly, when the sun is at a height of 
42° 2', the arc disappears entirely below the horizon. Hence, the phe¬ 
nomenon of the rainbow never takes place except in the morning and 
evening. 

What has been said refers to the interior arc. The secondary bow is 



















836 


METEOROLOGY. 


[ 846 - 

formed by rays which have undergone two reflections, as shown by the 
ray S'a dfeO, in the drop p. The angle STO formed by the emergent 
and incident ray is called the angle of deviation. This angle is no longer 
susceptible of a maximum, but of a minimum, which varies for each 
kind of rays, and to which also efficient rays correspond. It is calculated 
that the minimum angle for violet rays is 54° 7', and for red rays only 
50° 57'; hence it is that the red bow is here on the inside, and the violet 
arc on the outside. There is a loss of light for every internal reflection 
in the drop of rain, and, therefore, the colours of the secondary bow are 
always feebler than those of the internal one. The secondary bow ceases 
to be visible when the sun is 54° above the horizon. 

The moon sometimes produces rainbows like the sun, but they are 
very pale. 

846. Aurora borealis. — The aurora borealis, or northern ‘light, 
or more properly polar aurora , is a remarkable luminous phenomenon 
which is frequently seen in the atmosphere at the two terrestrial poles. 
The following is a description of an aurora borealis observed at Bossekop, 
in Lapland, Lat. 70°, in the winter of 1838—1839. 

In the evening, between 4 and 8 o’clock, the upper part of the fog 
which usually prevails to the north of Bossekop became coloured. This 
light became more regular, and formed an indistinct arc of a pale yellow, 
with its concave side turned towards the earth, while its summit was in 
the magnetic meridian. 

Blackish rays soon separated the luminous parts of the arc. Luminous 
rays formed, becoming alternately rapidly and slowly longer and shorter, 
their lustre suddenly increasing and diminishing. The bottom of these 
rays always showed the brightest light, and formed a more or less regular 
arc. The length of the rays was very variable, but they always con¬ 
verged towards the same point of the horizon, which was in the prolon¬ 
gation of the north end of the dipping needle ; sometimes the rays were 
prolonged as far as their point of meeting, and thus appeared like a 
fragment of an immense cupola. 

The arc continued to rise in an undulatory motion towards the zenith. 
Sometimes one of its feet or even both left the horizon ; the folds became 
more distinct and more numerous; the arc was now nothing more than a 
long band of rays convoluted in very graceful shapes, forming what is 
called the boreal crown. The lustre of the rays varied suddenly in in¬ 
tensity, and attained that of stars of the first magnitude; the rays darted 
with rapidity, the curves formed and reformed like the folds of a serpent 
(fig. 668), the base was red, the middle green, while the remainder re¬ 
tained its bright yellow colour. Lastly, the lustre diminished, the colours 
disappeared : everything became feebler or suddenly went out. 

A French scientific commission to the North observed 150 aurora 


AURORA BOREALIS. 


837 


- 846 ] 

boreales in 200 days; it appears that at tbe poles, nights without an 
aurora borealis are quite exceptional, so that it may be assumed that 
they take place every night, though with varying intensity. They are 



Fig. 668. 


visible at a considerable distance from the poles, and over an immense 
area. Sometimes the same aurora borealis has been seen at the same 
time at Moscow, Warsaw, Rome, and Cadiz. 

Numerous hypotheses have been devised to account for the aurorae 
boreales. The constant direction of their arc as regards the magnetic 
meridian, and their action on the magnetic needle (606), show that they 
ought to be attributed to electric currents in the higher regions of the 
atmosphere. This hypothesis is confirmed by the circumstance observed 
in France and other countries on August 29 and September 1, 1859, that 
two brilliant aurorae boreales acted powerfully on the wires of the electric 
telegraph ; the alarums were for a long time violently rung, and des¬ 
patches were frequently interrupted by the spontaneous abnormal working 
of the apparatus. 

According to M. De la Rive the aurorae boreales are due to electric 
discharges which take place in polar regions between the positive elec¬ 
tricity of the atmosphere and the negative electricity of the terrestrial 
globe; electricities which themselves are separated by the action of the 
sun, principally on the equatorial regions. 

The occurrence of irregular currents of electricity which manifest 
themselves by abnormal disturbances of telegraphic communications is 













838 


METEOROLOGY. 


[ 847 - 

not infrequent; such currents have received the name of earth currents. 
Sabine has found that these magnetic disturbances are due to a peculiar 
action of the sun, and probably independently of its radiant heat and 
light. It has also been ascertained that the aurora borealis as well 
as earth currents invariably accompany these magnetic disturbances. 
According to Balfour Stewart aurorae and earth currents are to 
be regarded as secondary currents due to small but rapid changes 
in the earth’s magnetism ; he likens the body of the earth to the magnetic 
core of a RuhmkorfFs machine, the lower strata of the atmosphere forming 
the insulator, while the upper and rarer, and therefore electrically con¬ 
ducting strata, may be considered as the secondary coil. 

On this analogy the sun may perhaps be likened to the primary current 
which performs the part of producing changes in the magnetic state of 
the core. Now in RuhmkorfFs machine the energy of the secondary 
current is derived from that of the primary current. Thus if the analogy 
be correct the energy of the aurora borealis may in like manner come from 
the sun; but until we know more of the connection between the sun and 
terrestrial magnetism these ideas are to be accepted with some reserve. 

CLIMATOLOGY. 

847. Mean temperature.— The mean daily temperature , or simply 
temperature, is that obtained by adding together 24 hourly observations, 
and dividing by 24. A very close approximation to the mean temperature 
is obtained by taking the mean of the maxima and minima temperatures 
of the day and of the night, which are determined by means of the 
maximum and minimum thermometers (262). These ought to be pro¬ 
tected from the solar rays, raised above the ground, and far from all 
objects which might influence them by their radiation. 

The temperature of a month is the mean of those of 30 days, and the 
temperature of the year is the mean of those of 12 months. Finally, 
the temperature of a place is the mean of its annual temperature, for a 
great series of years. The mean temperature of London is 8-28° C, or 
46-9° F. The temperatures in all cases are those of the air and not those 
of the ground. 

848. Causes which modify the temperature of the air._ The 

principal causes which modify the temperature of the air are the latitude of 
a place, its height, the direction of the winds, and the proximity of seas. 

Influence of the latitude. The influence of the latitude arises from the 
greater or less obliquity of the solar rays, for as the quantity of heat 
absorbed is greater the nearer the rays are to the normal incidence (354), 
the heat absorbed decreases from the equator to the poles, for the rays 
are then more oblique. This loss is, however, in summer, in the tem- 


CLIMATOLOGY. 


839 


- 848 ] 

perate and arctic zones, partially compensated by the length of the days. 
Under the equator, where the length of the days is constant, the tem¬ 
perature is almost invariable; in the latitude of London, and in more 
northerly countries, where the days are very unequal, the temperature 
varies greatly ; but in summer it sometimes rises almost as high as under 
the equator. The lowering of the temperature produced by the latitude 
is small; thus in a latitude of 115 miles north of France, the temperature 
is only 1° C. lower. 

Influence of altitude. The height of a place has a much more consider¬ 
able influence on the temperature than its latitude. In the temperate 
zone a diminution of 1° C. corresponds in the mean to an ascent of 180 
yards. 

The cooling on ascending in the atmosphere has been observed in 
balloon ascents, and a proof of it is seen in the perpetual snows which 
cover the highest mountains. It is caused by the greater rarefaction of 
the air, which necessarily diminishes its absorbing power, besides which 
the air is at a greater distance from the ground, which heats it by contact, 
and finally there is the great diathermanous power of dry air. 

The law of the diminution of temperature corresponding to a greater 
height in the atmosphere has not been made out, in consequence of the 
numerous perturbing causes which modify it, such as the prevalent winds, 
the hvgrometric state, the time of day, &c. The difference between the 
temperature of two places at unequal heights is not proportional to the 
difference of level, but for moderate heights an approximation to the law 
may be made. As the mean of a series of very careful observations made 
by Mr. Walsh during balloon ascents, a diminution of 1° C. corresponded 
to an increase in height of 232 yards. 

Direction of winds. As winds share the temperature of the countries 
which they have traversed, their direction exercises great influence on 
the air in any place. In Paris the hottest winds are the south, then 
come the south-east, the south-west, the west, the east, the north-west, 
north, and, lastly, the north-east, which is the .coldest. The character 
of the wind changes with the seasons ; the east wind, which is cold in 
winter, is hot in summer. 

Proximity of the seas. The neighbourhood of the sea tends to raise 
the temperature of the air, and to render it uniform. The average 
temperature of the sea in equatorial and polar countries is always higher 
than that of the atmosphere. With reference to the uniformity of 
the temperature, it has been found that in temperate regions, that is 
from 25° to 50° of latitude, the difference between the maximum and 
minimum temperature of a day does not exceed, on the sea, 2° to 3°; 
while upon the continent this amounts to 12° to 15°. In islands the 
uniformity of temperature is very perceptible, even during the greatest 


840 


METEOROLOGY. 


[ 849 - 

heats. In continents, on the contrary, the winters for the same latitudes 
become colder, and the difference between the temperature of summer 
and winter becomes greater. 

849. Gulf stream. —A similar influence to that of the winds is exerted 
by currents of warm water. To one of these, the Gulf stream, the mild¬ 
ness of the climate in the north-west of Europe is mainly due. This 
great body of water, taking its origin in equatorial regions, flows through 
the Gulf of Mexico, from whence it derives its name; passing by the 
southern shores of North America it makes its way in a north-westerly 
direction across the Atlantic, and finally washes the coast of Ireland and 
the north-west of Europe generally. Its temperature in the Gulf is about 
28° C. (and generally it is a little more than 5° C.) higher than the rest 
of the ocean on which it floats, owing to its lower specific gravity. To 
its influence is due the milder climate of west Europe as compared with 
that of the opposite coast of America; thus the river Hudson, in the 
latitude of Rome, is frozen over three months in the year. It also causes 
the polar regions to be separated from the coasts of Europe by a girdle of 
open sea; and thus the harbour of Hammergest is open the year round. 
Besides its influence in thus moderating climate the Gulf stream is an 
important help to navigators. 

850. Isothermal lines. —When on a map all the points whose tem¬ 
perature is known to be the same are joined, curves are obtained which 
Humboldt first noticed, and which he called isothermal lines. If the 
temperature of a place only varied with the obliquity of the sun’s rays, 
that is, with the latitude, isothermal lines would all be parallel to the 
equator; but as the temperature is influenced by many local causes, 
especially by the height, the isothermal lines are always more or less 
curved. On the sea, however, they are almost parallel. A distinction 
is made between isothermal lines , isotheral lines , and isochimenal lines , 
where the mean genial, the mean summer , and the mean winter tem¬ 
perature are respectively constant. An isothermal zone is the space 
comprised between two isothermal lines. Kupffer also distinguishes 
isogeothermic lines where the mean temperature of the soil is constant. 

851. Climate. —By the climate of a place is understood the whole 
of the meteorological conditions to which a place is subjected ; its mean 
annual temperature, summer and winter temperatures, and by the extremes 
within which these are comprised. Some writers distinguish seven classes 
of climates, according to their mean annual temperature, a hot climate from 
29° 5' to 25° C.; a warm climate from 25° to 20° C.; a mild climate from 
20° to 15°; a temperate climate from 15° to 10° C. ; a cold climate from 
10° to 5°; a very cold climate from 5° to zero; and an arctic climate where 
the temperature is below zero. 

Those climates, again, are classed as constant climates , where the dif- 


CLIMATOLOGY. 


841 


- 852 ] 

ference between the mean and summer and winter temperature does not 
exceed 6° to 8°; variable climates, where the difference amounts to from 
16° to 20° ; and extreme climates, where the difference is greater than 
30°. The climates of Paris and London are variable ; those of Pekin and 
New York are extreme. Island climates are generally little variable, as 
the temperature of the sea is constant; and hence the distinction between 
land and sea climates. Marine climates are characterised by the fact that 
the difference between the temperature of summer and winter is always 
less than in the case of continental climates. But the temperature is by 
no means the only character which influences climates; there are, in 
addition, the humidity of the air, the quantity and frequency of the rains, 
the number of storms, the direction and intensity of the winds, and the 
nature of the soil. 

852. Distribution of temperature on the surface of the globe. 

The temperature of the air on the surface of the globe decreases from 
the equator to the poles; but it is subject to perturbing causes so nume¬ 
rous and so purely local, that its decrease cannot be expressed by any law. 
It has hitherto not been possible to do more than obtain by numerous 
observations the mean temperature of each place, or the maximum and 
minimum temperatures. The following table gives a general idea of the 
distribution of heat in the northern hemisphere. 

Mean temperatures at different latitudes. 


Abyssinia . . , . 

, 310 C. 

Paris .... 

. . 10-8° 

Calcutta .... 

. 28-5 

London . . . 

. . 10-4 

Jamaica .... 

. 26-1 

Brussels. . . 

. . 10-2 

Senegal ... . 

. 24-6 

Strasburg . . 

. . 9-8 

Rio Janeiro . . 

. 23*1 

Geneva . . . 

. . 9-7 

Cairo. 

22-4 

Boston . . . 

. . 9-3 

Constantine . . , 

, 17*2 

Stockholm . . 

. . 5-6 

Naples . . . . , 

. 16*7 

Moscow . . . 

. . 3-6 

Mexico .... 

. 16-6 

St. Petersburg 

. . 3-5 

Marseilles . . . 

. 14*1 

St. Gothard . 

. . -10 

Constantinople 

. 13-7 

Greenland . . 

. . -7-7 

Pekin. 

. 12-7 

Melville Island 

. .-18-7 


These are mean temperatures. The highest temperature which has 
been observed on the surface of the globe is 47*4° at Esne, in Egypt, and 
the lowest is —56-7 at Fort Reliance, in North America; which gives 
a difference of 104T° between the extreme temperatures observed on the 
surface of the globe. 

The highest temperature observed at Paris was 38*4° on July 8, 1793 
and the lowest —23*5° on December 26, 1798. The highest observed at 
Greenwich was 35° C. in 1808, and the lowest —20° C. in 1838. 










842 


METEOROLOGY. 


[ 853 - 

No arctic voyagers have succeeded in reaching the poles, in consequence 
of these seas being completely frozen, and hence the temperature is not 
known. In our hemisphere the existence of a single glacial pole, that is, 
a place where there was the maximum cold, has been long assumed. But 
the bendings which the isothermal lines present in the northern hemi¬ 
sphere have shown that in this hemisphere there are two cold poles, one 
in Asia to the north of Gulf Taymour, and the other in America, north 
of Barrow’s Straits, about 15° from the earth’s north pole. The mean 
temperature of the first of these poles has been estimated at —17°, and 
that of the second at —19°. With respect to the austral hemisphere, 
the observations are not sufficiently numerous to tell whether there are 
one or two poles of greatest cold, or to determine their position. 

853. Temperature of lakes, seas, and spring's.— In the tropics the 
temperature of the sea is generally the same as that of the air; in polar 
regions the sea is always warmer than the atmosphere. 

The temperature of the sea under the torrid zone is always about 26° 
to 27° at the surface ; it diminishes as the depth increases, and in tempe¬ 
rate as well as in tropical regions the temperature of the sea at great 
depths is between 2-5° and 3-5°. This temperature of the lower layers 
* is caused by submarine currents which carry the cold water of the polar 
seas towards the equator. 

The variations in the temperature of lakes are more considerable ; their 
surface, which becomes frozen in winter, may become heated to 20° or 
25° in summer. The temperature of the bottom, on the contrary, is 
virtually 4°, which is that of the maximum density of water. 

Springs which arise from rain w r ater which has penetrated into the 
crust of the globe to a greater or less depth necessarily tend to assume 
the temperature of the terrestrial layers which they traverse (413). 
Hence when they reach the surface their temperature depends on the 
depth which they have attained. If this depth is that of the layer of 
invariable temperature, the springs have a temperature of 10° or 11° in 
this country, for this is the temperature of this layer, or about the mean 
annual temperature. If the springs are not very copious their tempera¬ 
ture is raised in summer and cooled in winter, by that of the layers which 
they traverse in passing from the invariable layer to the surface. But if 
they come from below the layer of invariable temperature, their tem¬ 
perature may cohsiderably exceed the mean temperature of the place, and 
they are then called thermal springs. The following list gives the tem¬ 
perature of some of them. 

Wildbad.37-5° C. 

Vichy.40 

Bath.46 


-854] 


CLIMATOLOGY. 


843 


Ems. 

56° C. 

Baden-Baden. 

67-5 

Chaudes-Aigues ..... 

88 

Trincheras. 

97 

Great Geyser, in Iceland, at a depth of 66 ft. 

124 


From their high temperature they have the property of dissolving 
many mineral substances which they traverse in this passage, and hence 
form mineral waters. The temperature of mineral waters is not modified 
in general by the abundance of rain or of dryness; but it is by earth¬ 
quakes, after which they have sometimes been found to rise and at others 
to sink. 

854. Distribution of land and water. —The distribution of water 
on the surface of the earth exercises great influence on climate. The 
extent covered by water is considerably greater than that of dry land, and 
the distribution is unequal in the two hemispheres. The entire surface 
of the globe occupies about 200 millions of square miles, nearly § of 
which is covered by water; that is, that the surface of the water is nearly 
three times as great as that of the land. The surface of the sea in the 
southern hemisphere is to that in the northern in about the ratio of 13 
to 9. 

The depth of the sea is very variable, the lead generally reaches the 
bottom at a depth of 300 to 450 yards; in the open sea it is often 1300 
yards, and instances are known in which a bottom has not been reached 
at a depth of 4500. Hence the total mass of the water does not exceed 
that of a liquid layer surrounding the earth, which would be about 1100 
yards deep. 


o o 2 





INDEX 


ABE 

BERK, ATI ON, chromatic, 456 ; 
spherical, 422 
Absolute expansion of mercury, 235 
Absorbing power, 319 
Absorption, 104; of gases, 104; in 
plants, 105; in animals, 105; of 
gases by liquids, 132; of heat by 
gases, 339; by vapours, 335; heat 
produced by, 381 
Acceleration of a force, 12, 51 
Accidental images, 506 
Achromatism, 460; of the microscope, 
470 

Achromatopsy, 510 
Acidometer, 92 
Acoustics, 161 
Actinic rays, 329, 451 
Action and reaction, 22 
Adhesion, 58, 59 
Affinity, 58, 59 
Agents, 2 
Agonic line, 566 

Air balloons, 134; chamber, 152 
air pump, 138, condensing, 145 
Bianchi’s, 142, Sprengel’s, 143, 
gauge, 140, uses of, 147 
Air, heating by, 386; thermometer, 
245 

Ajutage, 156 
Alcarrazas, 276 
Alcohol thermometer, 222 
Alcoholic value of wines, 280 
Alcoholometer, 92; Gay Lussac’s, 93 ; 

centesimal, 93 - 

Alloys, 250 


ART 

Amalgam, 612 
Amalgamated zinc, 669 
Amici’s microscope, 467; camera 
lucida, 484 

Ampere’s memoria technica, 672 ; 

stand, 706; theory of magnetism, 718 
Amplitude of vibration, 33 
Analectrics, 585, 605 
Analogous pole, 591 
Analyser, 532 

Analysis, spectral, 653 ; of solar light, 
325 

Anemometer, 811 
Aneroid barometer, 130 
Angle of deviation, 430; of polarisa¬ 
tion, 531; of repose, 23 
Animals, absorption in, 105 
Annealing, 63 
Annual variations, 566 
Anode, 693 
Antilogous pole, 591 
Aqueous humour, 495 
Aqueous vapour, its influence on cli¬ 
mate, 822 

Arago’s experiment, 145 
Arbor Dianae, 700 ; Saturni, 700 
Arc of vibration, 33 ; voltaic, 687 
Archimedes’ principle, 82; applied to 
gases, 133 
Area, unit of, 10 

Armatures, 580, 628 ; Siemens’, 760 
Arms of levers, 23 

Armstrong’s hydroelectrical machine, 
613 

Artesian wells, 80 





846 


INDEX. 


BUO 


ASC 

Ascent of liquids in capillary tubes, 96; 

between surfaces, 96 
Astatic needle, 572 
Athermancy, 331 

Atmosphere, its composition, 110; 
crushing force of, 110, determination 
of amount of, 112, 114 
Atmospheric electricity, 826 
Atomic heat, 357; weight deduced 
from specific heat, 357 
Atoms, 1 

Attraction, capillary, 95 ; and repul¬ 
sion produced by capillarity, 97; 
molecular, 58 ; universal, 40 
Attractions, magnetic laws of, 5; elec¬ 
trical, laws of, 592 
Attwood’s machine, 50 
Aurora borealis, 567, 838 
Austral magnetism, 560 ; poles, 563 
Avoirdupois, 11 
Axis of oscillation, 54 


B ABINET’S stopcock, 142 

Bain’s electrochemical telegraph, 
735 

Balance, 43 ; beam of, 46; compen¬ 
sation, 234 ; hydrostatical, 82, 87 ; 
knife edge of, 46; physical and 
chemical, 48; torsion, 62, 574, 592 
Balloons, 134; construction and man¬ 
agement of, 135 
Bands of spectrum, 457 
Barker’s mill, 158 

Barometers, 114; aneroid, 130; Bun- 
ten’s, 117 ; cistern, 115; corrections 
in, 118, 119; determination of 

heights by, 122 ; Eortin’s, 115 ; Gay 
Lussac’s, 116; height of, 115; pre¬ 
cautions with, 117; wheel, 121 ; va¬ 
riations of, 119 

Barometric formula, Laplace’s, 124; 

height of corrected for heat, 238 
Baroscope, 133 

Battery, Bunsen’s, 664; Callan’s, 666; 
Daniell’s 663 ; electric, 631 ; gra¬ 
vity, 667 ; Leyden, charged by coil, 


771; local, 734 ; magnetic, 580 ; 
Menotti’s, 668 ; Marie Davy’s, 667 ; 
tension of, 669; thermo-electric, 
785 ; voltaic, 659 
Beam of a balance, 46 
Beats, 187 

Beaume’s hydrometer, 92 
Becquerel’s thermoelectric battery, 737 
Bell of a trumpet, 174 
Bellows, 178-194; hydrostatic, 72 
Berthollet’s experiment, 132 
Bianchi’s air-pump, 142 
Biaxial crystals, double refraction in, 
522 

Binnacle, 568 
Binocular vision, 501 
Black’s experiments in latent heat, 360 
I Bladder, swimming, 86 
' Block and tackle, 24 
Blood globules, 5 

Boiling, 255 ; laws of, 266 ; by cool¬ 
ing, 269 

Boiling point, influence of dissolved 
substances on, % 67 ; of nature of 
vessel, 269; of pressure, 267; 
measure of heights by, 270 ; in a 
thermometer, 219 
Boreal magnetism, 560 ; pole, 563 
, Boussole tangent, 676; sine, 792 
Boutigny’s experiments, 288 
| Boyle and Marriotte’s law, 125, 126 
I Bramah’s hydraulic press, 96 
Breaking weight, 63 
Breezes, land and sea, 813 
Breguet’s thermometer, 224 
Bridge, Wheatstone’s, 797 
British Association unit, 793 
British imperial yard, 10 ; and French 
system of weights and measures, 91 
Brush discharge, 639 
Bull’s eye, 469 

Bunsen’s battery, 665; burner, 455 ; 
photometer, 405 

Bunsen and Kirchhoff’s researches, 
453 

Bunten’s barometer, 117 
Buoyancy of liquids, 70 







CAE 


INDEX. 


847 


/"CESIUM, 456 

Cagniard Latour’s syren, 176; experi¬ 
ments on formation of vapour, 271 
Calorescence, 330 
Caloric, 348 

Calorific effects of electrical discharge, 
642 ; of current electricity, 683 ; of 
Ruhmkorffs coil, 769 
Calorimeter, ice, 350; Favre and Silber- 
mann’s, 363 
Calorimetry, 348 

Camera lucida, 483 ; Amici’s obscura, 
481, 491 

Capacity, specific inductive, 604 
Capillarity, 95 ; attraction and repul¬ 
sion produced by, 97; difficulty of 
theory of, 99 

Capillary phenomena, 95-99; tubes, 
95 ; ascent and depression in, 96 
Carry’s mode of freezing, 275, 276 
' Carriage lamps, 424; 

Cartesian diver, 85 
Cascade charging by, 632 
Cathetometer, 60 
Catoptric telescopes, 476 
Caustics, 422 
Celsius’ scale, 220 
Centesimal alcoholometer, 94 
Centigrade scale, 220 
Centimeter, 92 

Centre of gravity, 42 ; of parallel 
forces, 22 

Charge of a Leyden jar, penetration of, 
630 ; measurement of, 634 ; laws of, 
635; residual, 630 

Chemical combination, 383 ; effects of 
electrical discharge, 646, of voltaic 
current,673, of Kuhmkorffs coil,769; 
harmonicon, 200 ; hygrometer, 296 
Chemistry, 1 
Cheval-vapeur, 378 
Chevallier’s microscope, 467 
Chimes, electrical, 620 
Chladni’s experiments, 204 
Chords, major and minor, 182; tones 
dominant and subdominant, 183; 
physical constitution of, 189 


COM 

Choroid, 196 

Chromatic scale, 184 ; aberration, 460' 
Circular polarisation, 544 
Cirrocumulus, 815 
Cirrostratus, 816 
Cirrus, 814 

Cistern barometer, 115 
Clarke’s machine, 770 
Cleavage, electricity produced by, 590 
Climate, 840; influence of aqueous 
vapour on, 821 
Climatology, 838-843 
Clocks, 56 ; electrical, 736 
Clouds, 814; formation of, 817 ; electri¬ 
city of, 829 

Coatings, 328; Leyden jar with move- 
able, 629 

Coercive force, 562 

Coefficients of linear expansion, 227, 
230 

Cohesion, 58 

Coil, Kuhmkorff’s,765; effects produced 
by, 768-775 

Cold, apparent reflection of, 317 ; pro¬ 
duced by evaporation, 274; sources, 
of, 389, 390 

Colladon and Sturm’s experiments, 170 
Collimation, 674 
Collision of bodies, 37 
Colloids, 102 

Coloration produced by rotatory pola¬ 
risation, 338 
Colour, 3 ; of heat, 337 
Colour disease, 510 
Colours, simple,446complementary, 430 
Combustion, 383 
Common reservoir, 587 
Communicator, 729 
Commutator, 727, 753, 767 
Compensation pendulum, 233 ; strips, 
234, balance, 234 
Component forces, 15 
Composition of velocities, 30 
Compressed glass, colours produced by, 
543 

Compressibility, 3, 7; of gases, 125; 
of liquids, 66 




INDEX. 


848 

COM 

Compass, declination, 567 ; mariner’s, 
568 ; inclination, 570 ; sine, 782; tan¬ 
gent, 676 
Concert pitch, 185 
Concordant tones, 182 
Condensation of vapours, 278 
Condensed wave, 163 
Condenser, 618, 622; limits to charge 
of, 617 ; of RuhmkorfTs coil, 767; 
Liebig’s, 279 

Condensing engine, 377; pump, 145; 

force, calculation of, 626 
Conduction of heat, 305; of electricity, 
585 ; lightning, 834 
Conductivity of bodies for heat, 305; 
of liquids and of gases, 307 ; for 
electricity, 378; 790; 798 
Conductors, equivalent, 796 
Congelation, 251 
Conjugate mirrors, 316 
Conservation of vis viva, 39 
Constant currents, 662-668 
Contractile force, 232 
Convection, 308 

Convex meniscus, 96 ; mirrors, 416 
Cooling, method of, 354; Newton’s 
law of, 313 
Cornea, 494 

Corpuscular theory, 395 
Cosine, law of the, 313, 405 
Couple, 21; voltaic, 650; thermoelec¬ 
tric, 785 ; terrestrial magnetic, 564 
Couronne des tasses, 661 
Critical angle, tf 2-'7 
Crystals, expansion of, 230; doubly 
refracting, 519; uniaxial, 519 
Crystal, hemihedral, 591 
Crystalline, 495 
Crystallisation, 252 
Crystalloids, 102 
Cube, Leslie’s, 318 
Cumulostratus, 818 
Cumulus, 817 

Currents, action on currents, 704- 
711; action of magnets, 711; action of 
earth on, 714-716; action on solenoids, 
717; derived, 801; detection and mea- 


DIA 

surement of voltaic, 671; direct and 
inverse, 739 ; effects of enfeeblement 
of, 662, 682-703 ; extra, 747; inten¬ 
sity of, 677 ; induction by, 738; mag¬ 
netism by, 720; motion and sounds 
produced by, 723; terrestrial, 719 ; 
transmissions by, 695; current 
electricity, 656 ; intensity of, 677 
Curvature of liquid surfaces, 97; influ¬ 
ence of on capillary phenomena, 98 

AGUERREOTYPE, 480 
Dalton’s method of determining 
the tension of aqueous vapour, 259 ; 
law of mixture of gases and vapours, 
28 

Daltonism, 510 

Daniell’s battery, 669; hygrometer, 
227; pyrometer, 226 
Dark lines of spectrum, 452 ; of solar 
spectrum, 457 
Day, apparent, 10 
Decimetre, 11 

Declination, magnetic, 565; of a star,479 
Decomposition, chemical, 693, 604 ; of 
white light, 445 
Deflagrator, Hare’s, 661, 685 
Degrees of a thermometer, 220 
De la Rive’s apparatus, 706 ; experi¬ 
ment, 775 

Delicacy of thermometer, 223 k 
Densimeter, 94 

Density, 11; of the earth, 42 ; electric, 
597; of gases, 246-248 ; maximum 
of water, 239; of vapours, Gay- 
Lussac’s method, 291; Dumas’s, 
292 ; Deville and Troost’s, 294 
Depolarisation, 519, 539 
Depression of liquids in capillary tube, 
86 ; between surfaces, 96 
Despretz’s experiment, 305 
Deviation, angle of, 430, 431 
Diabetic urine, analysis of, 555 
Dialyser, 102 
Dialysis, 102 
Dial telegraphs, 727 






DIA 


INDEX. 


849 


Diamagnetism, 797, 

Diapason, 185 
Diathermancy, 331 
Dielecaics, 605 

Differential thermometer, Leslie’s ,223; 

Matthiessen’s, 223 ; tone, 189 
Diffraction, 398, 525 
Diffusion of heat, 347 ; of liquids, 101 
Digester, Papin’s, 272 
Dioptric telescopes, 476 
Diplopy, 510 

Discharge, electrical, 625; effects of 
the, 638-647 

Discharger, universal, 632 
Dip, magnetic, 569 
Dipping needle, 569 
Dispersion, 430 
Dispersive power, 446 
Distance, estimation of, 498; adapta¬ 
tion of eye to, 499 
Distillation, 278 

Distribution of electricity, 594— 599; 
of magnetism, 583 ; of temperature, 
844; of land and water, 845 
Diurnal variations, 566 
Diver, Cartesian, 85 
Divisibility, 3, 5 
Dobereiner’s lamp, 382 
Dominant, 183 
Double refraction, 519—522 
Double action steam engine, 367—372 
Doublet, Wollaston’s, 463 
Dove’s law of storms, 814 
Draught of a fire-place, 385 
Drummond’s light, 488 
Duchenne’s electrovoltaic apparatus, 
807 

Ductility, 3, 64 

Duhamel’s graphic method, 179 
Dulong and Arago’s experiments on 
Boyle’s ; law, 127; method of deter¬ 
mining the tension of aqueous vapour, 
259 

Dulong and Petit’s determination of 
absolute expansion of mercury, 237 
Dulong and Petit’s method of cooling, 
353; law, 357 


ELE 

Dumas’s methodfor vapour density,293 
Duration of electrical spark, 650 
Dutrochet’s endosmometer, 100 
Dynamic radiation and absorption, 343 
Dynamical theory of heat, 323 
Dynamo magnetic machine, 763 

T^ARTH, its action on currents, 714 
—716; action on solenoids, 717 ; 
flattening of by rotation, 59 ; poles 
of the, 58 ; magnetisation by, 578 
Ear trumpet, 174 

Earnshawon velocity of sound, 168 
Ebullition, 255 ; laws of, 266 
Eccentric, 370 
Echelon lenses, 481 
Echoes, 172; monosyllabic, trisyllabic, 
multiple, 173 

Efflux, velocity of, 154; quantity of, 
156 ; influence of tubes on, 156 
Effusion of gases, 104 
Elasticity, 3, 8; of traction, 60, mo¬ 
dulus of, 61, of torsion, 62, of flexure, 
63 

Elastic force, 107 ; of vapours, 255 
Electricity, 2 ; atmospheric, 827-836 ; 
current, 656; communication of, 
606 ; dynamical, 653; disengagement 
of in chemical actions, 655; dis¬ 
tribution of, 594; loss of, 643; 
produced by induction, 600 ; velocity 
of, 650; theories of, 588 
Electric batteries, 631; charge, 635 ; 
chimes, 620; clocks, 736; density, 
597 ; egg, 690 ; fish, 804; light, 686 
—692, stratification of the, 772 ; 
machines, 608—619; pendulum, 

584; wheel, 621 

Electrified bodies, motion of, 606 
Electrochemical telegraph, 735 
Electrodes, 659 
Electrodynamics, 704—720 
Electrogilding, 702 
Electrolysis, 693 
Electromagnets, 721 
Electromagnetic machine, 737 






850 


ELE 


INDEX. 


Electrometallurgy, 701 
Electrometer, 608 ; Lane’s, 635; quad¬ 
rant, 613; Thomson’s, 633 
Electromotive series, 656, force, 658 
677 ; determination of, 779 ; force of 
elements, 668 
Electrophorus, 608 
Electropyrometer, 789 
Electroscope, 584; Bohnenberger’s, 
670; condensing, 636; gold lea£ 
607 

Electrosilvering, 703 
Electrostatics, 704 

Elements, electronegative and electro¬ 
positive, 694 

Elliptical polarisation, 544, 547 
Emissive power, 320 
Endosmose, 100 ; of gases, 103 
Endosmometer, 100 
Endosmotic equivalent, 100 
Energy, 37 ; conservation of, 39 
Engines, steam, 366; double action, 
367 ; single action, 372; locomotive, 
373 ; fire, 154 
Eolipyle, 376 
Equator, magnetic, 570 
Equilibrium, 9 ; of forces, 18; of float¬ 
ing bodies, 84 ; of heavy bodies, 43; 
of a liquid, 73—76 ; mobile, of tem¬ 
perature, 313; neutral, 45; stable, 
44; unstable, 44 
Equivalent endosmotic, 101 
Escapement, 56 ; wheel, 56 
Ether, 324; luminiferous, 395 
Exchanges, theory of, 313 
Exhaustion, produced by air-pump, 
144 ; by Sprengel’s pump, 145 
Exosmose, 100 
Expansibility of gases, 107 
Expansion, apparent and real, 235; 
apparent of mercury, 237 ; of liquids, 
238; of solids, 215 ; of liquids, 216; 
of gases, 216, 240, 242, 243; linear 
and cubical, coefficients of, 226; 
measurement of linear, 227, 228 ; 
of crystals, 230; applications of, 
232; force of, 232, 253 


FOO 

Expansion of gases, cold produced by, 
389 

Expansive force of ice, 253 
Experiment, Berthollet’s, 132; Frank- 
lin’s, 270; Florentine, 67; Pascal’s, 
113 ; Torricellian, 112 
Extension, 3, 4 
Extra current, 747, 749 
Eye, 493; refractive indices of media 
of, 496; path of rays in, 496; di¬ 
mensions of various parts of, 396 
Eye glass, 470; glasses, 509; lens, 
471; piece, 464, 466; Campani’s, 
470 


ALLING- bodies, laws of, 49 

Favre and Silbermann’s calori¬ 
meter, 364; determination of heat 
of combustion, 384 

Field of a microscope, 469 ; of view, 
471 

Field lens, 471 ; glass, 470 
Figures, Lichtenberg’s, 630 
Finder, 473 

Fire engine, 154 ; places, 385; works, 
159 

Fishes, swimming bladder of, 86 
Fixed liquids, 255 

Fizeau’s determination of velocity of 
light, 403 
Flame, 383 

Flask, specific gravity, 88 
Flattening of the earth, 57 
Florentine experiment, 7, 67 
Fluid, 2; imponderable, 3; elastic, 
107 ; magnetic, 559 
Fluidity, 3 
Fluorescence, 459 
Fluxes, 250 
Focal distance, 315 
Foci, acoustic, 173 ; of convex mirrors, 
416 

Focus, 315; conjugate, 413 
Fogs, 814 
Foot, 10 

Foot-pound, 38, 377 






INDEX. 


FOR 

Forces, 2 ; impulsive, 35; molecular, 
38 ; moments of, 22 ; polygon of, 19; 
triangle of, 19 

Force, 9; conservation of, 39; direc¬ 
tion of, 14; elastic, of gases, 107; of 
expansion and contraction, 232 ; re¬ 
presentation of, 14; parallelogram 
of, 15 

Formula for expansion, 231; barome¬ 
tric, 124; for sound, 169 ; for spheri- 
cal mirrors, 420—422; for lenses, 663 
Fortin’s barometer, 115 
Foucault’s determination of velocity of 
light, 401; experiment, 689 
Fountain in vacuo, 147; at Giggles- 
wick, 151; intermittent, 159 ; Hero’s, 
149 

Franklin’s experiment, 270, 825; 

theory of electricity, 588 
Fraunhofer’s lines, 452, 453 
Freezing, apparatus for, 274—277 
Freezing mixtures, 254; point in a 
thermometer, 219 
French weights and measures, 91 
Fresnel’s experimentum crucis, 523; 
rhomb, 546 

Friction, 12, 27; heat of, 378; hy¬ 
draulic, 157 ; development of elec¬ 
tricity by, 584, 589 
Friction wheels, 51 
Frigorific rays, 317 
Fringes, 525 
Frog current, 655 
Frost, 821 
Fulcrum, 23 
Fulminating pane, 627 
Fuse, Abel’s, 649 ; Chatham, 683 
Fusing point, 249 

Fusion, laws of, 284; vitreous, 249; 
latent heat of, 360 


G alleries, whispering, 173 

Gallon, 91 

Galvani’s experiment, 653 
Galvanometer, 672 ; differential, 675; 
Sir W. Thomson’s, 675 


851 

GUL 

Galvanoscope, 674 
Galvanothermometer, 684 
Gases, absorption of by liquids, 132; 
application of Archimedes’ principle 
to, 133; compressibility of, 108, 
125 ; conductivity of, 308 ; diamag¬ 
netism of, 781 ; density of, 246 ; 
expansion of, 108, 240—245 ; endos- 
mose of, 103 ; effusion and transfor¬ 
mation, 104; laws of mixture of, 
132; and vapours, mixtures of, 285 ; 
problems in, 287 ; liquefaction of, 
282—285 ; physical properties of, 
107 ; pressure exerted by, 109 ; ra¬ 
diation of, 343; specific heat of, 308 
Gaseous state, 2 

Gauge, air pump, 140 ; rain, 819 
Gay Lussac’s alcoholometer, 93 ; baro¬ 
meter, 116; determination and ex¬ 
pansion of gases, 240 ; of vapour- 
density, 291 ; stopcock, 286 
Geissler’s tubes, 145, 773 
Gimbald’s, 508 

Glass, expansion of, 238; magnifying, 
462 ; object, 346; opera, 475 
Glasses, periscopic, 509 ; weather, 122 
Glaciers, 823 

Glaisher’s balloon ascents, 135; factors, 
301 

Glow, electrical, 640 
Goniometers, 423 
Gramme, 11, 91 

Graphic method, Duhamel’s, 179 
Gratings, 526 
Gravesande’s ring, 215 
Gravitation, 2, 40; terrestrial, 41; 
gravity, 12, 40; accelerative effect 
of, 13; centre of, 43; specific, 11 
Gravity battery, 668 
Gridiron pendulum, 233 
Grimaldi’s experiment, 523 
Grotthuss’ hypothesis, 696; 

Grove’s gas battery, 699 
Gulf stream, 842 






852 


HAI 


INDEX. 


H ail, 822 

Haldat’s apparatus, 70 
Hallstrom’s experiments, 240 
Haloes, 517 

Hardness, 3 ; scale of, 65 
Hare’s deflagrator, 661 ; 685 
Harmonics, 186 

Harmonic triad, 182; grave, 189 
Harmonicon, chemical, 200 
Harris’s unit jar, 635 
Heat, 2; diffusion of, 337; developed 
by induction, 776; hypothesis on, 
214; latent, 251 ; polarisation of, 
555, radiating, 305; radiant, 310; 
reflection of, 314; scattered, 319; 
sources of, 378—394 ; specific, 348 
Heating, 384—389 

Heights of places, determination of, 
by barometer, 122; by boiling- 
point, 260 

Height of barometer, 115; variation 
in, 119 

Hoar frost, 821 

Howard’s nomenclature of clouds, 818 
Heliostate, 423 
Helix, 26, 720 

Hemispheres, Magdeburg, 112 

Hemihedral crystal, 591 

Henley’s electrometer, 613 

Henry’s experiment, 749 

Herapath’s salt, 535 

Hero’s fountain, 149 

Herschelian rays, 326 

Holmes’ magnetoelectrical machine 750 

Holtz’s electrical machine, 616 

Homogeneous light, 450 

Hope’s experiments, 239 

Horizontalline, 42 

Horse power, 377 

Hotness, 216 

Hour, 10 

Humour, aqueous, 495 
Hydraulics, 60 

Hydraulic press, 76; friction, 157; 

tourniquet, 158 
Hydrodynamics, 66 
Hydroelectrical machine, 613 


IND 

Hydrometers, 86; Nicholson’s, 87; 
Fahrenheit’s, 99; with variable vol¬ 
ume, 92 ; Beaume’s, 92; of constant 
volume, 22 ; gravities, specific, 86 ; 
uses of tables of, 91 
Hydrostatic bellows, 72 ; paradox, 72 ; 
balance, 82 

Hygrometers, 296—302 
Hygro’metric plate, 295; substances, 295 
Hygrometry, 295 ; problem on, 302 
Hypsometer, 271 

TCE, 823 

1 Ice calorimeter, 350; expansive 
force of, 23 
Iceland spar, 535 
Idioelectrics, £85 

Images, accidental, 506; condition of 
distinctness of, 464 ; formation of, 
in concave mirrors, 418; in convex 
mirrors, 419 ; in plane mirrors, 409 ; 
of multiple, 411 ; produced by small 
apertures, 398; virtual and real, 
410 ; inversion of, 497 
Imbibition, 104 
Impenetrability, 3 
Imperial British yard, 10; 
Imponderable matter, 3 
Inch, 91 

Inclination, 579 ; compass, 570 
Inclined plane, 24; motion on, 30 
Incoercible, 3 

Index of refraction, 426 ; measurement 
of, in solids, 432; in liquids, 433; 
in gases, 433 
Indicator, 724 

Indices, refractive, table of, 634 
Induced currents, 738—750 
Induction, apparatus founded on, 750 
—778 ; by the earth, 746 ; by cur¬ 
rents, 738—741; of a current in 
itself, 747 ; electrical, 600 ; limit to, 
602 ; Faraday’s theory of, 603 ; heat- 
developed by, 776; by magnets, 742 
Inductive capacity, specific, 604 
Inductorium, 765 






INDEX. 


INE 

Inertia, 9, 12; applications of, 9 
Influence, magnetic, 362; electrical, 600 
Ingenhouse’s experiment, 305 
Insects, sounds produced by, 178, 
Insulating bodies, 587 ; stool, 619 
Insulation, 513 

Instruments, optical, 462 ; polarising 
532 ; mouth, 193, 203 ; stringed, 
203 ; wind, 193, 203 
Intensity of the current, 677 ; of the 
electric light, 691; of light, 403, 
412; of a musical tone, 182; 
of radiant heat, 311; of sound, 
causes which influence, 164; of ter¬ 
restrial magnetism, 572; of terres¬ 
trial gravity, 56 
Interference of light, 522 
Intermittent syphon, 150; springs, 151; 

fountain, 150 
Intervals, musical, 182 
Iris, 494 

Iron, passive state of, 699 
Irradiation, 506 
Irregular reflection, 412 
Isochimenal line, 842 
Isoelinic lines, 570 
Isodynamic lines, 573 
Isogonic line, 556 
Isotheral lines, 842 
Isothermal line, 842 ; zone, 142 


J ACOBI’S unit, 793 

Jar, Leyden, 628, 636 
Jar, luminous, 642 

Jet, lateral, 155; height of, 155; form 
of, 157 


ALEIDOPHONE, 506 
Kaleidoscope, 412 
Kamsin, 813 
Kathode, 693 
Keepers, 580 

Key, 727, 732, 753, 767note, 184 
Kienmayer’s amalgam, 512 
Kilogramme, 11, 91 


• 853 

LIG 

Kilogrammeter, 378 
Knife edge, 46 

L actometer 92,94 

Ladd’s dynamomagnetic machine, 
763 

Lane’s electrometer, 634 
Laplace’s barometric formula, 124 
Latent heat, 251; of fusion, 360; of 
vapours, 362 
Latitude, parallel of, 57 
Lavoisier and Laplace’s calorimeter, 
351; method of determining linear 
expansion, 227 
Law, 2 

Lead tree, 700 

Leidenfrost’s phenomenon, 288 
Length, unit of, 10 ; of undulation, 164 
Lenses, achromatic, 460 ; foci in double 
convex, 436; in double concave, 
438 ; formation of images in double 
convex, 440; in double concave, 
438; formulae relating to, 443; 
lighthouse, 488; optical centre, 
secondary axis of, 439 
Lenz’s law, 740 

Leslie’s cube, 318 ; experiment, 274; 

thermometer, 224 
Level, water, 78 ; spirit, 79 
Level, surface, 42 
Levelling staff, 79 
Lever, 23 

Leyden discharge, inductive action of, 
741 

Leyden jars, 628—636 ; charged by 
Ruhmkorff’s coil, 771 
Lichtenberg’s figures, 630 
Liebig’s condenser, 279 
Light, diffraction of, 525; interference 
of, 523; oxyhydrogen, 488 ; polari¬ 
sation of, .529; sources of, 512; 
theory of polarised light, 536 ; un- 
dulatory theory of, 516 
Lighthouse lenses, 488 
Lightning, 832; effects of, 833; con¬ 
ductor, 834 






854 


LIM 


INDEX. 


MEC 


Limit, magnetic, 580, 582 ; to induc¬ 
tion, 602; of perceptible sounds, 
178 

Line, actinic, 570; isoclinic, 570; 
agonic, 566 ; isogonic, 566 ; isody¬ 
namic, 573; of sight, 474 
Liquids, 9, 66; active, and inactive, 
550; buoyancy of, 70; compressi- 
• bility of, 66; conductivity of, 307; 
calculation of density of, 76; diffu¬ 
sion of, 101; diamagnetism of, 780 ; 
expansion of, 238, 239; equilibrium 
of, 73—76; manner in which they 
are heated, 308 ; rotating power of, 
549 ; spheroidal form of, 58 ; sphe¬ 
roidal rate of, 289 ; specific heat of, 
355; volatile, and fixed, 255; ten¬ 
sions of vapours of, 264; of mixed 
liquids, 264 

Liquefaction of gases, 282—285; of 
vapours, 278 

Lissajous’ experiments, 206—211 
Litre, 11 
Loadstone, 557 

Local battery, 739 ; currents, 669 
Locomotive, 373—376 
Long-sight, 499, 508 
Loops and nodes, 192 
Loss of electricity, 598 ; of weight in 
air, correction for, 303 
Loudness of a musical tone, 182 
Luminous bodies, 396; effects of the 
electric discharge, 639 ; of the elec¬ 
tric current, 686; of Ruhmkorff’s coil, 
769; pencil, 396; ray, 396; tube, 
square, and bottle, 641 


M achine, 391; Attwood’s, 50 ; 

electrical, 608—619; von Ebner’s, 
697; electromagnetic, 738 
Mackarel sky, 816 
Magdeburg hemispheres, 112 
Magnetic battery, 580; couple, 564; 
declination, 565 ; dip, 589 ; effects 
of electrical discharge, 644 ; equator, 
569; induction, 561 * inclination, 


569; limit. 582; meridian, 565; 
saturation, 579; storms, 567 
Magnetisation, 577; by the action of 
the earth, 578 ; by currents, 720 
Magnetism, 2, 557 ; Ampere’s theory of, 
718 ; remanent, 723 ; theory of, 559 ; 
terrestrial, distribution of free, 582 
Magnets, artificial, and natural, 537 ; 
broken, 560 ; action of earth on, 563; 
portative force of, 581; saturation 
of, 380; influence of heat, 582; in¬ 
duction by, 742 ; inductive action on 
moving bodies, 743; action on cur¬ 
rents, 712, 713; on solenoids, 717 ; 
on induced currents on, 775; optical 
effects of, 778 

Magnetoelectrical apparatus, 750; 

machines, 756—763 
Magnification, measure of, 465, 471; 

of a telescope, 473 ; 

Magnitude, 4; apparent of an object, 
465; of images in mirrors, 422 
Major chord, 182 
Malleability, 3, 65 

Manometer, 67; air, 129 ; with com¬ 
pressed air, 129 
Marie Davy battery, 667 
Mares’ tails, 815 
Mariner’s compass, 568 
Marine galvanometer, 675 
Mariotte’s tube, 125; bottle, 159 
Mariotte and Boyle’s law, 126, 126 
Marloye’s harp, 203 
Maskelyne’s experiment, 42 
Mason’s hygrometer, 300 
Mass, measure of, 10 ; unit of, 10 
Matter, 1 

Matteucci’s experiment, 741 
Matthiessen’s thermometer, 224 
Maximum thermometer, 225 
Measure of magnification, 465, 471; of 
time, 9; of space, 10; of velocity* 
12 ; of mass, 10 

Mechanical equivalent of heat, 3; 
effects of electrical discharge, 645 ; 
of voltaic battery sources of heat 
378 ; theory of heat, 323 



INDEX. 


MEN 

Melloni’s researches, 323 
Meniscus, 96 ; in barometer, 118 
Menotti’s battery, 668 
Mercury, frozen, 274, 285, 289; pen¬ 
dulum, 234; expansion of, 235, 
236 

Meridian, 10; magnetic, 565 
Metacentre, 84 

Metal, Rose’s and Wood’s fusible, 251 
Metre, 10, 91 
Micrometer, 5, 472 

Microscope, 5; Amici’s, 466; compound, 
460; magnifying powers of, 471; 
photoelectric, 487 ; simple, 462; 
solar, 485 
Mill, Barker’s, 158 
Mines, firing by electricity, 657, 683 
Minimum thermometer, 225 
Minor chord, 182 
Minute, 10 
Mirage, 428 

Mirrors, burning, 317, 423; concave, 
315; conjugate, 316; glass, 411; 
parabolic, 423 ; spherical, 413 
Mixture of gases, 131; of gases and 
liquids, 132 

Mixtures, freezing, 254 
Mobile equilibrium, 313 
Mobility, 3, 8 
Modulus of elasticity, 61 
Molecular forces, 1,58; state of bodies, 2 
Molecules, 1 
Moments of forces, 22 
Momentum, 13 
Monochord, 191 
Monochromatic light, 450 
Monosyllabic echo, 173 
Morgagni’s humour, 495 
Morse’s telegraph, 731 
Motion, 8, 9 ; curvilinear, 12; in a 
circle, 31, 32 ; rectilinear, 12; uni¬ 
formly accelerated rectilinear, 28; 
quantity of, 13 ; of a pendulum, 33 
Mouth instruments, 193 
Multiple echoes, 173 ; images formed 
by mirrors, 411 
Multiplier, 672 


855 

OUT 

Music, 161 ; physical theory of, 181 
Musical intervals, 182; scale, 182; 
temperament, 184; tones, proper¬ 
ties of, .181; intensity, pitch and 
timbre of, 181 
Myopy, 499, 508 


N AIRNE’S electrical machine, 613 
Nascent state, 59 
Natterer’s apparatus, 283 
Needle dipping, 569 ; astatic, 572 
Neutral line, 557 

Newton’s disc, 449 ; law of cooling, 313; 

rings, 528 ; theory of light, 450 
Nicholson’s hydrometer, 87 
Nicols’ prism, 335 
Nimbus, 815 

Nobili’s battery, 785; rings, 700; 
thermomultiples, 788; thermopile, 
323, 326 

Nodal point, 192; and ventral seg¬ 
ments, 157 

Nodes and loops, 192; of an organ 
pipe, 195 ; explanation of, 198 
Noise, 161 
Nonconductors, 585 
Norremberg’s apparatus, 533 
Notes in music, 182, 184 
Nut of a screw, 26 


BSCURE rays, 325 ; transmutation 
of, 329 

Objective, 466 
Oersted’s experiment, 671 
Ohm’s law, 677 
Opaque bodies, 396 
Opera glasses, 475 
Ophthalmoscope, 511 
Optic axis, angle, 497 
Optical effects of magnets, 779 
Optometer, 499 
Organ pipes, 193., 194 
Orrery, electrical, 622 
Oscillations, 33 ; method of, 576 
Outcrop, 80 







INDEX. 


85G 

OVE 

Overshot wheels, 159 
Oxyhydrogen light, 488 
Ozone, 646 


P ALLET, 56 

Pane, fulminating, 627; lumi¬ 
nous, 641 

Papin’s digester, 272 
Parabolic mirrors, 423 
Parachute, 137 
Paradox, hydrostatic, 72 
Parallel of latitude, 57; forces, 20; 
centre of, 22 

Parallelogram of forces, 15 
Paramagnetic bodies, 779 
Pascal’s law of equality of pressures, 
68; experiments, 113 
Passage tint, 552 
Passive state of iron, 699 
Peltier’s experiment, 790 
Pendulum, 33; application to clocks, 
>56 ; conical, 34 ; compensation, 233; 
electrical, 584 ; mercurial, 234; 
length of compound, 53; verifica¬ 
tion of laws of, 54 
Penumbra, 397 
Percussion, heat due to, 379 
Periscopic glasses, 509 
Persistance of impression on the retina, 
505 

Perturbation, magnetic, 565, 567 
Phenakistoscope, 506 
Phenomenon, 2 
Phial of four elements, 75 
Phonautograph, 211-213 
Phosphorogenic rays, 452 
Phosphorescence, 512-516 
Phosphoroscope, 514 
Photoelectric microscope, 487 
Photographs on paper, 492 ; on albu- 
menised paper and glass, 493 
Photography, 490-493 
Photometers, 405-407 
Physics, object of, 1 
Physiological effects of the electric 


POW 

discharge, 638 ; of the current, 682 ; 
of Ruhmkorff’s coil, 769 
Piezometer, 66 
Pile, voltaic, 653-670 
Pisa, tower of, 44 
Pistol, electric, 646 
Piston of air pump, 139 
Pitch concert, 185; of a note, 181 of 
a screw, 26 

Plane, 24 ; electrical inclined, 622 
Plants, absorption in, 105 
Plates, colours of thin, 528; vibra¬ 
tions of, 203 
Plumb-line, 42 
Pluviometer, 819 
Pneumatic syringe, 108, 379 
Poggendorff s law, 658 
Point, boiling, 267 
Points, power of, 597 
Polarisation, angle of, 531 ; by double 
refraction, 529; by reflection, 530; 
by single refraction, 532 ; elliptical 
and circular, 544 ; of heat, 555; 
galvanic, 662, 698; of the medium, 
603 

Polarised light, theory of, 536; colours 
produced by the interference of, 537 
-539 

Polariser, 532 
Polarising instruments, 532 
Polarity, 662 

Poles, 659; of the earth, 570 ; of a 
magnet, 557 ; mutual action of, 558; 
precise definition of, 559; austral 
and boreal, 563 
Polygon of forces, 19 
Ponderable matter, 3 
Pores, 6 

Porosity, 3, 6 ; application of, 7 
Portative force, 581 
Positives on glass, 493 
Postal battery, 735 
Potential energy, 39 
Pound, 91; avoirdupois, 11, 14 
Powders, radiation of, 346 
Power of a lever, 23 ; of a microscope, 
466 



INDEX. 


PRE 

Presbytism, 508, 499 
Press, hydraulic, 76 
Pressure, centre of, 72 ; on a body in 
a liquid, 81; atmospheric, 110; 
amount of, on human body, 114; 
experiment illustrating, 148; heat 
produced by, 379 ; electricity pro¬ 
duced by, 590 

Pressures, equality of, 68; vertical 
downward, 69 ; vertical upward, 70; 
independent of form of vessel 
Prevost’s theory, 313 
Primary coil, 739 
Principle of Archimedes, 82 
Prism, 429-432; Nicols’, 535 
Problems on expansion of gases, 242 ; 
on mixtures of gases and vapours, 
287 ; on hygrometry, 302 
Proof plane, 594 
Propagation of light, 397 
Pulleys, 24 

Pulvermacher’s chain, 809 
Pump, air, 136; condensing, 145 ; 
different kinds of, 151; suction, 
151 

Pupil, 494 
Psychrometer, 300 
Pyroelectricity, 591 
Pyroheliometer, 381 
Pyrometers, 226 


QUADBANT electrometer, 613 

ADI A TING- power, 320 

Kadiation, cold produced by, 389; 
of gases, luminous and obscure, 328 ; 
of heat, 310; solar, 610 
Bain, 819; clouds, 817; bow, 836; 

fall, 820; gauge, 819 
Bay, luminous, 396 ; ordinary and ex¬ 
traordinary, 520 

Bays actinic or Bitteric, 329; frigorific, 
317; of heat, 310, 324; invisible, 


857 

RHO 

325; path of in eye, 496; transmu¬ 
tation of thermal, 331 
Bamsden’s electrical machine, 610 
Barefaction in air pump, 141 ; by 
Springel's pump, 145 
Beaction and action, 22; machines. 
376 

Beal volume, 7 ; focus, 413, 414 
Beaumur scale, 221 
Beceiver of air pump, 138 
Becomposition of white light, 428 
Beed instruments, 193, 194 
Beflecting power, 317 
Beflection, apparent, of cold, 317; of 
heat, 314; from concave mirrors, 
315 ; demonstration of laws of, 316 ; 
in a vacuum, 317; of light, 407- 
424; irregular of found, 171 
Befraction, 174, 425-429; double, 

516 ; polarisation by, 519 ; explana¬ 
tion of single, 518 

Befractive index, 426; table of, 434 ; 

indices of media of eye, 496 
Befractory substances, 249 
Befrangibility of light, alteration of, 
459 

Begelation, 823 

Begnault’s determination of density of 
gases, 247; of specific heat, 353 ; 
of tension of aqueous vapour, 259, 
261; hygrometer, 298 
Begulator of the electric light, 689 
Belay, 733 

Bemanent magnetism, 723 
Bepulsions, electrical laws of, 592 
Beservoir, common, 587 
Besistance of a conductor, 678 
Besonance, 172; box, 185; globe, 186 
Best, 8 

Besultant of forces, 15, 17 
Betina, 495; persistance of impression 
on, 505 

Beversion, method of, 568 
Bheometer, 675 
Bheoscope, 674 
Bheostate, 790 
Bhomb, Fresnel’s, 546 




INDEX. 


858 

RHU 

Rhumbs, 568 
Right ascension, 479 
Rime, 832 

Rings, Newton’s, 529; Nobili’s, 700 
Ritchie’s experiment, 321 
Ritteric rays, 329 
Rods, vibrations of, 203 
Rose’s fusible metal, 250t 
Rotation of the earth, 57 ; of currents, 
709 

Rotatory power of liquids, 549 ; po¬ 
larisation, 545, 547 ; coloration pro¬ 
duced by, 548 

Roy and Ramsden’s measurement of 
linear expansion, 228 
Rubidium, 456 
Ruhmkorff’s coil, 765 
Rumford’s photometer, 405 
Rutherford’s thermometer, 225 


S ACCHARIMETER, 551 
Saccharometer, 92 
Safety valve, 78, 272 ; tube, 281 
Sagitta of meniseus, 118 
Salimeter, 94 

Salts, decomposition of, 695 
Saturation, degree of, 295 ; magnetic, 
579 

Savart’s toothed wheel, 175 
Scale of hardness, 65 
Scales in music, 183 ; chromatic, 184 ; 
of a thermometer, 220 ; conversion 
of, into one ’other, 221 
Scattered light, *12 
Schehallien experiment, 41 
Sclerotica, 494 
Scott’s phonautograph, 211 
Screw, 5, 25 
Second of time, 9, 10 
Seconds pendulum, 54 
Secondary batteries, 699; currents, 
662; coil, 739 

Secular magnetic variations, 565 
Segments, ventral and nodal, 157, 192 
Segner’s water-wheel, 159 
Semi-conductors^ 586 


SOU 

Semitone, 183, 184 

Senarmont’s experiment, 307 

Series, thermoelectric, 783 

Shadow, 397 

Shock, electric, 638 

Shortsight, 499, 508 

Siemens’ armature, 760; unit, 793; 

electrical thermometer, 800 
Sight, line of, 474 
Simoom, 812 
Sine compass, 792 
Singing of liquids, 267 
Sinuous currents, 706 
Sirocco, 813 
Size, estimation of, 498 
Sleet, 822 

Smee’s battery, 667 
Snow, 822 

Soap bubble, colours of, 528 
Solar microscope, 485 ; light, thermal 
analysis of, 325; radiation, 380; 
spectrum, 445; properties of the, 
451 ; dark lines of, 452 ; time, 10; 
day, 10 

Soleil’s saccharimeter, 551 
Solenoids, 716, 718 ; action of currents 
on, 717 ; of magnets and of earth 
on, 717 ; on solenoids, 718 
Solidification, change of volume on, 
253 ; retardation of, 252 
Solidity, 2, 3 

Solids, diamagnetism of, 729 
Solution, 251 

Sondhauss’ experiments, 174 
Sonometer, 191 
Sonorous body, 161 
Sound, 161 ; cause of, 161 ; not pro¬ 
pagated in vacuo, 162; propagated 
in all elastic bodies, 163 ; propaga¬ 
tion of, in ai , 163; causes which 
influence intefl / ty of, 164 ; appara¬ 
tus to strengthen, 165 ; velocity of, ir 
gases, 2’"', '; r,Y n liquids and solids 
170 ; reflection'of, 171; refraction of, 
174 

Sounds, limit of perceptible, 178 ; pro 
duced by currents, 723 




INDEX. 


SPA 

Space, measure of, 9, 10 
Spark, electrical, 619, 639; duration 
of, 650 

Speaking trumpet, 174; tubes, 167 
Specific gravity, 11, 86; flask, 88, 90; 
of liquids, 90, 91 

Specific heat, 348, 359 ; determination 
of, by fusion of ice, 350; by method 
of mixtures, 351 ; by Regnault’s 
apparatus, 352 ; of solids and liquids, 
355 ; of gases, 356 
Specific inductive capacity, 604 
Spectacles, 509 
Spectral analysis, 453 
Spectroscope, 453, 456 
Spectrum, 325 ; solar, 445 
Specular reflection, 412 
Spherical aberration, 422, 443; mirrors, 
413 ; focus of, 413 

Spheroidal form of liquids, 58; state, 
289 

Spiral, 720 
Spirit level, 79 
Sprengel’s air-pump, 144 
Stars, spectral analysis of, 458 
Staubbach, 50 

Steam engines, 366; boiler, 367; 
double action, or Watt’s, 367; va¬ 
rious kinds of, 377; work of, 377 ; 
heating by, 386 
Stereoscope, 502-5 
Stethoscope, 167 
Stills, 278 

Stool, insulating, 619 

Stopcock, doubly-exhausting, 142; 

Gay-Lussac’s, 286 
Stoves, 386 

Stratification of electric light, 772 
Stratus, 815 
Strings, 190 

Sturm’s theory of ‘sion, 500 
Subdominant, 183 

Stictionpump, 151; ai ' ^ e pump, 152 
Sun, analysis of, 458; constitution of, 
458 

Sun spots, 574 

Swimming, 86; bladder of fishes, 86 


859 

THE 

Symmer’s theory of elasticity, 588 
Syphon barometer, 117 
Syphon, 150; intermittent, 150 
Syren, 176 

Syringe, pneumatic, 108, 379 


AMTAM metal, 65 
Tangent compass, or boussole, 676 
Telegraph, electric, 724, 736 
Telescopes, 462 ; astronomical, 473 ; 
terrestrial, 474; Galilean, 475 ; re¬ 
flecting Gregorian, 477; Newtonian, 
478; Herschelian, 480 
Temperature, 216; correction for, in 
barometer, 119; of a body, determined 
by specific heat, 356 
Temperature, influence of, on specific 
gravity, 90 ; mean, 840 ; how modi¬ 
fied, 840; distribution of, 843 ; of 
lakes, springs, 849 

Temperatures, different remarkable, 
226 ; influence on expansion, 231 
Tempering, 63, 65 
Tenacity, 3, 63 

Tension, 107; maximum of electrical 
machine, 613; maximum of vapours, 
256; of aqueous vapour at various 
temperatures, 258—264; of vapours 
of different liquids, 264; of mixed 
liquids in two communicating vessels, 
265 

Terrestrial currents, 719; heat, 381 ; 

telescope, 474 
Thaumatrope, 506 
Theodolite, 4 
Theory, 2 

Thermal analysis, 325; unit, 348 
Thermocrosis, 337 

Thermoelectric, currents, 784 789; 
pile, 323 

Thermoelectricity, 782 
Thermoelement, 783 
Thermomultiplier, 789 
Thermometers, 216; division of tubes 
in, 217 ; filling, 217; graduating in, 

» 218; determination of fixed points 





860 


INDEX. 


THE 

of, 218 ; scale of, 220; limits to use 
of, 222 ; alcohol, 232 ; conditions of 
delicacy of, 223 ; Leslie’s, 223; Mat- 
thiesen’s, 224; Bregnet’s, 224 ; max¬ 
imum and minimum, 225; weight, 
237 ; air, 240, 245 
Thermobarometer, 271 
Thermometer, electric, 645 
Thomson’s electrometer, 637 ; galva¬ 
nometer, 675 
Thread of a screw, 25 
Thunder, 332 
Timbre, 181 

Time, measure of, 9 ; mean solar, 10 
Tint, transition, 551 
Tone, 183 
Tonic, 183 

Torricelli’s experiments, 112; theo¬ 
rem, 150; vacuum, 117 
Torsion, angle of, 62, balance, 62, 
576, 592; force of, 62 
Tourmaline, 334; pincette, 54 
Tourniquet, hydraulic, 158 
Triad, harmonic, 182 
Triangle of forces, 19 
Transition tint, 551, 552 
Transparency, 3, 396 
Transpiration of gases, 104 
Translucent bodies, 396 
Transmission of heat, 304; of light, 429 
Transmission of sound, 166 
Trumpet speaking, ear, 174 
Tubes, Geissler’s, 773 ; luminous, 641; 

safety, 381; speaking, 267 
Tuning fork, 185 
Turbine,-7-59 I 

Tyndall’s researches, 326 et seq. 


NANNEALED glass, colours pro¬ 
duced by, 543 
Undershot wheels, 159 
Undulation, length of, 163 
Uniaxial crystals, 519,521; positive 
and negative, 521 

Unit of length, area and volume, 10 ; 
heat, 348 


VIB 

Unit, jar, Norris’s, 635 
Urinometer, 94 


T7ACUUM, application of, to con- 
> struction of air-pump, 144; 
extent of, produced by air-pump, 
141; fall of bodies in a, 49 ; forma¬ 
tion of vapour, in, 250 ; heat radi¬ 
ated in, 311 ; reflection in a, 317 ; 
Torricellian, 117 
Yalve, safety, 78, 212 
Yane, electrical, 621 
Vaporisation, 255; latent heat of, 273, 
362 

Vapour, aqueous, tension of, at various 
temperatures, 258-264 ; formation 
of, in closed tube; latent heat of, 
273 

Vapours, 255; absorption of heat by, 
335; density of, Gay Lussac’s me¬ 
thod, 291; Dumas’s method, 292 ; 
elastic force of, 255 ; formation of, 
in vacuo, 256 ; saturated, 256 ; un¬ 
saturated, 257 

Variations, barometric, 119; causes 
of, 120 ; relation of, to weather 120 ; 
in magnetic declination, 565, 567 
Velocity, 12; direction of, 34; of 
efflux, 154; of electricity, 650; of 
light, 399-403 ; graphic representa¬ 
tions of, changes of, 34; of sound 
in gases, 168; formula for calculat¬ 
ing, 169 

Velocities, composition of, 30 
Vena contracta, 156 
Ventral segment, 157, 1 
Vernier, 4 

Vertical focus, 413, 415; images, 410 
Vertical line, 42 

Vibration, 161; arc of, 33; produced 
by currents, 723 

Vibrations, 395; of membranes, 204; 
laws of, 191; measurement of; 
number of, 17 5 ; number of, produc¬ 
ing each note, 185 ; of rods, 202 ; of 
plates, 203; of strings, 190 



INDEX. 


861 


vis 

isiometer, 94 

Vision, distance of distinct, 464, 499; 
Sturm’s theory of, 500; binocular, 
501 

Visual angle, 497 
Vis viva, 38 

Vitreous body, 495 ; fusion, 249 
Volatile liquids, 255 
Voltaic arc, 627; couple, 656; pile, 
653-670 

Volta’s condensing electroscope, 636 
Volume, 7; unit of, 10, 11; determina- 
• tion of, 83 ; change of on solidifica¬ 
tion, 253 

Von Ebner’s electrical machine, 648 

W ALKER’S battery, 667 

Water, decomposition of, 693 ; 
hammer, 50; hot, heating by, 387; 
level, 78 

Water, maximum density of, 239; 

spouts, 819 ; wheels, 159 
Watt’s engine, 367 

Wave, condensed, 163, 164; expanded, 
163, 164; lengths, 517 
Weather, its influence on barometric 
variations, 120 ; glasses, 122 
Wedge, 25 

Wedgewood’s pyrometer, 226 
Weighing, double method of, 49 
Weight, 23, 57 ; of gases, 109 ; ther¬ 
mometer, 237 
Weights and measures, 91 


ZON 

Wells, Artesian, 80 
Wells’s theory of dew, 821 
Wet bulb hygrometer, 300 
Wheatstone’s photometer, 407; and 
Cooke’s telegraph, 727 
Wheel barometer, 121 
Wheels friction, 51 ; escapement, 56 ; 
water, 159 

Whirl, electrical, 621 
Whispering galleries, 173 
White’s pulley, 24 

White light, decomposition of, 445 ; 

recomposition of, 448 
Wild’s magnetoelectrical machine, 
761 

Windchest, 194; instruments, 193, 
203 

Winds, 811 

Wines, alcoholic value of, 280 
Wollaston’s battery, 661; doublet, 463 
Wood, conductivity of, 307 
Work, 37 ; of an engine, 377 ; rate of, 
378 


YARD, British, 10, 91 


Z AMBONI’S pile, 670 

Zero, absolute, 390 displacement 
of, 222 

Zinc, amalgamated, 669 
Zone, isothermal, 842 


LONDON: PRINTED BY 

SPOTTISWOODE AND CO., NEW-STBEET SQUARE, 
AND PARLIAMENT STREET 



Errata. 

.-'SI, bottom line, after Germany add a vibration comprises a motion to 
and fro. 

„ 164, line 24, for d (1 +a read d (1 +ct£). 

„ 434, line 5 from bottom, for reflective read refractive. 






































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